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Class 12 • Physics
Atoms & Nuclei
Chapter-12
664 Questions
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126 Easy529 Medium9 Hard
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1
Medium
15 eV is given to electron in 4th orbit then find its final energy when it comes out of H-atom.
Options:
A) 14.15 eV
B) 13.6 eV
C) 12.08 eV
D) 15.85 eV
2
Medium
If half life of an element is $69.3 \mathrm{~h}, then how much of its percent will decay in 10th to 11th \mathrm{h}. Initial activity =50 ~\mu \mathrm{~Ci}
Options:
A) 1%
B) 2%
C) 3%
D) 4%
3
Medium
Assertion : Heavy water is used to slow neutron in nuclear reactor. Reason : It does not react with slow neutron and mass of deuterium is comparable to the neutron.
Options:
A) If both assertion and reason are true and reason is the correct explanation of assertion.
B) If both assertion and reason are true, but reason is not the correct explanation of assertion.
C) If assertion is true, but reason is false.
D) If both assertion and reason are false.
4
Medium
Assertion : For an element generally $N \geq Z ( N= number of neutrons, Z=$ atomic number) Reason : Neutrons always experience attractive nuclear force.
Options:
A) If both assertion and reason are true and reason is the correct explanation of assertion.
B) If both assertion and reason are true, but reason is not the correct explanation of assertion.
C) If assertion is true, but reason is false.
D) If both assertion and reason are false.
5
Medium
The half-life of a radioactive substance is $20 \mathrm{~min}. The approximate time interval \left(t_2-t_1\right) between the time t_2, when \frac{2}{3} of it has decayed and time t_1 when \frac{1}{3}$ of it had decayed is
Options:
A) 14 min
B) 20 min
C) 28 min
D) 7 min
6
Medium
Assertion If electrons in an atom were stationary, then they would fall into the nucleus. Reason Electrostatic force of attraction acts between negatively charged electrons and positive nucleus.
Options:
A) Both Assertion and Reason are correct, Reason is the correct explanation of Assertion
B) Both Assertion and Reason are correct but Reason is not the correct explanation of Assertion
C) Assertion is correct and Reason is incorrect
D) Assertion is incorrect and Reason is correct
7
Medium
Assertion Radioactive nuclei emits $\beta^{-}$-particles. Reason Electrons exist inside the nucleus.
Options:
A) Both Assertion and Reason are correct, Reason is the correct explanation of Assertion
B) Both Assertion and Reason are correct but Reason is not the correct explanation of Assertion
C) Assertion is correct and Reason is incorrect
D) Assertion is incorrect and Reason is correct
8
Medium
A nuclear explosive is designed to deliver $1 \mathrm{~MW} power in the form of heat energy. If the explosion is designed with nuclear fuel consisting of U^{235} to run a reactor at this power level for one year, then the amount of fuel needed is (Given energy per fission is 200 \mathrm{~MeV}$)
Options:
A) 1 \mathrm{~kg}
B) 0.01 \mathrm{~kg}
C) 3.84 \mathrm{~kg}
D) 0.384 \mathrm{~kg}
9
Medium
Assertion : A beam of charged particles is employed in the treatment of cancer. Reason : Charged particles on passing through a material medium lose their energy by causing ionization of the atoms along their path.
Options:
A) Both assertion and reason are true and reason is the correct explanation of assertion
B) Both assertion and reason are true but reason is not the correct explanation of assertion
C) Assertion is true but reason is false
D) Both assertion and reason are false.
10
Medium
Assertion : In He-Ne laser, population inversion takes place between energy levels of neon atoms. Reason : Helium atoms have a metastable energy level.
Options:
A) Both assertion and reason are true and reason is the correct explanation of assertion
B) Both assertion and reason are true but reason is not the correct explanation of assertion
C) Assertion is true but reason is false
D) Both assertion and reason are false.
11
Medium
Assertion : In $\alpha-decay atomic number of daughter nucleus reduces by 2 units from the parent nucleus. Reason : An \alpha$-particle carries four units of mass.
Options:
A) Both assertion and reason are true and reason is the correct explanation of assertion
B) Both assertion and reason are true but reason is not the correct explanation of assertion
C) Assertion is true but reason is false
D) Both assertion and reason are false.
12
Medium
Which of the following transitions of \mathrm{He}^{+} ion will give rise to spectral line which has same wavelength as the spectral line in hydrogen atom?
Options:
A) n=4 to n=2
B) n=6 to n=5
C) n=6 to n=3
D) None of these
13
Medium
The total energy of an electron in the second excited state of hydrogen atom is about $-1.51 \mathrm{~eV}$. Its kinetic energy in this state is
Options:
A) -1.5 \mathrm{~eV}
B) -3.02 \mathrm{~eV}
C) 3.02 eV
D) 1.51 eV
14
Medium
After two hours one-eight of the starting amount of a certain radioactive isotope remained undecayed. The half-life of the isotope is
Options:
A) 15 min
B) 40 min
C) 45 min
D) 4 h
15
Medium
In a radioactive material the activity at time t1, is A1 and at a later time t2, it is A2. If the decay constant of the material is $\lambda$, then
Options:
A) {A_1} = {A_2}\,{e^{ - \lambda ({t_1} - {t_2})}}
B) {A_1} = {A_2}\,{e^{\lambda ({t_1} - {t_2})}}
C) {A_1} = {A_2}({t_2}/{t_1})
D) {A_1} = {A_2}
16
Medium
A proton has kinetic energy E = 100 eV which is equal to that of a photon. The wavelength of photon is $\lambda2 and that of proton is \lambda1. The ratio {{{\lambda _2}} \over {{\lambda _1}}}$ is proportional to
Options:
A) E2
B) E$^{{1 \over 2}}
C) E$-$1
D) E$^{ - {1 \over 2}}
17
Medium
The radius of a muonic hydrogen atom is 2.5 $\times 10-13 m. The total atomic volume (in m3) of a mole of such hydrogen atoms is (Take, \pi$ = 3.14)
Options:
A) 3.94 $\times 10-$14
B) 3.09 $\times 10-$14
C) 4 $\times 10-$14
D) 3.9 $\times 10-$14
18
Medium
A radioactive sample at any instant has its disintegration rate 5000 disintegrations per min. After 5 min, the rate is 1250 disintegrations per min. Then, the disintegration constant (per min) is
Options:
A) 0.4 loge 2
B) 0.2 loge 2
C) 0.1 loge 2
D) 0.8 loge 2
19
Medium
Identify the hydrogen-like element whose spectral lines are four times shorter in wavelength compared to those of atomic hydrogen.
Options:
A) Lithium
B) Helium
C) Berilliyum
D) Potassium
20
Medium
The decay constants of two radioactive substances X and Y are 4$\lambda and \lambda respectively. At t = 0, a sample has the same number of two nuclei. The time taken for the ratio of number of nuclei to become {1 \over {{e^3}}}$ will be
Options:
A) {1 \over {3\lambda }}
B) {1 \over {2\lambda }}
C) {2 \over {3\lambda }}
D) {3 \over {2\lambda }}
21
Medium
If the mass numbers of two nuclei are in the ratio 5: 2 and their diameters are in ratio 2: 6. Then their nuclear densities will be in the ratio
Options:
A) 1: 1
B) 2: 5
C) 10: 12
D) 6: 5
22
Medium
Which of the following is correct in the case of the Bohr model of atoms? A. Predicts continuous emission spectra for all atoms B. Assumes that the angular momentum of electrons is quantised C. Predicts same emission spectrum for singly ionised neon atom and hydrogen atom D. Predicts same emission spectrum for singly ionised neon atom and singly ionised helium atom
Options:
A) C
B) B
C) A
D) D
23
Medium
The minimum energy required by a hydrogen atom in ground state to emit radiation in Paschen series is nearly:
Options:
A) 13.6 eV
B) 12.75 eV
C) 10.75 eV
D) 1.5 eV
24
Medium
Radium having mass number 200 and binding energy per nucleon 5.6 MeV , splits into two fragments Cadmium of mass number 112 and Hassium of mass number 108. If the binding energy per nucleon for Cadmium and Hassium is approximately 8.0 MeV , then the energy Q released per fission will be:
Options:
A) 598 MeV
B) 176 MeV
C) 640 MeV
D) 475 MeV
25
Medium
Select the correct statement from the following:
Options:
A) Nuclear force is a long range force
B) Nuclear force is the weakest force in nature
C) Nuclear force is a non central force
D) Nuclear force depends on the charge of the nucleons
26
Medium
When { }^{10} \mathrm{~B}_5 nuclei are bombarded by neutrons, one of the resultant nuclei is { }^7 \mathrm{Li}_3. Then the emitted particle will be:
Options:
A) Alpha particle
B) Neutrons
C) Gamma particle
D) Beta particle
27
Medium
What is the frequency ' \nu ' of the electron in Bohr's first orbit of radius ' r ' of the hydrogen atom?
Options:
A) v=\frac{e^2}{4 \pi \varepsilon_0 h r}
B) v=\frac{e^2}{2 \pi \varepsilon_0 h r^2}
C) v=\frac{e^2}{4 \pi \varepsilon_0 h r^2}
D) v=\frac{e^2}{2 \pi \varepsilon_0 h r}
28
Medium
To get 300 MW electric power for half an hour, how much mass is to be completely converted into energy?
Options:
A) 6 \times 10^{-2} \mathrm{~kg}
B) 3 \times 10^{-6} \mathrm{~kg}
C) 6 \times 10^{-3} \mathrm{~kg}
D) 6 \times 10^{-6} \mathrm{~kg}
29
Medium
Fusion reaction is more energetic than fission reaction because
Options:
A) Uncontrolled chain reaction is taking place In the fusion reaction.
B) Fusion reaction is taking place at very high temperature
C) The energy released per unit mass of the fuel in fusion reaction is larger than the energy released per unit mass of the fuel in fission reaction.
D) In the fusion reaction lighter nuclei combine to form a heavier nucleus
30
Medium
The nucleus of oxygen atom contains 8 protons and 8 neutrons. What is the mass defect in amu? [Given Mass of proton =1.00727 \mathrm{amu} Mass of neutron =1.00866 \mathrm{amu} and the mass of oxygen nucleus =15.99053 \mathrm{amu}. ]
Options:
A) 0.12691 amu
B) 0.13692 amu
C) 0.13691 amu
D) 0.12961 amu
31
Medium
According to Bohr's theory of hydrogen atom, the speed of the electron, its energy and radius of its orbit vary with the principal quantum number n, respectively as
Options:
A) \frac{1}{n}, n^2, \frac{1}{n^2}
B) \frac{1}{n}, \frac{1}{n^2}, n^2
C) n, \frac{1}{n^2}, n^2
D) \frac{1}{n^2}, \frac{1}{n}, n^2
32
Medium
Which, of the following is true of the Balmer series of the hydrogen spectrum? a. The series is in the visible region. b. The entire series falls in the ultraviolet region c. The entire series falls in the infrared region d. The series is partly in the visible region and partly in the infrared region
Options:
A) b
B) c
C) a
D) d
33
Medium
In a nuclear fusion reaction, two nuclei, A and B fuse to produce a nucleus C, releasing an amount of energy \Delta \mathrm{E} in the process. If the mass defects of the three nuclei are \Delta M_A, \Delta M_B and \Delta M_C respectively, then which of the following relations is true? ( c is the speed of light).
Options:
A) \Delta M_A+\Delta M_B=\Delta M_C+\frac{\Delta E}{c^2}
B) \Delta M_A-\Delta M_B=\Delta M_C+\frac{\Delta E}{c^2}
C) \Delta M_A-\Delta M_B=\Delta M_C-\frac{\Delta E}{c^2}
D) \Delta M_A+\Delta M_B=\Delta M_C-\frac{\Delta E}{c^2}
34
Medium
The binding energy per nucleon for $\mathrm{C}^{12} is 7.68 \mathrm{~MeV} and that for \mathrm{C}^{13} is 7.47 \mathrm{~MeV}. The energy required to remove a neutron from \mathrm{C}^{13}$ is
Options:
A) 7.92 \times 10^{-13} \mathrm{~MeV}
B) 4.95 \times 10^{-13} \mathrm{eV}
C) 7.92 \times 10^{-13} \mathrm{~J}
D) 7.92 \times 10^{-19} \mathrm{~J}
35
Medium
The distance of closest approach when an alpha particle of kinetic energy $6.5 \mathrm{~MeV}$ strikes a nucleus of atomic number 50 is
Options:
A) 0.221 fm
B) 1.101 fm
C) 0.0221 fm
D) 4.42 fm
36
Medium
If an electron in a hydrogen atom jumps from the third orbit to the second orbit, it emits a photon of wavelength $\lambda$. When it jumps from the second to the first orbit, the corresponding wavelength of the photon will be
Options:
A)
\frac{5 \lambda}{27}
B)
\frac{7 \lambda}{20}
C)
\frac{16 \lambda}{9}
D)
\frac{20 \lambda}{7}
37
Medium
An electron has a mass of $9.1 \times 10^{-31} \mathrm{~kg}. It revolves round the nucleus in a circular orbit of radius 0.529 \times 10^{-10} \mathrm{~m} at a speed of 2.2 \times 10^6 \mathrm{~ms}^{-1}$. The magnitude of its angular momentum is
Options:
A) 1.06 \times 10^{-34} \mathrm{Kg} \mathrm{m}^2 \mathrm{~s}^{-1}
B) 1.06 \times 10^{-24} \mathrm{Kg} \mathrm{m}^2 \mathrm{~s}^{-1}
C) 2.06 \times 10^{-34} \mathrm{Kg} \mathrm{m}^2 \mathrm{~s}^{-1}
D) 2.06 \times 10^{-24} \mathrm{Kg} \mathrm{m}^2 \mathrm{~s}^{-1}
38
Medium
\text { If the nuclear radius of }{ }^{27} \mathrm{Al} \text { is } 3.6 \text { fermi, the nuclear radius of }{ }^{125} \mathrm{Fe} \text { is }
Options:
A) 6 \times 10^{-10} \mathrm{~m}
B) 6 \times 10^{-13} \mathrm{~m}
C) 6 \times 10^{-15} \mathrm{~m}
D) 6 \times 10^{-12} \mathrm{~m}
39
Medium
A nucleus with mass number 190 initially at rest emits an alpha particle. If the $\mathrm{Q} value of the reaction is 4.5 \mathrm{~MeV}$, the kinetic energy of the alpha particle is
Options:
A) 4 MeV
B) 3.2 MeV
C) 0.43 MeV
D) 4.4 MeV
40
Medium
In a hydrogen atom, if electron is replaced by a particle which is 40 times heavier but has the same charge, then, the ratio of the radius of the first excited state of a normal hydrogen atom to the ground state of the above atom is
Options:
A) 40 : 1
B) 1 : 160
C) 1 : 40
D) 160 : 1
41
Medium
The shortest wavelengths of Paschen, Lymen and Balmer series are in the ratio
Options:
A) 9: 1: 4
B) 4: 1: 9
C) 2:1:3
D) 3: 1: 2
42
Medium
The radius of a nucleus as measured by electron scattering is $4.8 \mathrm{~fm}$. The mass number of nucleus is most likely to be
Options:
A) 46
B) 16
C) 64
D) 48
43
Medium
The ratio of the radii of the nucleus of two element $\mathrm{X} and \mathrm{Y}$ having the mass numbers 232 and 29 is:
Options:
A) 4 : 1
B) 1 : 4
C) 1 : 2
D) 2 : 1
44
Medium
The closest approach of an alpha particle when it make a head on collision with a gold nucleus is $10 \times 10^{-14} \mathrm{~m}$, then the kinetic energy of the alpha particle is :
Options:
A) 3640 J
B) 3.64 J
C)
3.64 \times 10^{-16} \mathrm{~J}
D)
3.64 \times 10^{-13} \mathrm{~J}
45
Medium
Find the binding energy of the tritium nucleus: [Given: mass of $1 \mathrm{H}^3=3.01605 \mathrm{~u} ; \mathrm{~m}_{\mathrm{p}}=1.00782 \mathrm{~u} ; \mathrm{~m}_{\mathrm{n}}=1.00866 \mathrm{~u}$.]
Options:
A) 8.5 MeV
B) 8.5 J
C) 0.00909 MeV
D) 0.00909 eV
46
Medium
The mass density of a nucleus varies with mass number $A$ as
Options:
A) \mathop A\limits^o
B) A^2
C) \frac{1}{A}
D) \ln A
47
Medium
The wavelength of the first line of Lyman series for $\mathrm{H} - atom is equal to that of the second line of Balmer series for a \mathrm{H}-like ion. The atomic number \mathrm{Z} of \mathrm{H}$-like ion is
Options:
A) 4
B) 1
C) 2
D) 3
48
Medium
The first emission of hydrogen atomic spectrum in Lyman series appears at a wavelength of
Options:
A) \frac{3 R}{4} \mathrm{~cm}^{-1}
B) \frac{4}{3 R} \mathrm{~cm}
C) \frac{7 R}{144} \mathrm{~cm}^{-1}
D) \frac{400}{9 R} \mathrm{~cm}
49
Medium
The mass number of two nuclei $\mathrm{P} and \mathrm{Q} are 27 and 125 respectively. The ratio of their radii R_P: R_Q$ is given by:
Options:
A) 9 : 25
B) 3 : 5
C) 27 : 25
D) 5 : 3
50
Medium
In a nuclear reaction 2 deuteron nuclei combine to form a helium nucleus. The energy released in $\mathrm{MeV} will be: (Given mass of deuteron =2.01355 \mathrm{~amu}. and mass of helium nucleus =4.0028 \mathrm{~amu}$.
Options:
A) 24.3 MeV
B) 2.262 MeV
C) 22.62 MeV
D) 0.0243 MeV
51
Medium
A particle at rest decays in to two particles of mass $m_1 and m_2 and move with velocities v_1 and v_2. The ratio of their de Broglie wave length \frac{\lambda_1}{\lambda_2}$ is:
Options:
A) 1 : 4
B) 1 : 1
C) 1 : 2
D) 2 : 1
52
Medium
The ground state energy of hydrogen atom is $-13.6 \mathrm{~eV}. If the electron jumps from the 3^{\text {rd }}$ excited state to the ground state then the energy of the radiation emitted will be:
Options:
A) 1.275 MeV
B) 12.75 eV
C) 12.75 J
D) 12.75 MeV
53
Medium
In the head-on collision of two alpha particles $\alpha_1 and \alpha_2 with the gold nucleus, the closest approaches are 31.4 fermi and 94.2 fermi respectively. Then the ratio of the energy possessed by the alpha particles \alpha_2 / \alpha_1$ is:
Options:
A) 1: 3
B) 9: 1
C) 3: 1
D) 1: 9
54
Medium
Which of the following statement is true when a gamma decay occurs from the nucleus of an atom?
Options:
A) Mass number is reduced by 4 and atomic number remains the same
B) Mass number remains the same and atomic number increases by 1
C) Mass number and atomic number are not changed
D) Mass number is reduced by 4 and atomic number is reduced by 2
55
Medium
During $\alpha$-decay, atomic mass of parent nuclei is
Options:
A) decreased by 2 units
B) increased by 2 units
C) decreased by 4 units
D) increased by 4 units
56
Medium
Which of the following series spectrum of hydrogen atom lies in ultraviolet region?
Options:
A) Paschen series
B) Brackett series
C) Pfund series
D) Lyman series
57
Medium
The wavelength of the second line of Balmer series is 486.4 nm. What is the wavelength of the first line of Lyman series?
Options:
A) 78.8 nm
B) 121.6 nm
C) 418.2 nm
D) 610.5 nm
58
Medium
The Lyman series of a hydrogen atom belongs in which category
Options:
A) ultraviolet region
B) infrared region
C) visible region
D) None of these
59
Medium
If an electron in hydrogen atom jumps from an orbit of level $n=3 to an orbit at level n=2$, emitted radiation has a frequency of (R = Rydberg's constant and c = velocity of light)
Options:
A) \frac{3Rc}{27}
B) \frac{Rc}{25}
C) \frac{8Rc}{9}
D) \frac{5Rc}{36}
60
Medium
Ba-122 has half-life of 2 min. Experiment has to be done using Ba-122 and it takes 10 min to set up the experiment. It initially 80 g at Ba-122 was taken, how much Ba was left when experiment was started?
Options:
A) 2.5 g
B) 5 g
C) 10 g
D) 20 g
61
Medium
When the speed of light becomes $\frac{2}{3}$ of its present value, then the energy released in a given atomic explosion would
Options:
A) decrease by a factor $\frac{2}{3}
B) decrease by a factor $\frac{4}{9}
C) decrease by a factor $\frac{5}{9}
D) decrease by a factor $\frac{\sqrt5}{9}
62
Medium
An electron of an atom transits from $n_1 to n_2$. In which of the following maximum frequency of photon will be emitted?
Options:
A) n_1=1 to n_2=2
B) n_1=2 to n_2=1
C) n_1=2 to n_2=6
D) n_1=6 to n_2=2
63
Medium
Two protons are kept at a separation of 40 $\mathop A\limits^o . F_n is the nuclear force and F_e$ is the electrostatic force between them. Then,
Options:
A) F_n< < F_e
B) F_n\approx F_e
C) F_n> > F_e
D) F_n= F_e
64
Medium
Two radioactive materials X$_1 and X_2 have decay constant 5\lambda and \lambda, respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of X_1 to X_2 will be 1/e$ after a time
Options:
A) 1/4\lambda
B) e/\lambda
C) \lambda
D) \frac{1}{2}\lambda
65
Hard
List-I shows various functional dependencies of energy (E) on the atomic number (Z). Energies associated with certain phenomena are given in List-II. Choose the option that describes the correct match between the entries in List-I to those in List-II. List–I List–II (P) E \propto Z^2 (1) energy of characteristic x-rays (Q) E \propto (Z - 1)^2 (2) electrostatic part of the nuclear binding energy for stable nuclei with mass numbers in the range 30 to 170 (R) E \propto Z(Z - 1) (3) energy of continuous x-rays (S) E is practically independent of Z (4) average nuclear binding energy per nucleon for stable nuclei with mass number in the range 30 to 170 (5) energy of radiation due to electronic transitions from hydrogen-like atoms
Options:
A) P→4, Q→3, R→1, S→2
B) P→5, Q→2, R→1, S→4
C) P→5, Q→1, R→2, S→4
D) P→3, Q→2, R→1, S→5
66
Medium
List-I shows different radioactive decay processes and List-II provides possible emitted particles. Match each entry in List-I with an appropriate entry from List-II, and choose the correct option. List - I List - II (P) { }_{92}^{238} U \rightarrow{ }_{91}^{234} \mathrm{~Pa} (1) one \alpha particle and one \beta^{+}particle (Q) { }_{82}^{214} \mathrm{~Pb} \rightarrow{ }_{82}^{210} \mathrm{~Pb} (2) three \beta^{-}particles and one \alpha particle (R) { }_{81}^{210} \mathrm{Tl} \rightarrow{ }_{82}^{206} \mathrm{~Pb} (3) two \beta^{-}particles and one \alpha particle (S) { }_{91}^{228} \mathrm{~Pa} \rightarrow{ }_{88}^{224} \mathrm{Ra} (4) one \alpha particle and one \beta^{-}particle (5) one \alpha particle and two \beta^{+}particles
Options:
A) P \rightarrow 4, Q \rightarrow 3, R \rightarrow 2, S \rightarrow 1
B) P \rightarrow 4, Q \rightarrow 1, R \rightarrow 2, S \rightarrow 5
C) P \rightarrow 5, Q \rightarrow 3, R \rightarrow 1, S \rightarrow 4
D) P \rightarrow 5, Q \rightarrow 1, R \rightarrow 3, S \rightarrow 2
67
Easy
A heavy nucleus Q of half-life 20 minutes undergoes alpha-decay with probability of 60% and beta-decay with probability of 40%. Initially, the number of Q nuclei is 1000. The number of alpha-decays of Q in the first one hour is
Options:
A) 50
B) 75
C) 350
D) 525
68
Medium
In a radioactive sample, ${}_{19}^{40}K nuclei either decay into stable {}_{20}^{40}Ca nuclei with decay constant 4.5 \times 10-10 per year or into stable {}_{18}^{40}Ar nuclei with decay constant 0.5 \times 10-10 per year. Given that in this sample all the stable {}_{20}^{40}Ca and {}_{18}^{40}Ar nuclei are produced by the {}_{19}^{40}K nuclei only. In time t \times 109 years, if the ratio of the sum of stable {}_{20}^{40}Ca and {}_{18}^{40}Ar nuclei to the radioactive {}_{19}^{40}K$ nuclei is 99, the value of t will be [Given : In 10 = 2.3]
Options:
A) 9.2
B) 1.15
C) 4.6
D) 2.3
69
Easy
An accident in a nuclear laboratory resulted in deposition of a certain amount of radioactive material of half-life 18 days inside the laboratory. Tests revealed that the radiation was 64 times more than the permissible level required for safe operation of the laboratory. What is the minimum number of days after which the laboratory can be considered safe for use?
Options:
A) 64
B) 90
C) 108
D) 120
70
Hard
The electrostatic energy of Z protons uniformly distributed throughout a spherical nucleus of radius R is given by $E = {3 \over 5}{{Z(Z - 1){e^2}} \over {4\pi {\varepsilon _0}R}}The measured masses of the neutron, _1^1H, _7^{15}N and _8^{15}O are 1.008665u, 1.007825u, 15.000109u and 15.003065u, respectively. Given that the radii of both the _7^{15}N and _8^{15}O nuclei are same, 1 u = 931.5 MeV/c2 (c is the speed of light) and e2/(4\pi{{\varepsilon _0}}) = 1.44 MeV fm. Assuming that the difference between the binding energies of _7^{15}N and _8^{15}O is purely due to the electrostatic energy, the radius of either of the nuclei is (1 fm = 10-$15 m)
Options:
A) 2.85 fm
B) 3.03 fm
C) 3.42 fm
D) 3.80 fm
71
Medium
Match the nuclear processes given in Column I with the appropriate option(s) in Column II:
Options:
A) (A)→(R) or (RT), (T); (B)→(P), (S); (C)→(Q), (T); (D)→(R)
B) (A)→(R), (T); (B)→(Q), (S); (C)→(Q), (T); (D)→(R)
C) (A)→(R) or (RT), (T); (B)→(P), (S); (C)→(S), (T); (D)→(R)
D) (A)→(P), (T); (B)→(P), (S); (C)→(Q), (T); (D)→(R)
72
Medium
If $\lambdaCu is the wavelength of K\alpha X-ray line of copper (atomic number 29) and \lambdaMo is the wavelength of the K\alpha X-ray line of molybdenum (atomic number 42), then the ratio \lambdaCu/\lambda$Mo is close to
Options:
A) 1.99
B) 2.14
C) 0.50
D) 0.48
73
Easy
The mass of a nucleus $_Z^AX is less than the sum of the masses of (A-Z) number of neutrons and Z number of protons in the nucleus. The energy equivalent to the corresponding mass difference is known as the binding energy of the nucleus. A heavy nucleus of mass M can break into two light nuclei of masses m1 and m2 only if (m1 + m2) < M. Also two light nuclei of masses m3 and m4 can undergo complete fusion and form a heavy nucleus of mass M' only if (m3 + m4) > M'. The masses of some neutral atoms are given in the table below : _1^1H 1.007825 u _1^2H 2.014102 u _3^6Li 6.015123 u _3^7Li 7.016004 u _{64}^{152}Gd 151.919803 u _{82}^{206}Pb 205.974455 u _1^3H 3.016050 u _2^4He 4.002603 u _{30}^{70}Zn 69.925325 u _{34}^{82}Se 81.916709 u _{83}^{209}Bi 208.980388 u _{84}^{210}Po$ 209.982876 u (1 u = 932 MeV/c2)
Options:
A) the nucleus $_3^6Li$ can emit an alpha particle.
B) the nucleus $_{84}^{210}Po$ can emit a proton.
C) deuteron and alpha particle can undergo complete fusion.
D) the nuclei $_{30}^{70}Zn and _{34}^{82}Se$ can undergo complete fusion.
74
Medium
The mass of a nucleus $_Z^AX is less than the sum of the masses of (A-Z) number of neutrons and Z number of protons in the nucleus. The energy equivalent to the corresponding mass difference is known as the binding energy of the nucleus. A heavy nucleus of mass M can break into two light nuclei of masses m1 and m2 only if (m1 + m2) < M. Also two light nuclei of masses m3 and m4 can undergo complete fusion and form a heavy nucleus of mass M' only if (m3 + m4) > M'. The masses of some neutral atoms are given in the table below : _1^1H 1.007825 u _1^2H 2.014102 u _3^6Li 6.015123 u _3^7Li 7.016004 u _{64}^{152}Gd 151.919803 u _{82}^{206}Pb 205.974455 u _1^3H 3.016050 u _2^4He 4.002603 u _{30}^{70}Zn 69.925325 u _{34}^{82}Se 81.916709 u _{83}^{209}Bi 208.980388 u _{84}^{210}Po$ 209.982876 u (1 u = 932 MeV/c2)
Options:
A) 5319
B) 5422
C) 5707
D) 5818
75
Medium
Match List I of the nuclear processes with List II containing parent nucleus and one of the end products of each process and then select the correct answer using the codes given below the lists : List I List II P. Alpha decay 1. $_8^{15}O \to _7^{15}N + ... Q. {\beta ^ + } decay 2. _{91}^{238}U \to _{90}^{234}Th + ... R. Fission 3. _{83}^{185}Bi \to _{82}^{184}Pb + ... S. Proton emission 4. _{94}^{239}Pu \to _{57}^{140}La + ...
Options:
A) P-4, Q-2, R-1, S-3
B) P-1, Q-3, R-2, S-4
C) P-2, Q-1, R-4, S-3
D) P-4, Q-3, R-2, S-1
76
Medium
The $\beta-decay process, discovered in around 1900, is basically the decay of a neutron (n). In the laboratory, a proton (p) and an electron (e-) are observed as the decay products of the neutron. Therefore, considering the decay of a neutron as a two-body decay process, it was predicted theoretically that the kinetic energy of the electron should be a constant. But experimentally, it was observed that the electron kinetic energy has continuous spectrum. Considering a three-body decay process, that is, n \to p + e- + {\overline v _e}, around 1930, Pauli explained the observed electron energy spectrum. Assuming the anti-neutrino ({\overline v _e}) to be massless and possessing negligible energy, and the neutron to be at rest, momentum and energy conservation principles are applied. From this calculation, the maximum kinetic energy of the electron is 0.8 \times$ 106 eV. The kinetic energy carried by the proton is only the recoil energy.
Options:
A) Zero.
B) Much less than 0.8 $\times$ 106 eV.
C) Nearly 0.8 $\times$ 106 eV.
D) much larger than 0.8 $\times$ 106 eV.
77
Medium
The $\beta-decay process, discovered in around 1900, is basically the decay of a neutron (n). In the laboratory, a proton (p) and an electron (e-) are observed as the decay products of the neutron. Therefore, considering the decay of a neutron as a two-body decay process, it was predicted theoretically that the kinetic energy of the electron should be a constant. But experimentally, it was observed that the electron kinetic energy has continuous spectrum. Considering a three-body decay process, that is, n \to p + e- + {\overline v _e}, around 1930, Pauli explained the observed electron energy spectrum. Assuming the anti-neutrino ({\overline v _e}) to be massless and possessing negligible energy, and the neutron to be at rest, momentum and energy conservation principles are applied. From this calculation, the maximum kinetic energy of the electron is 0.8 \times$ 106 eV. The kinetic energy carried by the proton is only the recoil energy.
Options:
A) 0 $\le K \le 0.8 \times$ 106 eV
B) 3.0 eV $\le K \le 0.8 \times$ 106 eV
C) 3.0 eV $\le K < 0.8 \times$ 106 eV
D) 0 $\le K < 0.8 \times$ 106 eV
78
Medium
The wavelength of the first spectral line in the Balmer series of hydrogen atom is 6561 $\mathop A\limits^o $. The wavelength of the second spectral line in the Balmer series of singly-ionized helium atom is
Options:
A) 1215 $\mathop A\limits^o
B) 1640 $\mathop A\limits^o
C) 2430 $\mathop A\limits^o
D) 4687 $\mathop A\limits^o
79
Easy
The key feature of Bohr's theory of spectrum of hydrogen atom is the quantization of angular momentum when an electron is revolving around a proton. We will extend this to a general rotational motion to find quantized rotational energy of a diatomic molecule assuming it to be rigid. The rule to be applied is Bohr's quantization condition.
Options:
A) {1 \over {{n^2}}}\left( {{{{h^2}} \over {8{\pi ^2}I}}} \right)
B) {1 \over n}\left( {{{{h^2}} \over {8{\pi ^2}I}}} \right)
C) n\left( {{{{h^2}} \over {8{\pi ^2}I}}} \right)
D) {n^2}\left( {{{{h^2}} \over {8{\pi ^2}I}}} \right)
80
Medium
The key feature of Bohr's theory of spectrum of hydrogen atom is the quantization of angular momentum when an electron is revolving around a proton. We will extend this to a general rotational motion to find quantized rotational energy of a diatomic molecule assuming it to be rigid. The rule to be applied is Bohr's quantization condition.
Options:
A) 2.76 $\times 10-$46 kg m2
B) 1.87 $\times 10-$46 kg m2
C) 4.67 $\times 10-$47 kg m2
D) 1.17 $\times 10-$47 kg m2
81
Medium
The key feature of Bohr's theory of spectrum of hydrogen atom is the quantization of angular momentum when an electron is revolving around a proton. We will extend this to a general rotational motion to find quantized rotational energy of a diatomic molecule assuming it to be rigid. The rule to be applied is Bohr's quantization condition.
Options:
A) 2.4 $\times 10-$10 m
B) 1.9 $\times 10-$10 m
C) 1.3 $\times 10-$10 m
D) 4.4 $\times 10-$11 m
82
Easy
When a particle is restricted to move along x-axis between x = 0 and x = a, where a is of nanometer dimension, its energy can take only certain specific values. The allowed energies of the particle moving in such a restricted region, correspond to the formation of standing waves with nodes at its ends x = 0 and x = a. The wavelength of this standing wave is related to the linear momentum p of the particle according to the de Broglie relation. The energy of the particle of mass m is related to its linear momentum as $E = {{{p^2}} \over {2m}}. Thus, the energy of the particle can be denoted by a quantum number 'n' taking values 1, 2, 3, ... (n = 1, called the ground state) corresponding to the number of loops in the standing wave. Use the model described above to answer the following three questions for a particle moving in the line x = 0 to x = a. Take h = 6.6 \times {10^{ - 34}} J-s and e = 1.6 \times {10^{ - 19}}$ C.
Options:
A) {n^{ - 3/2}}
B) {n^{ - 1}}
C) {n^{1/2}}
D) n
83
Easy
Scientists are working hard to develop nuclear fusion reactor. Nuclei of heavy hydrogen, $_1^2H, known as deuteron and denoted by D, can be thought of as a candidate for fusion reactor. The D-D reaction is _1^2H + _1^2H \to _2^3He + n + energy. In the core of fusion reactor, a gas of heavy hydrogen is fully ionized into deuteron nuclei and electrons. This collection of _1^2H nuclei and electrons is known as plasma. The nuclei move randomly in the reactor core and occasionally come close enough for nuclear fusion to take place. Usually, the temperatures in the reactor core are too high and no material wall can be used to confine the plasma. Special techniques are used which confine the plasma for a time t_0 before the particles fly away from the core. If n is the density (number/volume) of deuterons, the product nt_0 is called Lawson number. In one of the criteria, a reactor is termed successful if Lawson number is greater than 5 \times 10^{14} s/cm^3. It may be helpful to use the following : Boltzmann constant k = 8.6 \times {10^{ - 5}} eV/K; {{{e^2}} \over {4\pi {\varepsilon _0}}} = 1.44 \times {10^9}$ eVm.
Options:
A) strong nuclear force acting between the deuterons.
B) Coulomb force acting between the deuterons.
C) Coulomb force acting between deuteron-electrons pairs.
D) the high temperature maintained inside the reactor core.
84
Medium
Scientists are working hard to develop nuclear fusion reactor. Nuclei of heavy hydrogen, $_1^2H, known as deuteron and denoted by D, can be thought of as a candidate for fusion reactor. The D-D reaction is _1^2H + _1^2H \to _2^3He + n + energy. In the core of fusion reactor, a gas of heavy hydrogen is fully ionized into deuteron nuclei and electrons. This collection of _1^2H nuclei and electrons is known as plasma. The nuclei move randomly in the reactor core and occasionally come close enough for nuclear fusion to take place. Usually, the temperatures in the reactor core are too high and no material wall can be used to confine the plasma. Special techniques are used which confine the plasma for a time t_0 before the particles fly away from the core. If n is the density (number/volume) of deuterons, the product nt_0 is called Lawson number. In one of the criteria, a reactor is termed successful if Lawson number is greater than 5 \times 10^{14} s/cm^3. It may be helpful to use the following : Boltzmann constant k = 8.6 \times {10^{ - 5}} eV/K; {{{e^2}} \over {4\pi {\varepsilon _0}}} = 1.44 \times {10^9}$ eVm.
Options:
A) 1.0 \times {10^9}K < T < 2.0 < {10^9}K
B) 2.0 \times {10^9}K < T < 3.0 < {10^9}K
C) 3.0 \times {10^9}K < T < 4.0 < {10^9}K
D) 4.0 \times {10^9}K < T < 5.0 < {10^9}K
85
Easy
Scientists are working hard to develop nuclear fusion reactor. Nuclei of heavy hydrogen, $_1^2H, known as deuteron and denoted by D, can be thought of as a candidate for fusion reactor. The D-D reaction is _1^2H + _1^2H \to _2^3He + n + energy. In the core of fusion reactor, a gas of heavy hydrogen is fully ionized into deuteron nuclei and electrons. This collection of _1^2H nuclei and electrons is known as plasma. The nuclei move randomly in the reactor core and occasionally come close enough for nuclear fusion to take place. Usually, the temperatures in the reactor core are too high and no material wall can be used to confine the plasma. Special techniques are used which confine the plasma for a time t_0 before the particles fly away from the core. If n is the density (number/volume) of deuterons, the product nt_0 is called Lawson number. In one of the criteria, a reactor is termed successful if Lawson number is greater than 5 \times 10^{14} s/cm^3. It may be helpful to use the following : Boltzmann constant k = 8.6 \times {10^{ - 5}} eV/K; {{{e^2}} \over {4\pi {\varepsilon _0}}} = 1.44 \times {10^9}$ eVm.
Options:
A) Deuteron density = $2.0\times10^{12}~\mathrm{cm^{-3}}; Confinement time = 5.0\times10^{-3}~\mathrm{s}$.
B) Deuteron density = $8.0\times10^{14}~\mathrm{cm^{-3}}; Confinement time = 9.0\times10^{-1}~\mathrm{s}$.
C) Deuteron density = $4.0\times10^{23}~\mathrm{cm^{-3}}; Confinement time = 1.0\times10^{-11}~\mathrm{s}$.
D) Deuteron density = $1.0\times10^{24}~\mathrm{cm^{-3}}; Confinement time = 4.0\times10^{-12}~\mathrm{s}$.
86
Easy
A radioactive sample S1 having activity of 5 $\muCi has twice the number of nuclei as another sample S2 which has an activity of 10 \mu$Ci. The half lives of S1 and S2 can be :
Options:
A) 20 years and 5 years, respectively
B) 20 years and 10 years, respectively
C) 10 years each
D) 5 years each
87
Medium
In a mixture of H - He$^+ gas (He^+ is singly ionized He atom), H atoms and He^+ ions are excited to their respective first excited states. Subsequently, H atoms transfer their total excitation energy to He^+$ ions (by collisions). Assume that the Bohr model of atom is exactly valid.
Options:
A) 2
B) 3
C) 4
D) 5
88
Medium
In a mixture of H - He$^+ gas (He^+ is singly ionized He atom), H atoms and He^+ ions are excited to their respective first excited states. Subsequently, H atoms transfer their total excitation energy to He^+$ ions (by collisions). Assume that the Bohr model of atom is exactly valid.
Options:
A) 6.5\times10^{-7}$ m
B) 5.6\times10^{-7}$ m
C) 4.8\times10^{-7}$ m
D) 4.0\times10^{-7}$ m
89
Easy
In a mixture of H - He$^+ gas (He^+ is singly ionized He atom), H atoms and He^+ ions are excited to their respective first excited states. Subsequently, H atoms transfer their total excitation energy to He^+$ ions (by collisions). Assume that the Bohr model of atom is exactly valid.
Options:
A) \frac{1}{4}
B) \frac{1}{2}
C) 1
D) 2
90
Medium
In the option given below, let E denote the rest mass energy of a nucleus and n a neutron. The correct option is
Options:
A) E\left( {_{92}^{236}U} \right) > E\left( {_{53}^{137}I} \right) + E\left( {_{39}^{97}Y} \right) + 2E(n)
B) E\left( {_{92}^{236}U} \right) < E\left( {_{53}^{137}I} \right) + E\left( {_{39}^{97}Y} \right) + 2E(n)
C) E\left( {_{92}^{236}U} \right) < E\left( {_{56}^{140}Ba} \right) + E\left( {_{36}^{94}Kr} \right) + 2E(n)
D) E\left( {_{92}^{236}U} \right) = E\left( {_{56}^{140}Ba} \right) + E\left( {_{36}^{94}Kr} \right) + 2E(n)
91
Medium
The largest wavelength in the ultraviolet region of the hydrogen spectrum is 122 nm. The smallest wavelength in the infrared region of the hydrogen spectrum (to the nearest integer) is
Options:
A) 802 nm
B) 823 nm
C) 1882 nm
D) 1648 nm
92
Medium
\text { Match the following Columns. } Column I Column II (A) Nuclear fusion. (P) Converts some matter into energy. (B) Nuclear fission. (Q) Generally possible for nuclei with low atomic number. (C) \beta$-decay. (R) Generally possible for nuclei with higher atomic number. (D) Exothermic nuclear reaction. (S) Essentially proceeds by weak nuclear forces.
Options:
A) [\mathrm{A} \rightarrow( \mathrm{Q}) ; \mathrm{B} \rightarrow(\mathrm{P}, \mathrm{R}) ; \mathrm{C} \rightarrow(\mathbf{P}, \mathbf{S}) ; \mathbf{D} \rightarrow( \mathbf{R})]
B) [\mathrm{A} \rightarrow(\mathrm{P}) ; \mathrm{B} \rightarrow(\mathrm{P}, \mathrm{R}) ; \mathrm{C} \rightarrow(\mathbf{P}) ; \mathbf{D} \rightarrow(\mathbf{P}, \mathbf{Q}, \mathbf{R})] .
C) [\mathrm{A} \rightarrow(\mathrm{P}, \mathrm{Q}) ; \mathrm{B} \rightarrow(\mathrm{P}, \mathrm{R}) ; \mathrm{C} \rightarrow(\mathbf{P}, \mathbf{S}) ; \mathbf{D} \rightarrow(\mathbf{P}, \mathbf{Q}, \mathbf{R})] .
D) [\mathrm{A} \rightarrow(\mathrm{P}, \mathrm{Q}) ; \mathrm{B} \rightarrow(\mathrm{P}, \mathrm{R}) ; \mathrm{C} \rightarrow( \mathbf{S}) ; \mathbf{D} \rightarrow(\mathbf{P}, \mathbf{Q})] .
93
Medium
\text { Match the following Columns. } Column I Column II (A) Dielectric ring uniformly charged. (P) Time independent electrostatic field out of system. (B) Dielectric ring uniformly charged rotating with angular velocity \omega. (Q) Magnetic field. (C) Constant current in ring io (R) Induced electric field. (D) i=i_o \cos \omega \mathrm{t}$ (S) Magnetic moment.
Options:
A) [\mathbf{A} \rightarrow(\mathbf{P}) ; \mathbf{B} \rightarrow(\mathbf{Q}, \mathbf{S}) ; \mathbf{C} \rightarrow (\mathrm{Q}) ; \mathrm{D} \rightarrow(\mathrm{Q})]
B) [\mathbf{A} \rightarrow(\mathbf{P}) ; \mathbf{B} \rightarrow( \mathbf{S}) ; \mathbf{C} \rightarrow (\mathrm{Q}) ; \mathrm{D} \rightarrow(\mathrm{Q}, \mathrm{R})]
C) [\mathbf{A} \rightarrow(\mathbf{P}) ; \mathbf{B} \rightarrow( \mathbf{S}) ; \mathbf{C} \rightarrow (\mathrm{Q}, \mathrm{~S}) ; \mathrm{D} \rightarrow(\mathrm{Q}, \mathrm{R})]
D) [\mathbf{A} \rightarrow(\mathbf{P}) ; \mathbf{B} \rightarrow(\mathbf{Q}, \mathbf{S}) ; \mathbf{C} \rightarrow (\mathrm{Q}, \mathrm{~S}) ; \mathrm{D} \rightarrow(\mathrm{Q}, \mathrm{R}, \mathrm{~S})]
94
Medium
Highly energetic electrons are bombarded on a target of an element containing 30 neutrons. The ratio of radii of nucleus to that of Helium nucleus is $(14)^{\frac{1}{3}}. Find (A) Atomic number of the nucleus; (B) the frequency of \mathrm{K}_{\alpha} line of the X-ray produced. \left(\mathrm{R}=1.1 \times 10^{7} \mathrm{~m}^{-1}\right. and \left.c=3 \times 10^{8} \mathrm{~m} / \mathrm{s}\right)
Options:
A) (A) 26 ; (B) $2.55 \times 10^{18} \mathrm{~Hz}
B) (A) 26 ; (B) $1.55 \times 10^{18} \mathrm{~Hz}
C) (A) 36 ; (B) $1.55 \times 10^{18} \mathrm{~Hz}
D) (A) 46 ; (B) $2.55 \times 10^{18} \mathrm{~Hz}
95
Medium
A particle of mass m is moving in a circular orbit under the influence of the central force F(r)=-k r, corresponding to the potential energy V(r)=k r^2 / 2, where k is a positive force constant and r is the radial distance from the origin. According to the Bohr's quantization rule, the angular momentum of the particle is given by L=n \hbar, where \hbar=h /(2 \pi), h is the Planck's constant, and n a positive integer. If v and E are the speed and total energy of the particle, respectively, then which of the following expression(s) is(are) correct?
Options:
A) r^2=n \hbar \sqrt{\frac{1}{m k}}
B) v^2=n \hbar \sqrt{\frac{k}{m^3}}
C) \frac{L}{m r^2}=\sqrt{\frac{k}{m}}
D) E=\frac{n \hbar}{2} \sqrt{\frac{k}{m}}
96
Hard
The binding energy of nucleons in a nucleus can be affected by the pairwise Coulomb repulsion. Assume that all nucleons are uniformly distributed inside the nucleus. Let the binding energy of a proton be E_{b}^{p} and the binding energy of a neutron be E_{b}^{n} in the nucleus. Which of the following statement(s) is(are) correct?
Options:
A) E_{b}^{p}-E_{b}^{n} is proportional to Z(Z-1) where Z is the atomic number of the nucleus.
B) E_{b}^{p}-E_{b}^{n} is proportional to A^{-\frac{1}{3}} where A is the mass number of the nucleus.
C) E_{b}^{p}-E_{b}^{n} is positive.
D) E_{b}^{p} increases if the nucleus undergoes a beta decay emitting a positron.
97
Medium
A heavy nucleus N, at rest, undergoes fission N $\to P + Q, where P and Q are two lighter nuclei. Let \delta = MN - MP -$ MQ, where MP, MQ and MN are the masses of P, Q and N, respectively. EP and EQ are the kinetic energies of P and Q, respectively. The speeds of P and Q are vP and vQ, respectively. If c is the speed of light, which of the following statement(s) is(are) correct?
Options:
A) {E_P} + {E_Q} = {c^2}\delta
B) {E_P} = \left( {{{{M_P}} \over {{M_P} + {M_Q}}}} \right){c^2}\delta
C) {{{v_P}} \over {{v_Q}}} = {{{M_Q}} \over {{M_P}}}
D) The magnitude of momentum for P as well Q is $c\sqrt {2\mu \delta } , where \mu = {{{M_P}{M_Q}} \over {({M_P} + {M_Q})}}
98
Medium
Which of the following statement(s) is(are) correct about the spectrum of the hydrogen atom?
Options:
A) The ratio of the longest wavelength to the shortest wavelength in Balmer series is 9/5
B) There is an overlap between the wavelength ranges of Balmer and Paschen series
C) The wavelengths of Lyman series are given by $\left( {1 + {1 \over {{m^2}}}} \right){\lambda _0}, where {\lambda _0}$ is the shortest wavelength of Lyman series and m is an integer
D) The wavelength ranges of Lyman and Balmer series do not overlap
99
Medium
In an X-ray tube, electrons emitted from a filament (cathode) carrying current I hit a target (anode) at a distance d from the cathode. The target is kept at a potential V higher than the cathode resulting in emission of continuous and characteristic X-rays. If the filament current I is decreased to ${1 \over 2}, the potential difference V is increased to 2V, and the separation distance d is reduced to {d \over 2}$, then
Options:
A) the cut-off wavelength will reduce to half, and the wavelengths of the characteristic X-rays will remain the same
B) the cut-off wavelength as well as the wavelengths of the characteristic X-rays will remain the same
C) the cut-off wavelength will reduce to half, and the intensities of all the X-rays will decrease
D) the cut-off wavelength will become two times larger, and the intensity of all the X-rays will decrease
100
Medium
A particle of mass m moves in circular orbits with potential energy V(r) = Fr, where F is a positive constant and r is its distance from the origin. Its energies are calculated using the Bohr model. If the radius of the particle’s orbit is denoted by R and its speed and energy are denoted by v and E, respectively, then for the nth orbit (here h is the Planck’s constant)
Options:
A) R \propto {n^{{1 \over 3}}} and v \propto {n^{{2 \over 3}}}
B) R \propto {n^{{2 \over 3}}} and v \propto {n^{{1 \over 3}}}
C) E = {3 \over 2}{\left( {{{{n^2}{h^2}{F^2}} \over {4{\pi ^2}m}}} \right)^{{1 \over 3}}}
D) E = 2{\left( {{{{n^2}{h^2}{F^2}} \over {4{\pi ^2}m}}} \right)^{{1 \over 3}}}
101
Medium
A free hydrogen atom after absorbing a photon of wavelength $\lambda a gets excited from the state n = 1 to the state n = 4. Immediately after that the electron jumps to n = m state by emitting a photon of wavelength \lambda e. Let the change in momentum of atom due to the absorption and the emission be \Delta {p_a} and \Delta {p_e}, respectively. If {{{\lambda _a}} \over {{\lambda _e}}} = {1 \over 5}$, which of the option(s) is/are correct? [Use hc = 1242 eVnm; 1 nm = 10-9 m, h and c are Planck's constant and speed of light in vacuum, respectively]
Options:
A) The ratio of kinetic energy of the electron in the state n = m to the state, n = 1 is ${1 \over 4}
B) m = 2
C) {{\Delta {p_a}} \over {\Delta {p_e}}} = {1 \over 2}
D) \lambda $e = 418 nm
102
Medium
In a radioactive decay chain, ${}_{90}^{232}Th nucleus decays to {}_{82}^{212}Pb nucleus. Let {N_\alpha } and {N_\beta } be the number of \alpha and {\beta ^ - }$ particles, respectively, emitted in this decay process. Which of the following statements is (are) true?
Options:
A) {N_\alpha } = 5
B) {N_\alpha } = 6
C) {N_\beta } = 2
D) {N_\beta } = 4
103
Medium
Highly excited states for hydrogen-like atoms (also called Rydberg states) with nuclear charge Ze are defined by their principle quantum number n, where n >> 1. Which of the following statement(s) is(are) true?
Options:
A) Relative change in the radii of two consecutive orbitals does not depend on Z.
B) Relative change in the radii of two consecutive orbitals varies as 1/n
C) Relative change in the energy of two consecutive orbitals varies as 1/n3
D) Relative change in the angular momenta of two consecutive orbitals varies as 1/n
104
Hard
A fission reaction is given by $_{92}^{236}U \to _{54}^{140}Xe + _{38}^{94}Sr + x + y, where x and y are two particles. Considering _{92}^{236}U to be at rest, the kinetic energies of the products are denoted by {K_{Xe}},{K_{Sr}},{K_x}(2MeV) \text { and } \mathrm{K}_{\mathrm{y}}(2 \mathrm{MeV}) , respectively. Let the binding energies per nucleon of _{92}^{236}U, _{54}^{140}Xe and _{38}^{94}Sr$ be 7.5 MeV, 8.5 MeV and 8.5 MeV, respectively. Considering different conservation laws, the correct options is/are
Options:
A) x = n, y = n, Ksr = 129 MeV, KXe = 86 MeV
B) x = p, y = e$-$, Ksr = 129 MeV, KXe = 86 MeV
C) x = p, y = n, Ksr = 129 MeV, KXe = 86 MeV
D) x = n, y = n, Ksr = 86 MeV, KXe = 129 MeV
105
Medium
The radius of the orbit of an electron in a hydrogen-like atom is 4.5a0, where a0 is the Bohr radius. Its orbital angular momentum is ${{3h} \over {2\pi }}$. It is given that h is Planck constant and R is Rydberg constant. The possible wavelength(s), when the atom de-excites, is(are)
Options:
A) {9 \over {32R}}
B) {9 \over {16R}}
C) {9 \over {5R}}
D) {4 \over {3R}}
106
Medium
Assume that the nuclear binding energy per nucleon (B/A) versus mass number (A) is as shown in the figure. Use this plot to choose the correct choice(s) given below.
Options:
A) Fusion of two nuclei with mass number lying in the range of 1 < A < 50 will release energy
B) Fusion of two nuclei with mass numbers lying in the range of 51 < A < 100 will release energy
C) Fission of a nucleus lying in the mass range of 100 < A < 200 will release energy when broken into two equal fragments
D) Fission of a nucleus lying in the mass range of 200 < A < 260 will release energy when broken into two equal fragments
107
Easy
In a radioactive decay process, the activity is defined as A=-\frac{d N}{d t}, where N(t) is the number of radioactive nuclei at time t. Two radioactive sources, S_1 and S_2 have same activity at time t=0. At a later time, the activities of S_1 and S_2 are A_1 and A_2, respectively. When S_1 and S_2 have just completed their 3^{\text {rd }} and 7^{\text {th }} half-lives, respectively, the ratio A_1 / A_2 is _________.
Options:
108
Easy
In a radioactive decay chain reaction, { }_{90}^{230} \mathrm{Th} nucleus decays into { }_{84}^{214} \mathrm{Po} nucleus. The ratio of the number of \alpha to number of \beta^{-}particles emitted in this process is ________.
Options:
109
Hard
The minimum kinetic energy needed by an alpha particle to cause the nuclear reaction { }_{7}^{16} \mathrm{~N}+ { }_{2}^{4} \mathrm{He} \rightarrow{ }_{1}^{1} \mathrm{H}+{ }_{8}^{19} \mathrm{O} in a laboratory frame is n (in M e V. Assume that { }_{7}^{16} \mathrm{~N} is at rest in the laboratory frame. The masses of { }_{7}^{16} \mathrm{~N},{ }_{2}^{4} \mathrm{He},{ }_{1}^{1} \mathrm{H} and { }_{8}^{19} \mathrm{O} can be taken to be 16.006 u, 4.003 u, 1.008 u and 19.003 u, respectively, where 1 u=930 \,\mathrm{MeVc}^{-2}. The value of n is ________ .
Options:
110
Medium
Suppose a $_{88}^{226}Ra nucleus at rest and in ground state undergoes \alpha -decay to a _{86}^{222}Rn nucleus in its excited state. The kinetic energy of the emitted \alpha particle is found to be 4.44 MeV. _{86}^{222}Rn nucleus then goes to its ground state by \gamma -decay. The energy of the emitted \gamma photon is ............ keV.[Given : atomic mass of _{86}^{226}Ra = 226.005 u, atomic of _{86}^{222}Rn = 222.000 u, atomic mass of \alpha $ particle = 4.000 u, 1 u = 931 MeV/e2, c is speed of the light]
Options:
111
Medium
Consider a hydrogen-like ionized atom with atomic number $Z with a single electron. In the emission spectrum of this atom, the photon emitted in the n=2 to n=1 transition has energy 74.8eV higher than the photon emitted in the n=3 to n=2 transition. The ionization energy of the hydrogen atom is 13.6 eV. The value of Z$ is ____________.
Options:
112
Medium
An electron in a hydrogen atom undergoes a transition from an orbit with quantum number ${n_i} to another with quantum number {n_f}. {V_i} and {V_f} are respectively the initial and final potential energies of the electron. If {{{V_i}} \over {{V_f}}} = 6.25, then the smallest possible {n_f}$ is
Options:
113
Medium
{}^{131}{\rm I} is an isotope of Iodine that B decays to an isotope of Xenon with a half-life of 8 days. A small amount of a serum labelled with {}^{131}{\rm I} is injected into the blood of a person. The activity of the amount of {}^{131}{\rm I} injected was 2.4 \times {10^5} Becquerel (Bq). It is known that the injected serum will get distributed uniformly in the blood stream in less than half an hour. After 11.5 hours, 2.5 ml of blood is drawn from person's body, and gives an activity of 115 Bq. The total volume of blood in the person's body, in liters is approximately (you may use {e^x} \approx 1 + x\,\, for \left| x \right| < < 1 and \ln 2 \approx 0.7).
Options:
114
Medium
A hydrogen atom in its ground state is irradiated by light of wavelength 970$\mathop A\limits^o .Taking hc = 1.237 \times 10-6 eVm and the ground state energy of hydrogen atom as -$ 13.6 eV, the number of lines present in the emission spectrum is
Options:
115
Medium
The isotope $_5^{12}B having a mass 12.014 u undergoes \beta -decay to _6^{12}C. _6^{12}C has an excited state of the nucleus (_6^{12}C*) at 4.041 MeV above its ground state. If _5^{12}B decays to _6^{12}C*, the maximum kinetic energy of the \beta$-particle in units of MeV is (1u = 931.5 MeV/c2, where c is the speed of light in vacuum).
Options:
116
Medium
For a radioactive material, its activity A and rate of change of its activity R are defined as $A = - {{dN} \over {dt}} and R = - {{dA} \over {dt}}, where N(t) is the number of nuclei at time t. Two radioactive source P(mean life \tau ) and Q (mean life 2\tau ) have the same activity at t = 0. Their rate of change of activities at t = 2\tau are RP and RQ, respectively. If {{{R_P}} \over {{R_Q}}} = {n \over e}$, then the value of n is
Options:
117
Medium
Consider a hydrogen atom with its electron in the nth orbital. An electromagnetic radiation of wavelength 90 nm is used to ionize the atom. If the kinetic energy of the ejected electron is 10.4 eV, then the value of n is (hc = 1242 eV nm)
Options:
118
Easy
A nuclear power plant supplying electrical power to a village uses a radioactive material of half life T years as the fuel. The amount of fuel at the beginning is such that the total power requirement of the village is 12.5 % of the electrical power available from the plant at that time. If the plant is able to meet the total power needs of the village for a maximum period of nT years, then the value of n is
Options:
119
Easy
A freshly prepared sample of a radioisotope of half-life 1386 s has activity 103 disintegrations per second. Given that ln2 = 0.693, the fraction of the initial number of nuclei (expressed in nearest integer percentage) that will decay in the first 80 s after preparation of the sample is __________.
Options:
120
Medium
To determine the half-life of a radioactive element, a student plots a graph of $\ln \left| {{{dN(t)} \over {dt}}} \right| versus t. Here, {{dN(t)} \over {dt}}$ is the rate of radioactive decay at time t. If the number of radioactive nuclei of this element decreases by a factor of p after 4.16 years, the value of p is __________.
Options:
121
Medium
In hydrogen-like atom (z=11), nth line of Lyman series has wavelength A equal to the de Broglie's wavelength of electron in the level from which it originated. What is the value of n ?
Options:
122
Easy
Match List - I (Experiment performed) with List - II (Phenomena discovered/associated) and select the correct option from the options given below the lists : List - I List - II (a) Davisson and Germer Experiment (i) Wave nature of electrons (b) Millikan’s oil drop experiment (ii) Charge of an electron (c) Rutherford experiment (iii) Quantisation of energy levels (d) Franck - Hertz experiment (iv) Existence of nucleus
Options:
A) (a)-(i), (b)-(ii), (c)-(iii), (d)-(iv)
B) (a)-(i), (b)-(ii), (c)-(iv), (d)-(iii)
C) (a)-(iii), (b)-(iv), (c)-(i), (d)-(ii)
D) (a)-(iv), (b)-(iii), (c)-(ii), (d)-(i)
123
Easy
A piece of wood from a recently cut tree shows 20 decays per minute. A wooden piece of same size placed in a museum (obtained from a tree cut many years back) shows 2 decays per minute. If half life of C14 is 5730 years, then age of the wooden piece placed in the museum is approximately :
Options:
A) 10439 years
B) 13094 years
C) 19039 years
D) 39049 years
124
Easy
A nucleus has mass number \alpha and radius R_{\alpha}. Another nucleus has mass number \beta and radius R_{\beta}.If \beta = 8\alpha then R_{\alpha} / R_{\beta} is :
Options:
A) 1
B) 2
C) 8
D) 0.5
125
Medium
An atom { }_3^8 X is bombarded by shower of fundamental particles and in 10 s this atom absorbed 10 electrons, 10 protons and 9 neutrons. The percentage growth in the surface area of the nucleons is recorded by :
Options:
A) 150 \%
B) 900\%
C) 125 \%
D) 225 \%
126
Medium
The binding energy for the following nuclear reactions are expressed in MeV . $ \begin{aligned} & { }_2 \mathrm{He}^3+{ }_0 \mathrm{n}^1 \rightarrow{ }_2 \mathrm{He}^4+20 \mathrm{MeV} \\ & { }_2 \mathrm{He}^4+{ }_0 \mathrm{n}^1 \rightarrow{ }_2 \mathrm{He}^5-0.9 \mathrm{MeV} \end{aligned} If \mathrm{X}_3, \mathrm{X}_4, \mathrm{X}_5 denote the stability of { }_2 \mathrm{He}^3,{ }_2 \mathrm{He}^4 and { }_2 \mathrm{He}^5$, respectively, then the correct order is :
Options:
A) X_4>X_5>X_3
B) X_4 < X_5 < X_3
C) X_4 > X_5 < X_3
D) X_4=X_5=X_3
127
Medium
Two electrons are moving in orbits of two hydrogen like atoms with speeds 3 \times 10^5 \mathrm{~m} / \mathrm{s} and 2.5 \times 10^5 \mathrm{~m} / \mathrm{s} respectively. If the radii of these orbits are nearly same then the possible order of energy states are \_\_\_\_ respectively.
Options:
A) 8 and 10
B) 10 and 12
C) 9 and 8
D) 6 and 5
128
Medium
Given below are two statements : Statement I : For all elements, greater the mass of the nucleus, greater is the binding energy per nucleon. Statement II : For all elements, nuclei with less binding energy per nucleon transforms to nuclei with greater binding energy per nucleon. In the light of the above statements, choose the correct answer from the options given below
Options:
A) Statement I is false but Statement II is true
B) Both Statement I and Statement II are true
C) Both Statement I and Statement II are false
D) Statement I is true but Statement II is false
129
Easy
Which of the following pair of nuclei are isobars of the element?
Options:
A) { }_1^3 \mathrm{H} and { }_2^3 \mathrm{He}
B) { }_{80}^{198} \mathrm{Hg} and { }_{79}^{197} \mathrm{Au}
C) { }_1^2 \mathrm{H} and { }_1^3 \mathrm{H}
D) { }_{92}^{236} \mathrm{U} and { }_{92}^{238} \mathrm{U}
130
Medium
In hydrogen atom spectrum, ( R \rightarrow Rydberg's constant) A. the maximum wavelength of the radiation of Lyman series is \frac{4}{3 R} B. the Balmer series lies in the visible region of the spectrum C. the minimum wavelength of the radiation of Paschen series is \frac{9}{R} D. the minimum wavelength of Lyman series is \frac{5}{4 R} Choose the correct answer from the options given below :
Options:
A) A, B Only
B) B, D Only
C) A, B and D Only
D) A, B and C Only
131
Medium
The smallest wavelength of Lyman series is 91 nm . The difference between the largest wavelengths of Paschen and Balmer series is nearly \_\_\_\_ nm.
Options:
A) 1784
B) 1875
C) 1217
D) 1550
132
Medium
The minimum frequency of photon required to break a particle of mass 15.348 amu into 4 \alpha particles is \_\_\_\_ kHz . [mass of He nucleus = 4.002 \mathrm{amu}, 1 \mathrm{amu}=1.66 \times 10^{-27} \mathrm{~kg}, \mathrm{~h}=6.6 \times 10^{-34} \mathrm{~J} . \mathrm{s} and \mathrm{c}=3 \times 10^8 \mathrm{~m} / \mathrm{s} ]
Options:
A) 14.94 \times 10^{20}
B) 9 \times 10^{19}
C) 9 \times 10^{20}
D) 14.94 \times 10^{19}
133
Medium
7.9 \mathrm{MeV} \alpha-particle scatters from a target material of atomic number 79 . From the given data the estimated diameter of nuclei of the target material is (approximately) \_\_\_\_ m. $ \left[\frac{1}{4 \pi \epsilon_{\mathrm{o}}}=9 \times 10^9 \mathrm{Nm}^2 / \mathrm{C}^2 \text { and electron charge }=1.6 \times 10^{-19} \mathrm{C}\right]
Options:
A) 2.88 \times 10^{-14}
B) 5.76 \times 10^{-14}
C) 1.44 \times 10^{-13}
D) 1.69 \times 10^{-12}
134
Medium
The energy of an electron in an orbit of the Bohr's atom is -0.04E_0 eV where E_0 is the ground state energy. If L is the angular momentum of the electron in this orbit and h is the Planck's constant, then \frac{2\pi L}{h} is ________ :
Options:
A) 6
B) 2
C) 5
D) 4
135
Medium
If an alpha particle with energy 7.7 MeV is bombarded on a thin gold foil, the closest distance from nucleus it can reach is \_\_\_\_ m. (Atomic number of gold =79 and \frac{1}{4 \pi \epsilon_{\mathrm{o}}}=9 \times 10^9 in SI units)
Options:
A) 2.95 \times 10^{-16}
B) 3.85 \times 10^{-14}
C) 2.95 \times 10^{-14}
D) 3.85 \times 10^{-16}
136
Easy
For a nucleus of mass number A and radius R, the mass density of nucleus can be represented as
Options:
A) A^{\frac{2}{3}}
B) Independent of A
C) A^3
D) A^{\frac{1}{3}}
137
Medium
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : The density of the copper (^ {64}_{29} \text{Cu}) nucleus is greater than that of the carbon (^ {12}_{6} \text{C}) nucleus. Reason (R) : The nucleus of mass number A has a radius proportional to A^{1/3} . In the light of the above statements, choose the most appropriate answer from the options given below :
Options:
A) (A) is correct but (R) is not correct
B) Both (A) and (R) are correct but (R) is not the correct explanation of (A)
C) (A) is not correct but (R) is correct
D) Both (A) and (R) are correct and (R) is the correct explanation of (A)
138
Medium
In a hydrogen like ion, the energy difference between the 2^{\text {nd }} excitation energy state and ground is 108.8 eV . The atomic number of the ion is:
Options:
A) 1
B) 4
C) 3
D) 2
139
Easy
For a hydrogen atom, the ratio of the largest wavelength of Lyman series to that of the Balmer series is
Options:
A) 5: 27
B) 27: 5
C) 3: 4
D) 5: 36
140
Easy
A radioactive material P first decays into Q and then Q decays to non-radioactive material R. Which of the following figure represents time dependent mass of P, Q and R ?
Options:
A)
B)
C)
D)
141
Easy
Given below are two statements : Statement (I) : The dimensions of Planck's constant and angular momentum are same. Statement (II) : In Bohr's model electron revolve around the nucleus only in those orbits for which angular momentum is integral multiple of Planck's constant. In the light of the above statements, choose the most appropriate answer from the options given below :
Options:
A) Both Statement I and Statement II are correct
B) Statement I is correct but Statement II is incorrect
C) Both Statement I and Statement II are incorrect
D) Statement I is incorrect but Statement II is correct
142
Easy
Considering the Bohr model of hydrogen like atoms, the ratio of the radius of 5^{\text {th }} orbit of the electron in \mathrm{Li}^{2+} and \mathrm{He}^{+}is
Options:
A) \frac{3}{2}
B) \frac{2}{3}
C) \frac{4}{9}
D) \frac{9}{4}
143
Medium
Given below are two statements: one is labelled as \mathbf{A s s e r t i o n} \mathbf{A} and the other is labelled as Reason \mathbf{R} Assertion A : The Bohr model is applicable to hydrogen and hydrogen-like atoms only. Reason \mathbf{R} : The formulation of Bohr model does not include repulsive force between electrons. In the light of the above statements, choose the correct answer from the options given below
Options:
A) \mathbf{A} is true but \mathbf{R} is false
B) Both \mathbf{A} and \mathbf{R} are true and \mathbf{R} is the correct explanation of \mathbf{A}
C) \mathbf{A} is false but \mathbf{R} is true
D) Both \mathbf{A} and \mathbf{R} are true but \mathbf{R} is NOT the correct explanation of \mathbf{A}
144
Medium
\text { Match the LIST-I with LIST-II } List - I List - II A. { }_0^1 \mathrm{n}+{ }_{92}^{235} \mathrm{U} \rightarrow{ }_{54}^{140} \mathrm{Xe}+{ }_{38}^{94} \mathrm{Sr}+2{ }_0^1 \mathrm{n} I. \text { Chemical reaction } B. 2 \mathrm{H}_2+\mathrm{O}_2 \rightarrow 2 \mathrm{H}_2 \mathrm{O} II. \text { Fusion with +ve } \mathrm{Q} \text { value } C. { }_1^2 \mathrm{H}+{ }_1^2 \mathrm{H} \rightarrow{ }_2^3 \mathrm{He}+{ }_0^1 \mathrm{n} III. \text { Fission } D. { }_1^1 \mathrm{H}+{ }_1^3 \mathrm{H} \rightarrow{ }_1^2 \mathrm{H}+{ }_1^2 \mathrm{H} IV. \text { Fusion with -ve } Q \text { value } \text { Choose the correct answer from the options given below: }
Options:
A) A-II, B-I, C-III, D-IV
B) A-III, B-I, C-II, D-IV
C) A-III, B-I, C-IV, D-II
D) A-II, B-I, C-IV, D-III
145
Easy
Energy released when two deuterons \left({ }_1 \mathrm{H}^2\right) fuse to form a helium nucleus \left({ }_2 \mathrm{He}^4\right) is : (Given : Binding energy per nucleon of { }_1 \mathrm{H}^2=1.1 \mathrm{MeV} and binding energy per nucleon of { }_2 \mathrm{He}^4=7.0 \mathrm{MeV} )
Options:
A) 26.8 MeV
B) 8.1 MeV
C) 23.6 MeV
D) 5.9 MeV
146
Easy
Assuming the validity of Bohr's atomic model for hydrogen like ions the radius of \mathrm{Li}^{++} ion in its ground state is given by \frac{1}{X} a_0, where X= __________ (Where \mathrm{a}_0 is the first Bohr's radius.)
Options:
A) 2
B) 9
C) 1
D) 3
147
Medium
Considering Bohr's atomic model for hydrogen atom : (A) the energy of H atom in ground state is same as energy of \mathrm{He}^{+}ion in its first excited state. (B) the energy of H atom in ground state is same as that for \mathrm{Li}^{++} ion in its second excited state. (C) the energy of H atom in its ground state is same as that of \mathrm{He}^{+}ion for its ground state. (D) the energy of \mathrm{He}^{+}ion in its first excited state is same as that for \mathrm{Li}^{++}ion in its ground state. Choose the correct answer from the options given below :
Options:
A) (A), (B) only
B) (A), (D) only
C) (A), (C) only
D) (B), (D) only
148
Easy
The number of spectral lines emitted by atomic hydrogen that is in the 4th energy level, is
Options:
A) 3
B) 6
C) 1
D) 0
149
Easy
The frequency of revolution of the electron in Bohr's orbit varies with n, the principal quantum number as:
Options:
A) \frac{1}{n^4}
B) \frac{1}{n^2}
C) \frac{1}{n^3}
D) \frac{1}{n}
150
Easy
Choose the correct nuclear process from the below options [ p : proton, n : neutron, \mathrm{e}^{-}: electron, \mathrm{e}^{+}: positron, v: neutrino, \bar{v}: antineutrino]
Options:
A) n \rightarrow p+e^{+}+{v}
B) \mathrm{n} \rightarrow \mathrm{p}+\mathrm{e}^{-}+\bar{v}
C) \mathrm{n} \rightarrow \mathrm{p}+\mathrm{e}^{+}+\bar{v}
D) \mathrm{n} \rightarrow \mathrm{p}+\mathrm{e}^{-}+v
151
Easy
The energy E and momentum p of a moving body of mass m are related by some equation. Given that c represents the speed of light, identify the correct equation
Options:
A) \mathrm{E}^2=\mathrm{pc}^2+\mathrm{m}^2 \mathrm{c}^4
B) \mathrm{E}^2=\mathrm{pc}^2+\mathrm{m}^2 \mathrm{c}^2
C) \mathrm{E}^2=\mathrm{p}^2 \mathrm{c}^2+\mathrm{m}^2 \mathrm{c}^4
D) \mathrm{E}^2=\mathrm{p}^2 \mathrm{c}^2+\mathrm{m}^2 \mathrm{c}^2
152
Medium
During the transition of electron from state A to state C of a Bohr atom, the wavelength of emitted radiation is 2000 \mathop A\limits^o and it becomes 6000 \mathop A\limits^o when the electron jumps from state B to state C. Then the wavelength of the radiation emitted during the transition of electrons from state A to state B is
Options:
A) 4000 \mathop A\limits^o
B) 6000 \mathop A\limits^o
C) 2000 \mathop A\limits^o
D) 3000 \mathop A\limits^o
153
Easy
Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : The binding energy per nucleon is found to be practically independent of the atomic number A , for nuclei with mass numbers between 30 and 170 . Reason (R) : Nuclear force is long range. In the light of the above statements, choose the correct answer from the options given below :
Options:
A) (A) is true but (R) is false
B) Both (A) and (R) are true and (R) is the correct explanation of (A)
C) (A) is false but (R) is true
D) Both (A) and (R) are true but (R) is NOT the correct explanation of (A)
154
Medium
A radioactive nucleus \mathrm{n}_2 has 3 times the decay constant as compared to the decay constant of another radioactive nucleus n_1. If initial number of both nuclei are the same, what is the ratio of number of nuclei of n_2 to the number of nuclei of n_1, after one half-life of n_1 ?
Options:
A) 1/4
B) 1/8
C) 4
D) 8
155
Easy
A nucleus at rest disintegrates into two smaller nuclei with their masses in the ratio of $2: 1$. After disintegration they will move :
Options:
A) in opposite directions with speed in the ratio of $1: 2$ respectively.
B) in the same direction with same speed.
C) in opposite directions with speed in the ratio of $2: 1$ respectively.
D) in opposite directions with the same speed.
156
Medium
The energy released in the fusion of $2 \mathrm{~kg} of hydrogen deep in the sun is E_H and the energy released in the fission of 2 \mathrm{~kg} of { }^{235} \mathrm{U} is E_U. The ratio \frac{E_H}{E_U} is approximately: (Consider the fusion reaction as 4_1^1H+2 \mathrm{e}^{-} \rightarrow{ }_2^4 \mathrm{He}+2 v+6 \gamma+26.7 \mathrm{~MeV}, energy released in the fission reaction of { }^{235} \mathrm{U} is 200 \mathrm{~MeV} per fission nucleus and \mathrm{N}_{\mathrm{A}}= 6.023 \times 10^{23})
Options:
A) 7.62
B) 25.6
C) 9.13
D) 15.04
157
Medium
A hydrogen atom in ground state is given an energy of $10.2 \mathrm{~eV}$. How many spectral lines will be emitted due to transition of electrons?
Options:
A) 3
B) 6
C) 10
D) 1
158
Easy
The energy equivalent of $1 \mathrm{~g}$ of substance is :
Options:
A) 5.6 \times 10^{26} \mathrm{~MeV}
B) 5.6 \times 10^{12} \mathrm{~MeV}
C) 5.6 \mathrm{~eV}
D) 11.2 \times 10^{24} \mathrm{~MeV}
159
Easy
If $M_0 is the mass of isotope { }_5^{12} B, M_p and M_n$ are the masses of proton and neutron, then nuclear binding energy of isotope is:
Options:
A) (5 M_p+7 M_n-M_o) C^2
B) (M_o-5 M_p-7 M_n) C^2
C) (M_o-5 M_p) C^2
D) (M_0-12 M_n) C^2
160
Easy
In a hypothetical fission reaction ${ }_{92} X^{236} \rightarrow{ }_{56} \mathrm{Y}^{141}+{ }_{36} Z^{92}+3 R$ The identity of emitted particles (R) is :
Options:
A) Proton
B) Neutron
C) Electron
D) \gamma$-radiations
161
Easy
Binding energy of a certain nucleus is $18 \times 10^8 \mathrm{~J}$. How much is the difference between total mass of all the nucleons and nuclear mass of the given nucleus:
Options:
A) 20 $\mu$g
B) 2 $\mu$g
C) 10 $\mu$g
D) 0.2 $\mu$g
162
Easy
The longest wavelength associated with Paschen series is : (Given $\mathrm{R}_{\mathrm{H}}=1.097 \times 10^7 \mathrm{SI}$ unit)
Options:
A) 2.973 \times 10^{-6} \mathrm{~m}
B) 1.876 \times 10^{-6} \mathrm{~m}
C) 1.094 \times 10^{-6} \mathrm{~m}
D) 3.646 \times 10^{-6} \mathrm{~m}
163
Easy
The ratio of the shortest wavelength of Balmer series to the shortest wavelength of Lyman series for hydrogen atom is :
Options:
A) 1: 2
B) 1: 4
C) 2: 1
D) 4: 1
164
Easy
The angular momentum of an electron in a hydrogen atom is proportional to : (Where $\mathrm{r}$ is the radius of orbit of electron)
Options:
A) \frac{1}{\mathrm{r}}
B) \frac{1}{\sqrt{\mathrm{r}}}
C) \sqrt{\mathrm{r}}
D) r
165
Easy
An electron rotates in a circle around a nucleus having positive charge $\mathrm{Ze}$. Correct relation between total energy (E) of electron to its potential energy (U) is :
Options:
A) 2 \mathrm{E}=3 \mathrm{U}
B) \mathrm{E}=\mathrm{U}
C) 2 \mathrm{E}=\mathrm{U}
D) \mathrm{E}=2 \mathrm{U}
166
Easy
According to Bohr's theory, the moment of momentum of an electron revolving in $4^{\text {th }}$ orbit of hydrogen atom is:
Options:
A) 2 \frac{h}{\pi}
B) \frac{h}{2 \pi}
C) \frac{h}{\pi}
D) 8 \frac{h}{\pi}
167
Easy
Which of the following nuclear fragments corresponding to nuclear fission between neutron $\left({ }_0^1 \mathrm{n}\right) and uranium isotope \left({ }_{92}^{235} \mathrm{U}\right)$ is correct :
Options:
A) { }_{56}^{140} \mathrm{Xe}+{ }_{38}^{94} \mathrm{Sr}+3{ }_0^1 \mathrm{n}
B) { }_{51}^{153} \mathrm{Sb}+{ }_{41}^{99} \mathrm{Nb}+3{ }_0^1 \mathrm{n}
C) { }_{56}^{144} \mathrm{Ba}+{ }_{36}^{89} \mathrm{Kr}+4{ }_0^1 \mathrm{n}
D) { }_{56}^{144} \mathrm{Ba}+{ }_{36}^{89} \mathrm{Kr}+3{ }_0^1 \mathrm{n}
168
Medium
From the statements given below : (A) The angular momentum of an electron in n^{\text {th }} orbit is an integral multiple of \hbar. (B) Nuclear forces do not obey inverse square law. (C) Nuclear forces are spin dependent. (D) Nuclear forces are central and charge independent. (E) Stability of nucleus is inversely proportional to the value of packing fraction. Choose the correct answer from the options given below :
Options:
A) (B), (C), (D), (E) only
B) (A), (C), (D), (E) only
C) (A), (B), (C), (E) only
D) (A), (B), (C), (D) only
169
Medium
The minimum energy required by a hydrogen atom in ground state to emit radiation in Balmer series is nearly :
Options:
A) 13.6 \mathrm{eV}
B) 1.5 \mathrm{eV}
C) 12.1 \mathrm{eV}
D) 1.9 \mathrm{eV}
170
Easy
The mass number of nucleus having radius equal to half of the radius of nucleus with mass number 192 is :
Options:
A) 32
B) 24
C) 20
D) 40
171
Easy
If the wavelength of the first member of Lyman series of hydrogen is $\lambda$. The wavelength of the second member will be
Options:
A) \frac{27}{5} \lambda
B) \frac{5}{27} \lambda
C) \frac{27}{32} \lambda
D) \frac{32}{27} \lambda
172
Medium
An electron revolving in $n^{\text {th }} Bohr orbit has magnetic moment \mu_n. If \mu_n \propto n^x, the value of x$ is
Options:
A) 2
B) 0
C) 3
D) 1
173
Medium
In a nuclear fission reaction of an isotope of mass $M, three similar daughter nuclei of same mass are formed. The speed of a daughter nuclei in terms of mass defect \Delta M$ will be :
Options:
A) c \sqrt{\frac{3 \Delta M}{M}}
B) \frac{\Delta M c^2}{3}
C) c \sqrt{\frac{2 \Delta M}{M}}
D) \sqrt{\frac{2 c \Delta M}{M}}
174
Easy
The ratio of the magnitude of the kinetic energy to the potential energy of an electron in the 5th excited state of a hydrogen atom is :
Options:
A) 4
B) 1
C) \frac{1}{2}
D) \frac{1}{4}
175
Easy
Given below are two statements: Statement I : Most of the mass of the atom and all its positive charge are concentrated in a tiny nucleus and the electrons revolve around it, is Rutherford's model. Statement II : An atom is a spherical cloud of positive charges with electrons embedded in it, is a special case of Rutherford's model. In the light of the above statements, choose the most appropriate from the options given below
Options:
A) Both Statement I and Statement II are true
B) Statement I is true but Statement II is false
C) Statement I is false but Statement II is true
D) Both statement I and statement II are false
176
Medium
The explosive in a Hydrogen bomb is a mixture of ${ }_1 \mathrm{H}^2,{ }_1 \mathrm{H}^3 and { }_3 \mathrm{Li}^6 in some condensed form. The chain reaction is given by \begin{aligned} & { }_3 \mathrm{Li}^6+{ }_0 \mathrm{n}^1 \rightarrow{ }_2 \mathrm{He}^4+{ }_1 \mathrm{H}^3 \\ & { }_1 \mathrm{H}^2+{ }_1 \mathrm{H}^3 \rightarrow{ }_2 \mathrm{He}^4+{ }_0 \mathrm{n}^1 \end{aligned} During the explosion the energy released is approximately [Given ; \mathrm{M}(\mathrm{Li})=6.01690 \mathrm{~amu}, \mathrm{M}\left({ }_1 \mathrm{H}^2\right)=2.01471 \mathrm{~amu}, \mathrm{M}\left({ }_2 \mathrm{He}^4\right)=4.00388 \mathrm{amu}, and 1 \mathrm{~amu}=931.5 \mathrm{~MeV}]
Options:
A) 22.22 MeV
B) 28.12 MeV
C) 16.48 MeV
D) 12.64 MeV
177
Easy
The atomic mass of ${ }_6 \mathrm{C}^{12} is 12.000000 \mathrm{~u} and that of { }_6 \mathrm{C}^{13} is 13.003354 \mathrm{~u}. The required energy to remove a neutron from { }_6 \mathrm{C}^{13}, if mass of neutron is 1.008665 \mathrm{~u}$, will be :
Options:
A) 62.5 MeV
B) 6.25 MeV
C) 4.95 MeV
D) 49.5 MeV
178
Easy
The radius of third stationary orbit of electron for Bohr's atom is R. The radius of fourth stationary orbit will be:
Options:
A) \frac{4}{3} \mathrm{R}
B) \frac{16}{9} R
C) \frac{3}{4} R
D) \frac{9}{16} \mathrm{R}
179
Easy
The half-life of a radioactive nucleus is 5 years. The fraction of the original sample that would decay in 15 years is:
Options:
A) \frac{1}{8}
B) \frac{3}{4}
C) \frac{7}{8}
D) \frac{1}{4}
180
Easy
Given below are two statements: one is labelled as Assertion $\mathbf{A} and the other is labelled as Reason \mathbf{R}$ Assertion A : The binding energy per nucleon is practically independent of the atomic number for nuclei of mass number in the range 30 to 170 . Reason R : Nuclear force is short ranged. In the light of the above statements, choose the correct answer from the options given below
Options:
A) \mathrm{A} is false but \mathbf{R}$ is true
B) \mathrm{A} is true but \mathbf{R}$ is false
C) Both $\mathbf{A} and \mathbf{R} are true and \mathbf{R} is the correct explanation of \mathbf{A}
D) Both $\mathbf{A} and \mathbf{R} are true but \mathbf{R} is NOT the correct explanation of \mathbf{A}
181
Easy
_{92}^{238}A \to _{90}^{234}B + _2^4D + Q In the given nuclear reaction, the approximate amount of energy released will be: [Given, mass of { }_{92}^{238} \mathrm{~A}=238.05079 \times 931.5 ~\mathrm{MeV} / \mathrm{c}^{2}, mass of { }_{90}^{234} B=234 \cdot 04363 \times 931 \cdot 5 ~\mathrm{MeV} / \mathrm{c}^{2}, mass of \left.{ }_{2}^{4} D=4 \cdot 00260 \times 931 \cdot 5 ~\mathrm{MeV} / \mathrm{c}^{2}\right]
Options:
A) 2.12 MeV
B) 4.25 MeV
C) 3.82 MeV
D) 5.9 MeV
182
Medium
A $12.5 \mathrm{~eV}$ electron beam is used to bombard gaseous hydrogen at room temperature. The number of spectral lines emitted will be:
Options:
A) 2
B) 4
C) 3
D) 1
183
Easy
The energy of $\mathrm{He}^{+} ion in its first excited state is, (The ground state energy for the Hydrogen atom is -13.6 ~\mathrm{eV})$ :
Options:
A) -13.6 ~\mathrm{eV}
B) -27.2 ~\mathrm{eV}
C) -3.4 ~\mathrm{eV}
D) -54.4 ~\mathrm{eV}
184
Easy
Two radioactive elements A and B initially have same number of atoms. The half life of A is same as the average life of B. If $\lambda_{A} and \lambda_{B}$ are decay constants of A and B respectively, then choose the correct relation from the given options.
Options:
A) \lambda_{\mathrm{A}}=\lambda_{\mathrm{B}} \ln 2
B) \lambda_{\mathrm{A}} \ln 2=\lambda_{\mathrm{B}}
C) \lambda_{\mathrm{A}}=2 \lambda_{\mathrm{B}}
D) \lambda_{\mathrm{A}}=\lambda_{\mathrm{B}}
185
Easy
The half life of a radioactive substance is T. The time taken, for disintegrating $\frac{7}{8}$th part of its original mass will be:
Options:
A) 8T
B) 3T
C) T
D) 2T
186
Easy
The angular momentum for the electron in Bohr's orbit is L. If the electron is assumed to revolve in second orbit of hydrogen atom, then the change in angular momentum will be
Options:
A) L
B) \frac{L}{2}
C) zero
D) 2 L
187
Easy
A radio active material is reduced to $1 / 8 of its original amount in 3 days. If 8 \times 10^{-3} \mathrm{~kg}$ of the material is left after 5 days the initial amount of the material is
Options:
A) 64 g
B) 256 g
C) 32 g
D) 40 g
188
Easy
The waves emitted when a metal target is bombarded with high energy electrons are
Options:
A) Infrared rays
B) Radio Waves
C) Microwaves
D) X-rays
189
Hard
For a nucleus ${ }_{\mathrm{A}}^{\mathrm{A}} \mathrm{X} having mass number \mathrm{A} and atomic number \mathrm{Z} A. The surface energy per nucleon \left(b_{\mathrm{s}}\right)=-a_{1} A^{2 / 3}. B. The Coulomb contribution to the binding energy \mathrm{b}_{\mathrm{c}}=-a_{2} \frac{Z(Z-1)}{A^{4 / 3}} C. The volume energy \mathrm{b}_{\mathrm{v}}=a_{3} A D. Decrease in the binding energy is proportional to surface area. E. While estimating the surface energy, it is assumed that each nucleon interacts with 12 nucleons. ( a_{1}, a_{2} and a_{3}$ are constants) Choose the most appropriate answer from the options given below:
Options:
A) C, D only
B) B, C, E only
C) B, C only
D) A, B, C, D only
190
Medium
A small particle of mass $m moves in such a way that its potential energy U=\frac{1}{2} m ~\omega^{2} r^{2} where \omega is constant and r is the distance of the particle from origin. Assuming Bohr's quantization of momentum and circular orbit, the radius of n^{\text {th }}$ orbit will be proportional to,
Options:
A) \sqrt{n}
B) n^{2}
C) \frac{1}{n}
D) n
191
Easy
The energy levels of an hydrogen atom are shown below. The transition corresponding to emission of shortest wavelength is :
Options:
A) A
B) C
C) B
D) D
192
Easy
An electron of a hydrogen like atom, having $Z=4, jumps from 4^{\text {th }} energy state to 2^{\text {nd }} energy state. The energy released in this process, will be : (Given Rch = 13.6~\mathrm{eV}$) Where R = Rydberg constant c = Speed of light in vacuum h = Planck's constant
Options:
A) 10.5 ~\mathrm{eV}
B) 40.8 ~\mathrm{eV}
C) 13.6 ~\mathrm{eV}
D) 3.4 ~\mathrm{eV}
193
Easy
The mass of proton, neutron and helium nucleus are respectively $1.0073~u,1.0087~u and 4.0015~u$. The binding energy of helium nucleus is :
Options:
A) 28.4~\mathrm{MeV}
B) 56.8~\mathrm{MeV}
C) 7.1~\mathrm{MeV}
D) 14.2~\mathrm{MeV}
194
Easy
The radius of electron's second stationary orbit in Bohr's atom is R. The radius of 3rd orbit will be
Options:
A) 2.25R
B) 3 \mathrm{R}
C) \frac{\mathrm{R}}{3}
D) 9 \mathrm{R}
195
Easy
A free neutron decays into a proton but a free proton does not decay into neutron. This is because
Options:
A) neutron is an uncharged particle
B) neutron has larger rest mass than proton
C) neutron is a composite particle made of a proton and an electron
D) proton is a charged particle
196
Medium
Given below are two statements: one is labelled as Assertion \mathbf{A} and the other is labelled as Reason \mathbf{R} Assertion A: The nuclear density of nuclides { }_{5}^{10} \mathrm{~B},{ }_{3}^{6} \mathrm{Li},{ }_{26}^{56} \mathrm{Fe},{ }_{10}^{20} \mathrm{Ne} and { }_{83}^{209} \mathrm{Bi} can be arranged as \rho_{\mathrm{Bi}}^{\mathrm{N}}>\rho_{\mathrm{Fe}}^{\mathrm{N}}>\rho_{\mathrm{Ne}}^{\mathrm{N}}>\rho_{\mathrm{B}}^{\mathrm{N}}>\rho_{\mathrm{Li}}^{\mathrm{N}} Reason R: The radius R of nucleus is related to its mass number A as R=R_{0} A^{1 / 3}, where R_{0} is a constant. In the light of the above statements, choose the correct answer from the options given below
Options:
A) {Both ~\mathbf{A}} and \mathbf{R} are true and \mathbf{R} is the correct explanation of \mathbf{A}
B) Both \mathbf{A} and \mathbf{R} are true but \mathbf{R} is NOT the correct explanation of \mathbf{A}
C) \mathbf{A} is false but \mathbf{R} is true
D) \mathbf{A} is true but \mathbf{R} is false
197
Easy
Speed of an electron in Bohr's $7^{\text {th }} orbit for Hydrogen atom is 3.6 \times 10^{6} \mathrm{~m} / \mathrm{s}. The corresponding speed of the electron in 3^{\text {rd }} orbit, in \mathrm{m} / \mathrm{s}$ is :
Options:
A) \left(1.8 \times 10^{6}\right)
B) \left(7.5 \times 10^{6}\right)
C) \left(8.4 \times 10^{6}\right)
D) \left(3.6 \times 10^{6}\right)
198
Medium
Substance A has atomic mass number 16 and half life of 1 day. Another substance B has atomic mass number 32 and half life of $\frac{1}{2}$ day. If both A and B simultaneously start undergo radio activity at the same time with initial mass 320 g each, how many total atoms of A and B combined would be left after 2 days.
Options:
A) 1.69\times10^{24}
B) 3.38\times10^{24}
C) 6.76\times10^{23}
D) 6.76\times10^{24}
199
Easy
If a radioactive element having half-life of $30 \mathrm{~min} is undergoing beta decay, the fraction of radioactive element remains undecayed after 90 \mathrm{~min}$. will be
Options:
A) \frac{1}{16}
B) \frac{1}{4}
C) \frac{1}{8}
D) \frac{1}{2}
200
Easy
The energy levels of an atom is shown in figure. Which one of these transitions will result in the emission of a photon of wavelength 124.1 nm? Given (h = 6.62 $\times 10^{-34}$ Js)
Options:
A) C
B) B
C) A
D) D
201
Easy
The ratio of the density of oxygen nucleus ($_8^{16}O) and helium nucleus (_2^{4}\mathrm{He}$) is
Options:
A) 4 : 1
B) 1 : 1
C) 2 : 1
D) 8 : 1
202
Easy
A photon is emitted in transition from n = 4 to n = 1 level in hydrogen atom. The corresponding wavelength for this transition is (given, h = 4 $\times 10^{-15}$ eVs) :
Options:
A) 99.3 nm
B) 94.1 nm
C) 974 nm
D) 941 nm
203
Easy
Consider the following radioactive decay process $_{84}^{218}A\buildrel \alpha \over \longrightarrow {A_1}\buildrel {{\beta ^ - }} \over \longrightarrow {A_2}\buildrel \gamma \over \longrightarrow {A_3}\buildrel \alpha \over \longrightarrow {A_4}\buildrel {{\beta ^ + }} \over \longrightarrow {A_5}\buildrel \gamma \over \longrightarrow {A_6} The mass number and the atomic number of A_6$ are given by :
Options:
A) 210 and 84
B) 210 and 80
C) 211 and 80
D) 210 and 82
204
Easy
Read the following statements : (A) Volume of the nucleus is directly proportional to the mass number. (B) Volume of the nucleus is independent of mass number. (C) Density of the nucleus is directly proportional to the mass number. (D) Density of the nucleus is directly proportional to the cube root of the mass number. (E) Density of the nucleus is independent of the mass number. Choose the correct option from the following options.
Options:
A) (A) and (D) only.
B) (A) and (E) only.
C) (B) and (E) only.
D) (A) and (C) only.
205
Easy
Find the ratio of energies of photons produced due to transition of an electron of hydrogen atom from its (i) second permitted energy level to the first level, and (ii) the highest permitted energy level to the first permitted level.
Options:
A) 3 : 4
B) 4 : 3
C) 1 : 4
D) 4 : 1
206
Easy
A radioactive sample decays $\frac{7}{8}$ times its original quantity in 15 minutes. The half-life of the sample is
Options:
A) 5 min
B) 7.5 min
C) 15 min
D) 30 min
207
Medium
The half life period of a radioactive substance is 60 days. The time taken for $\frac{7}{8}$th of its original mass to disintegrate will be :
Options:
A) 120 days
B) 130 days
C) 180 days
D) 20 days
208
Easy
The activity of a radioactive material is $6.4 \times 10^{-4} curie. Its half life is 5 days. The activity will become 5 \times 10^{-6}$ curie after :
Options:
A) 7 days
B) 15 days
C) 25 days
D) 35 days
209
Easy
What is the half-life period of a radioactive material if its activity drops to $1 / 16^{\text {th }}$ of its initial value in 30 years?
Options:
A) 9.5 years
B) 8.5 years
C) 7.5 years
D) 10.5 years
210
Easy
A nucleus of mass $M at rest splits into two parts having masses \frac{M^{\prime}}{3} and {{2M'} \over 3}(M' < M)$. The ratio of de Broglie wavelength of two parts will be :
Options:
A) 1 : 2
B) 2 : 1
C) 1 : 1
D) 2 : 3
211
Easy
Mass numbers of two nuclei are in the ratio of $4: 3$. Their nuclear densities will be in the ratio of
Options:
A) 4 : 3
B) \left(\frac{3}{4}\right)^{\frac{1}{3}}
C) 1 : 1
D) \left(\frac{4}{3}\right)^{\frac{1}{3}}
212
Easy
The disintegration rate of a certain radioactive sample at any instant is 4250 disintegrations per minute. 10 minutes later, the rate becomes 2250 disintegrations per minute. The approximate decay constant is : $\left(\right.Take \left.\log _{10} 1.88=0.274\right)
Options:
A) 0.02 \min ^{-1}
B) 2.7 \min ^{-1}
C) 0.063 \min ^{-1}
D) 6.3 \min ^{-1}
213
Easy
Hydrogen atom from excited state comes to the ground state by emitting a photon of wavelength $\lambda. The value of principal quantum number 'n' of the excited state will be : (\mathrm{R}:$ Rydberg constant)
Options:
A) \sqrt{\frac{\lambda \mathrm{R}}{\lambda-1}}
B) \sqrt{\frac{\lambda \mathrm{R}}{\lambda \mathrm{R}-1}}
C) \sqrt{\frac{\lambda}{\lambda \mathrm{R}-1}}
D) \sqrt{\frac{\lambda R^{2}}{\lambda R-1}}
214
Easy
The momentum of an electron revolving in $\mathrm{n}^{\text {th }}$ orbit is given by : (Symbols have their usual meanings)
Options:
A) \frac{\mathrm{nh}}{2 \pi \mathrm{r}}
B)
\frac{n h}{2 r}
C)
\frac{\mathrm{nh}}{2 \pi}
D) \frac{2 \pi r}{\mathrm{nh}}
215
Easy
The magnetic moment of an electron (e) revolving in an orbit around nucleus with an orbital angular momentum is given by :
Options:
A)
\vec{\mu}_{\mathrm{L}}=\frac{\overrightarrow{\mathrm{eL}}}{2 \mathrm{~m}}
B) \vec{\mu}_{\mathrm{L}}=-\frac{\overrightarrow{\mathrm{eL}}}{2 \mathrm{~m}}
C) \vec{\mu}_{l}=-\frac{\overrightarrow{e L}}{\mathrm{~m}}
D)
\vec{\mu}_{l}=\frac{2 \overrightarrow{\mathrm{eL}}}{\mathrm{m}}
216
Medium
A hydrogen atom in ground state absorbs 12.09 eV of energy. The orbital angular momentum of the electron is increased by :
Options:
A) 1.05 $\times 10-$34 Js
B) 2.11 $\times 10-$34 Js
C) 3.16 $\times 10-$34 Js
D) 4.22 $\times 10-$34 Js
217
Easy
In the following nuclear reaction, $D\buildrel \alpha \over \longrightarrow {D_1}\buildrel {{\beta ^ - }} \over \longrightarrow {D_2}\buildrel \alpha \over \longrightarrow {D_3}\buildrel \gamma \over \longrightarrow {D_4}$ Mass number of D is 182 and atomic number is 74. Mass number and atomic number of D4 respectively will be _________.
Options:
A) 174 and 71
B) 174 and 69
C) 172 and 69
D) 172 and 71
218
Easy
The activity of a radioactive material is 2.56 $\times 10-3 Ci. If the half life of the material is 5 days, after how many days the activity will become 2 \times 10-$5 Ci ?
Options:
A) 30 days
B) 35 days
C) 40 days
D) 25 days
219
Easy
Following statements related to radioactivity are given below : (A) Radioactivity is a random and spontaneous process and is dependent on physical and chemical conditions. (B) The number of un-decayed nuclei in the radioactive sample decays exponentially with time. (C) Slope of the graph of loge (no. of undecayed nuclei) Vs. time represents the reciprocal of mean life time ($\tau). (D) Product of decay constant (\lambda$) and half-life time (T1/2) is not constant. Choose the most appropriate answer from the options given below :
Options:
A) (A) and (B) only
B) (B) and (D) only
C) (B) and (C) only
D) (C) and (D) only
220
Easy
The Q-value of a nuclear reaction and kinetic energy of the projectile particle, Kp are related as :
Options:
A) Q = Kp
B) (Kp + Q) < 0
C) Q < Kp
D) (Kp + Q) > 0
221
Easy
Given below are two statements : Statement I : In hydrogen atom, the frequency of radiation emitted when an electron jumps from lower energy orbit (E1) to higher energy orbit (E2), is given as hf = E1 $- E2 Statement II : The jumping of electron from higher energy orbit (E2) to lower energy orbit (E1) is associated with frequency of radiation given as f = (E2 -$ E1)/h This condition is Bohr's frequency condition. In the light of the above statements, choose the correct answer from the options given below :
Options:
A) Both Statement I and Statement II are true.
B) Both Statement I and Statement II are false.
C) Statement I is correct but Statement II is false.
D) Statement I is incorrect but Statement II is true.
222
Medium
A hydrogen atom in its ground state absorbs 10.2 eV of energy. The angular momentum of electron of the hydrogen atom will increase by the value of : (Given, Planck's constant = 6.6 $\times 10-$34 Js).
Options:
A) 2.10 $\times 10-$34 Js
B) 1.05 $\times 10-$34 Js
C) 3.15 $\times 10-$34 Js
D) 4.2 $\times 10-$34 Js
223
Medium
A radioactive nucleus can decay by two different processes. Half-life for the first process is 3.0 hours while it is 4.5 hours for the second process. The effective half-life of the nucleus will be:
Options:
A) 3.75 hours
B) 0.56 hours
C) 0.26 hours
D) 1.80 hours
224
Easy
How many alpha and beta particles are emitted when Uranium 92U238 decays to lead 82Pb206 ?
Options:
A) 3 alpha particles and 5 beta particles
B) 6 alpha particles and 4 beta particles
C) 4 alpha particles and 5 beta particles
D) 8 alpha particles and 6 beta particles
225
Easy
Which of the following figure represents the variation of ${l_n}\left( {{R \over {{R_0}}}} \right) with {l_n}A$ (if R = radius of a nucleus and A = its mass number)
Options:
A)
B)
C)
D)
226
Easy
The ratio for the speed of the electron in the 3rd orbit of He+ to the speed of the electron in the 3rd orbit of hydrogen atom will be :
Options:
A) 1 : 1
B) 1 : 2
C) 4 : 1
D) 2 : 1
227
Medium
In Bohr's atomic model of hydrogen, let K, P and E are the kinetic energy, potential energy and total energy of the electron respectively. Choose the correct option when the electron undergoes transitions to a higher level :
Options:
A) All K, P and E increase.
B) K decreases, P and E increase.
C) P decreases, K and E increase.
D) K increases, P and E decrease.
228
Easy
Choose the correct option from the following options given below :
Options:
A) In the ground state of Rutherford's model electrons are in stable equilibrium. While in Thomson's model electrons always experience a net-force.
B) An atom has a nearly continuous mass distribution in a Rutherford's model but has a highly non-uniform mass distribution in Thomson's model.
C) A classical atom based on Rutherford's model is doomed to collapse.
D) The positively charged part of the atom possesses most of the mass in Rutherford's model but not in Thomson's model.
229
Easy
Nucleus A is having mass number 220 and its binding energy per nucleon is 5.6 MeV. It splits in two fragments 'B' and 'C' of mass numbers 105 and 115. The binding energy of nucleons in 'B' and 'C' is 6.4 MeV per nucleon. The energy Q released per fission will be :
Options:
A) 0.8 MeV
B) 275 MeV
C) 220 MeV
D) 176 MeV
230
Medium
The half life period of radioactive element x is same as the mean life time of another radioactive element y. Initially they have the same number of atoms. Then :
Options:
A) x-will decay faster than y.
B) y-will decay faster than x.
C) x and y have same decay rate initially and later on different decay rate.
D) x and y decay at the same rate always.
231
Medium
A sample of a radioactive nucleus A disintegrates to another radioactive nucleus B, which in turn disintegrates to some other stable nucleus C. Plot of a graph showing the variation of number of atoms of nucleus B versus time is :(Assume that at t = 0, there are no B atoms in the sample)
Options:
A)
B)
C)
D)
232
Easy
There are 1010 radioactive nuclei in a given radioactive element, its half-life time is 1 minute. How many nuclei will remain after 30 seconds? $\left( {\sqrt 2 = 1.414} \right)
Options:
A) 2 $\times$ 1010
B) 7 $\times$ 109
C) 105
D) 4 $\times$ 1010
233
Hard
At time t = 0, a material is composed of two radioactive atoms A and B, where NA(0) = 2NB(0). The decay constant of both kind of radioactive atoms is $\lambda$. However, A disintegrates to B and B disintegrates to C. Which of the following figures represents the evolution of NB(t) / NB(0) with respect to time t?[NA (0) = No. of A atoms at t = 0NB (0) = No. of B atoms at t = 0]
Options:
A)
B)
C)
D)
234
Easy
A particular hydrogen like ion emits radiation of frequency 2.92 $\times$ 1015 Hz when it makes transition from n = 3 to n = 1. The frequency in Hz of radiation emitted in transition from n = 2 to n = 1 will be :
Options:
A) 0.44 $\times$ 1015
B) 6.57 $\times$ 1015
C) 4.38 $\times$ 1015
D) 2.46 $\times$ 1015
235
Easy
Consider the following statements :A. Atoms of each element emit characteristics spectrum.B. According to Bohr's Postulate, an electron in a hydrogen atom, revolves in a certain stationary orbit.C. The density of nuclear matter depends on the size of the nucleus.D. A free neutron is stable but a free proton decay is possible.E. Radioactivity is an indication of the instability of nuclei.Choose the correct answer from the options given below :
Options:
A) A, B, C, D and E
B) A, B and E only
C) B and D only
D) A, C and E only
236
Easy
If 'f' denotes the ratio of the number of nuclei decayed (Nd) to the number of nuclei at t = 0 (N0) then for a collection of radioactive nuclei, the rate of change of 'f' with respect to time is given as :[$\lambda$ is the radioactive decay constant]
Options:
A) - \lambda (1 - e-\lambda$t)
B) \lambda (1 - e-\lambda$t)
C) \lambdae-\lambda$t
D) - \lambdae-\lambda$t
237
Medium
Some nuclei of a radioactive material are undergoing radioactive decay. The time gap between the instances when a quarter of the nuclei have decayed and when half of the nuclei have decayed is given as :(where $\lambda$ is the decay constant)
Options:
A) {1 \over 2}{{\ln 2} \over \lambda }
B) {{\ln 2} \over \lambda }
C) {{2\ln 2} \over \lambda }
D) {{\ln {3 \over 2}} \over \lambda }
238
Medium
The half-life of ${}^{198}Au is 3 days. If atomic weight of {}^{198}Au is 198 g/mol then the activity of 2 mg of {}^{198}Au$ is [in disintegration/second] :
Options:
A) 2.67 $\times$ 1012
B) 6.06 $\times$ 1018
C) 32.36 $\times$ 1012
D) 16.18 $\times$ 1012
239
Medium
A nucleus with mass number 184 initially at rest emits an $\alpha-particle. If the Q value of the reaction is 5.5 MeV, calculate the kinetic energy of the \alpha$-particle.
Options:
A) 5.5 MeV
B) 5.0 MeV
C) 5.38 MeV
D) 0.12 MeV
240
Medium
For a certain radioactive process the graph between In R and t(sec) is obtained as shown in the figure. Then the value of half life for the unknown radioactive material is approximately :
Options:
A) 9.15 sec
B) 6.93 sec
C) 2.62 sec
D) 4.62 sec
241
Medium
A radioactive material decays by simultaneous emissions of two particles with half lives of 1400 years and 700 years respectively. What will be the time after which one third of the material remains ? (Take ln 3 = 1.1)
Options:
A) 740 years
B) 1110 years
C) 700 years
D) 340 years
242
Medium
A nucleus of mass M emits $\gamma$ -ray photon of frequency 'v'. The loss of internal energy by the nucleus is :[Take 'c' as the speed of electromagnetic wave]
Options:
A) hv
B) hv\left[ {1 + {{hv} \over {2M{c^2}}}} \right]
C) hv\left[ {1 - {{hv} \over {2M{c^2}}}} \right]
D) 0
243
Medium
The decay of a proton to neutron is :
Options:
A) always possible as it is associated only with $\beta$+ decay
B) possible only inside the nucleus
C) not possible as proton mass is less than the neutron mass
D) not possible but neutron to proton conversation is possible
244
Medium
Imagine that the electron in a hydrogen atom is replaced by a muon ($\mu$). The mass of muon particle is 207 times that of an electron and charge is equal to the charge of an electron. The ionization potential of this hydrogen atom will be :
Options:
A) 13.6 eV
B) 2815.2 eV
C) 331.2 eV
D) 27.2 eV
245
Medium
A radioactive sample disintegrates via two independent decay processes having half lives $T_{1/2}^{(1)} and T_{1/2}^{(2)}$ respectively. The effective half-life T1/2 of the nuclei is :
Options:
A) None of the above
B) {T_{1/2}} = T_{1/2}^{(1)} + T_{1/2}^{(2)}
C) {T_{1/2}} = {{T_{1/2}^{(1)}T_{1/2}^{(2)}} \over {T_{1/2}^{(1)} + T_{1/2}^{(2)}}}
D) {T_{1/2}} = {{T_{1/2}^{(1)} + T_{1/2}^{(2)}} \over {T_{1/2}^{(1)} - T_{1/2}^{(2)}}}
246
Easy
The atomic hydrogen emits a line spectrum consisting of various series. Which series of hydrogen atomic spectra is lying in the visible region?
Options:
A) Brackett series
B) Balmer series
C) Paschen series
D) Lyman series
247
Easy
If an electron is moving in the nth orbit of the hydrogen atom, then its velocity (vn) for the nth orbit is given as :
Options:
A) {v_n} \propto {1 \over n}
B) vn $ \propto $ n2
C) vn $ \propto $ n
D) {v_n} \propto {1 \over {{n^2}}}
248
Easy
Which level of the single ionized carbon has the same energy as the ground state energy of hydrogen atom?
Options:
A) 8
B) 6
C) 1
D) 4
249
Medium
Calculate the time interval between 33% decay and 67% decay if half-life of a substance is 20 minutes.
Options:
A) 40 minutes
B) 60 minutes
C) 13 minutes
D) 20 minutes
250
Medium
The half-life of Au198 is 2.7 days. The activity of 1.50 mg of Au198 if its atomic weight is 198 g mol$-1 is, (Na = 6 \times$ 1023/mol).
Options:
A) 240 Ci
B) 357 Ci
C) 252 Ci
D) 535 Ci
251
Medium
A radioactive sample is undergoing $\alpha decay. At any time t1, its activity is A and another time t2, the activity is {A \over 5}$. What is the average life time for the sample?
Options:
A) {{\ln 5} \over {{t_2} - {t_1}}}
B) {{\ln ({t_2} + {t_1})} \over 2}
C) {{{t_1} - {t_2}} \over {\ln 5}}
D) {{{t_2} - {t_1}} \over {\ln 5}}
252
Medium
If $\lambda1 and \lambda2 are the wavelengths of the third member of Lyman and first member of the Paschen series respectively, then the value of \lambda1 : \lambda$2 is :
Options:
A) 7 : 135
B) 7 : 108
C) 1 : 9
D) 1 : 3
253
Easy
The wavelength of the photon emitted by a hydrogen atom when an electron makes a transition from n = 2 to n = 1 state is :
Options:
A) 194.8 nm
B) 490.7 nm
C) 913.3 nm
D) 121.8 nm
254
Medium
Two radioactive substances X and Y originally have N1 and N2 nuclei respectively. Half life of X is half of the half life of Y. After three half lives of Y, number of nuclei of both are equal. The ratio ${{{N_1}} \over {{N_2}}}$ will be equal to :
Options:
A) {1 \over 8}
B) {3 \over 1}
C) {1 \over 3}
D) {8 \over 1}
255
Easy
According to Bohr atomic model, in which of the following transitions will the frequency be maximum?
Options:
A) n = 2 to n = 1
B) n = 3 to n = 2
C) n = 4 to n = 3
D) n = 5 to n = 4
256
Medium
In the given figure, the energy levels of hydrogen atom have been shown along with some transitions marked A, B, C, D and E.The transitions A, B and C respectively represent :
Options:
A) The series limit of Lyman series, second member of Balmer series and second member of Paschen series.
B) The ionization potential of hydrogen, second member of Balmer series and third member of Paschen series.
C) The series limit of Lyman series, third member of Balmer series and second member of Paschen series.
D) The first member of the Lyman series, third member of Balmer series and second member of Paschen series.
257
Medium
Given the masses of various atomic particles mp = 1.0072 u, mn = 1.0087 u, me = 0.000548 u, ${m_{\overline v }} = 0, md = 2.0141 u, where p \equiv proton, n \equiv neutron, e \equiv electron, \overline v \equiv antineutrino and d \equiv $ deuteron. Which of the following process is allowed by momentum and energy conservation?
Options:
A) n + n $ \to $ deuterium atom
(electron bound to the nucleus)
B) n + p $ \to d + \gamma
C) p $ \to n + e+ + \overline v
D) e+ + e- $ \to \gamma
258
Medium
You are given that Mass of ${}_3^7Li = 7.0160u, Mass of {}_2^4He = 4.0026u and Mass of {}_1^1H = 1.0079u. When 20 g of {}_3^7Li is converted into {}_2^4He$ by proton capture, the energy liberated, (in kWh), is : [Mass of nucleon = 1 GeV/c2]
Options:
A) 6.82 $ \times $ 105
B) 4.5 $ \times $ 105
C) 8 $ \times $ 106
D) 1.33 $ \times $ 106
259
Medium
A radioactive nucleus decays by two different processes. The half life for the first process is 10 s and that for the second is 100 s. The effective half life of the nucleus is close to :
Options:
A) 12 sec
B) 9 sec
C) 55 sec
D) 6 sec
260
Medium
Activities of three radioactive substances A, B and C are represented by the curves A, B and C, in the figure. Then their half-lives ${T_{{1 \over 2}}}\left( A \right) : {T_{{1 \over 2}}}\left( B \right) : {T_{{1 \over 2}}}\left( C \right)$ are in the ratio :
Options:
A) 3 : 2 : 1
B) 2 : 1 : 1
C) 4 : 3 : 1
D) 2 : 1 : 3
261
Medium
Find the Binding energy per neucleon for ${}_{50}^{120}Sn$. Mass of proton mp = 1.00783 U, mass of neutron mn = 1.00867 U and mass of tin nucleus mSn = 119.902199 U. (take 1U = 931 MeV)
Options:
A) 9.0 MeV
B) 8.5 MeV
C) 8.0 MeV
D) 7.5 MeV
262
Medium
Hydrogen ion and singly ionized helium atom are accelerated, from rest, through the same potential difference. The ratio of final speeds of hydrogen and helium ions is close to :
Options:
A) 2 : 1
B) 1 : 2
C) 5 : 7
D) 10 : 7
263
Medium
The radius R of a nucleus of mass number A can be estimated by the formula R = (1.3 $ \times 10–15)A1/3 m. It follows that the mass density of a nucleus is of the order of : (Mprot. \cong Mneut \simeq 1.67 \times $ 10–27 kg)
Options:
A) 1024 kg m–3
B) 1010 kg m–3
C) 1017 kg m–3
D) 103 kg m–3
264
Medium
In a radioactive material, fraction of active material remaining after time t is 9/16. The fraction that was remaining after t/2 is
Options:
A) {3 \over 4}
B) {4 \over 5}
C) {3 \over 5}
D) {7 \over 8}
265
Medium
In a hydrogen atom the electron makes a transition from (n + 1)th level to the nth level. If n >> 1, the frequency of radiation emitted is proportional to :
Options:
A) {1 \over n}
B) {1 \over {{n^2}}}
C) {1 \over {{n^3}}}
D) {1 \over {{n^4}}}
266
Medium
In a reactor, 2 kg of 92U235 fuel is fully used up in 30 days. The energy released per fission is 200 MeV. Given that the Avogadro number, N = 6.023 $ \times $ 1026 per kilo mole and 1 eV = 1.6 × 10–19 J. The power output of the reactor is close to
Options:
A) 125 MW
B) 60 MW
C) 54 MW
D) 35 MW
267
Medium
The energy required to ionise a hydrogen like ion in its ground state is 9 Rydbergs. What is the wavelength of the radiation emitted when the electron in this ion jumps from the second excited state to the ground state ?
Options:
A) 35.8 nm
B) 11.4 nm
C) 8.6 nm
D) 24.2 nm
268
Medium
The graph which depicts the results of Rutherford gold foil experiment with $\alpha -particales is : \theta : Scattering angle Y : Number of scattered \alpha $-particles detected (Plots are schematic and not to scale)
Options:
A)
B)
C)
D)
269
Medium
The activity of a radioactive sample falls from 700 s–1 to 500 s–1 in 30 minutes. Its half life is close to:
Options:
A) 62 min
B) 66 min
C) 72 min
D) 52 min
270
Medium
The time period of revolution of electron in its ground state orbit in a hydrogen atom is 1.6 $ \times $ 10-16 s. The frequency of revolution of the electron in its first excited state (in s-1) is :
Options:
A) 5.6 $ \times $ 1012
B) 1.6 $ \times $ 1014
C) 7.8 $ \times $ 1014
D) 6.2 $ \times $ 1015
271
Medium
Half lives of two radioactive nuclei A and B are 10 minutes and 20 minutes, respectively, If initially a sample has equal number of nuclei, then after 60 minutes, the ratio of decayed numbers of nuclei A and B will be :
Options:
A) 9 : 8
B) 1 : 8
C) 8 : 1
D) 3 : 8
272
Medium
The electron in a hydrogen atom first jumps from the third excited state to the second excited state and subsequently to the first excited state. The ratio of the respective wavelengths, ${{{\lambda _1}} \over {{\lambda _2}}}$, of the photons emitted in this process is :
Options:
A) {{22} \over 5}
B) {7 \over 5}
C) {9 \over 7}
D) {{20} \over 7}
273
Medium
Consider an electron in a hydrogen atom revolving in its second excited state (having radius 4.65 $\mathop A\limits^o $). The de-Broglie wavelength of this electron is :
Options:
A) 6.6 $\mathop A\limits^o
B) 3.5 $\mathop A\limits^o
C) 9.7 $\mathop A\limits^o
D) 12.9 $\mathop A\limits^o
274
Medium
An excited He+ ion emits two photons in succession, with wavelengths 108.5 nm and 30.4 nm, in making a transition to ground state. The quantum number n, corresponding to its initial excited state is (for photon of wavelength $\lambda , energy E = {{1240\,eV} \over {\lambda (in\,nm)}}$) :
Options:
A) n = 4
B) n = 7
C) n = 5
D) n = 6
275
Medium
In Li+ +, electron in first Bohr orbit is excited to a level by a radiation of wavelength $\lambda . When the ion gets deexcited to the ground state in all possible ways (including intermediate emissions), a total of six spectral lines are observed. What is the value of \lambda $? (Given : H = 6.63 × 10–34 Js; c = 3 × 108 ms –1)
Options:
A) 10.8 nm
B) 12.3 nm
C) 9.4 nm
D) 11.4 nm
276
Medium
Two radioactive substances A and B have decay constants 5$\lambda and \lambda respectively. At t = 0, a sample has the same number of the two nuclei. The time taken for the ratio of the number of nuclei to become {\left( {{1 \over e}} \right)^2}$ will be :
Options:
A) {2 \over \lambda }
B) {1 \over {4\lambda }}
C) {1 \over {2\lambda }}
D) {1 \over {\lambda }}
277
Medium
Two radioactive materials A and B have decay constants 10$\lambda and \lambda $, respectively. It initially they have the same number of nuclei, then the ratio of the number of nuclei of A to that of B will be 1/e after a time :
Options:
A) 1/9$\lambda
B) 11/10$\lambda
C) 1/10$\lambda
D) 1/11$\lambda
278
Medium
A He+ ion is in its first excited state. Its ionization energy is :-
Options:
A) 13.60 eV
B) 6.04 eV
C) 48.36 eV
D) 54.40 eV
279
Medium
Taking the wavelength of first Balmer line in hydrogen spectrum (n = 3 to n = 2) as 660 nm, the wavelength of the 2nd Balmer line (n = 4 to n = 2) will be :
Options:
A) 642.7 nm
B) 488.9 nm
C) 889.2 nm
D) 388.9 nm
280
Medium
The ratio of mass densities of nuclei of 40Ca and 16O is close to :-
Options:
A) 1
B) 5
C) 0.1
D) 2
281
Medium
Radiation coming from transitions n = 2 to n = 1 of hydrogen atoms fall on He+ ions in n = 1 and n = 2 states. The possible transition of helium ions as they absorb energy from the radiation is :
Options:
A) n = 1 $ \to $ n = 4
B) n = 2 $ \to $ n = 5
C) n = 2 $ \to $ n = 4
D) n = 2 $ \to $ n = 3
282
Medium
In a radioactive decay chain, the initial nucleus is ${}_{90}^{232}Th. At the end there are 6 \alpha -particles and 4 \beta -particles which are emitted. If the end nucleus is {}_Z^A$X, A and Z are given by :
Options:
A) A = 208; Z = 80
B) A = 208; Z = 82
C) A = 200; Z = 81
D) A = 202; Z = 80
283
Medium
A particle of mass m moves in a circular orbit in a central potential field U(r) = ${1 \over 2}$ kr2. If Bohr 's quantization conditions are applied, radii of possible orbitls and energy levels vary with quantum number n as :
Options:
A) rn $ \propto \sqrt n , En \propto $ n
B) rn $ \propto \sqrt n , En \propto {1 \over n}
C) rn $ \propto n, En \propto $ n
D) rn $ \propto n2, En \propto {1 \over {{n^2}}}
284
Medium
In a hydrogen like atom, when an electron jumps from the M-shell to the L-shell, the wavelength of emitted radiation is $\lambda $. If an electron jumps from N-shell to the L-shell, the wavelength of emitted radiation will be:
Options:
A) {{25} \over {16}} \lambda
B) {{27} \over {20}} \lambda
C) {{16} \over {25}} \lambda
D) {{20} \over {27}} \lambda
285
Medium
A hydrogen atom, initially in the ground state is excited by absorbing a photon of wavelength 980$\mathop A\limits^ \circ . The radius of the atom in the excited state, in terms of Bohr radius a0 will be : (hc = 12500 eV\mathop A\limits^ \circ $)
Options:
A) 4a0
B) 9a0
C) 25a0
D) 16a0
286
Medium
Consider the nuclear fission Ne20 $ \to $ 2He4 + C12 Given that the binding energy/ nucleon of Ne20, He4 and C12 are, respectively, 8.03 MeV, 7.07 MeV and 7.86 MeV, identify the correct statement -
Options:
A) 8.3 MeV energy will be released
B) energy of 11.9 MeV has to be supplied
C) energy of 12.4 MeV will be supplied
D) energy of 3.6 MeV will be released
287
Medium
Using a nuclear counter the count rate of emitted particles from a radioactive source is measured. At t = 0 it was 1600 counts per second and t = 8 seconds it was 100 counts per second. The count rate observed, as counts per second, at t = 6 seconds is close to -
Options:
A) 200
B) 150
C) 400
D) 360
288
Medium
At a given instant, say t = 0, two radioactive substance A and B have equal activities. the ratio ${{{R_B}} \over {{R_A}}} of their activities after time t itself decays with time t as e-$3t. If the half-life of A is ln2, the half-life of B is :
Options:
A) 4ln2
B) {{\ln 2} \over 2}
C) {{\ln 2} \over 4}
D) 2ln2
289
Medium
A sample of radioactive material A, that has an activity of 10 mCi(1 Ci = 3.7 $ \times $ 1010 decays/s), has twice the number of nuclei as another sample of a different radioactive materail B which has an activity of 20 mCi. The correct choices for half-lives of A and B would then be respectively :
Options:
A) 5 days and 10 days
B) 10 days and 40 days
C) 20 days and 5 days
D) 20 days and 10 days
290
Medium
At some instant, a radioactive sample S1 having an activity 5 $\mu Ci has twice the number of nuclei as another sample S2 which has an activity of 10 \mu $Ci. The half lives of S1 and S2 are :
Options:
A) 20 years and 5 years, respectively
B) 20 years and 10years, respectively
C) 5 years and 20 years, respectively
D) 10 years and 20 years, respectively
291
Medium
An electron from various excited states of hydrogen atom emit radiation to come to the ground state. Let ${\lambda _n}, {\lambda _g} be the de Broglie wavelength of the electron in the nth state and the ground state respectively. Let {\Lambda _n}$ be the wavelength of the emitted photon in the transition from the nth state to the ground state. For large n, (A, B are constants)
Options:
A) {\Lambda _n} \approx A + {B \over {\lambda _n^2}}
B) {\Lambda _n} \approx A + B{\lambda _n}
C) \Lambda _n^2 \approx A + B\lambda _n^2
D) \Lambda _n^2 \approx \lambda
292
Medium
If the series limit frequency of the Lyman series is ${\nu _L}$, then the series limit frequency of the Pfund series is:
Options:
A) {\nu _L}/25
B) 25{\nu _L}
C) 16{\nu _L}
D) {\nu _L}/16
293
Medium
It is found that if a neutron suffers an elastic collinear collision with deuterium at rest, fractional loss of its energy is pd; while for its similar collision with carbon nucleus at rest, fractional loss of energy is pc. The values of pd and pc are respectively :
Options:
A) (0, 1)
B) (0.89, 0.28)
C) (0.28, 0.89)
D) (0, 0)
294
Medium
Muon ($\mu -) is a negatively charged (|q| = |e|) particle with a mass m\mu = 200 me, where me is the mass of the electron and e is the electronic charge. If \mu - is bond to a proton to form a hydrogen like atom, identify the correct statements. (A) Radis of the muonic orbit is 200 times smaller than that of the electron. (B) The speed of the \mu - in the nth orbit is {1 \over {200}}$ times that of the electron in the nth orbit. (C) The ionization energy of muonic atom is 200 timesmore than of an hydroen atom. (D) The momentum of the muon in the nth orbit is 200 times more than that of the electron.
Options:
A) (A), (B), (D)
B) (A), (C), (D)
C) (B), (D)
D) (C), (D)
295
Medium
An unstable heavy nucleus at rest breaks into two nuclei which move away with velocities in the ratio of 8 : 27. The ratio of the radii of the nuclei (assumed to be spherical) is :
Options:
A) 8 : 27
B) 4 : 9
C) 3 : 2
D) 2 : 3
296
Medium
The energy required to remove the electron from a singly ionized Helium atom is $2.2$ times the energies required to remove an electron from Helium atom. The total energy required to ionize the Helium atom completely is :
Options:
A) 20 eV
B) 34 eV
C) 79 eV
D) 109 eV
297
Medium
A solution containing active cobalt ${^{60}_{27}}Co having activity of 0.8 \mu Ci and decay constant \lambda is injected in an animal's body. If 1\,c{m^3} of blood is drawn from the animal's body after 10 hrs of injection, the activity found was 300 decays per minute What is the volume of blood that is flowing in the body ? \left( {\,\,Ci = 3.7 \times {{10}^{10}}\,} \right. decays per second and at t=10 hrs \left. {{e^{ - \lambda t}} = 0.84} \right)
Options:
A) 6$ liters
B) 7$ liters
C) 4$ liters
D) 5$ liters
298
Medium
The acceleration of an electron in the first orbit of the hydrogen atom (n = 1) is :
Options:
A) {{{h^2}} \over {{\pi ^2}{m^2}{r^3}}}
B) {{{h^2}} \over {{8\pi ^2}{m^2}{r^3}}}
C) {{{h^2}} \over {{4\pi ^2}{m^2}{r^3}}}
D) {{{h^2}} \over {{4\pi }{m^2}{r^3}}}
299
Medium
Imagine that a reactor converts all given mass into energy and that it operates at a power level of 109 watt. The mass of the fuel consumed per hour in the reactor will be : (velocity of light, c is 3×108 m/s)
Options:
A) 0.96 gm
B) 0.8 gm
C) 4 $ \times 10-$2 gm
D) 6.6 $ \times 10-$5 gm
300
Medium
Two deuterons undergo nuclear fusion to form a Helium nucleus. Energy released in this process is : (given binding energy per nucleon for deuteron = 1.1 MeV and for helium = 7.0 MeV)
Options:
A) 30.2 MeV
B) 32.4 MeV
C) 23.6 MeV
D) 25.8 MeV
301
Medium
According to Bohr’s theory, the time averaged magnetic field at the centre (i.e. nucleus) of a hydrogen atom due to the motion of electrons in the nth orbit is proportional to : (n = principal quantum number)
Options:
A) {n^{ - 4}}
B) {n^{ - 5}}
C) n$-$3
D) n$-$2
302
Medium
A radioactive nucleus A with a half life T, decays into a nucleus B. At t = 0, there is no nucleus B. At sometime t, the ratio of the number of B to that of A is 0.3. Then, t is given by :
Options:
A) t = {T \over {\log (1.3)}}
B) t = T\log (1.3)
C) t = {T \over 2}{{\log 2} \over {\log 1.3}}
D) t = T{{\log 1.3} \over {\log 2}}
303
Medium
Some energy levels of a molecule are shown in the figure. The ratio of the wavelengths r = ${{\lambda _1}}/{{\lambda _2}}$, is given by:
Options:
A) r = 1/3
B) r = 4/3
C) r = 2/3
D) r = 3/4
304
Medium
A hydrogen atom makes a transition from n = 2 to n = 1 and emits a photon. This photon strikes a doubly ionized lithium atom (z = 3) in excited state and completely removes the orbiting electron. The least quantum number for the excited state of the ion for the process is :
Options:
A) 2
B) 3
C) 4
D) 5
305
Medium
Half-lives of two radioactive elements $A and B are 20 minutes and 40 minutes, respectively. Initially, the samples have equal number of nuclei. After 80 minutes, the ratio of decayed number of A and B$ nuclei will be:
Options:
A) 1:4
B) 5:4
C) 1:16
D) 4:1
306
Medium
As an electron makes a transition from an excited state to the ground state of a hydrogen - like atom/ion :
Options:
A) kinetic energy decreases, potential energy increases but total energy remains same
B) kinetic energy and total energy decrease but potential energy increases
C) its kinetic energy increases but potential energy and total energy decrease
D) kinetic energy, potential energy and total energy decrease
307
Medium
The radiation corresponding to $3 \to 2 transition of hydrogen atom falls on a metal surface to produce photoelectrons. These electrons are made to enter a magnetic field 3 \times {10^{ - 4}}\,T. If the radius of the larger circular path followed by these electrons is 10.0 mm$, the work function of the metal is close to:
Options:
A) 1.8 eV
B) 1.1 eV
C) 0.8 eV
D) 1.6 eV
308
Medium
Hydrogen $\left( {{}_1{H^1}} \right), Deuterium \left( {{}_1{H^2}} \right), singly ionised Helium {\left( {{}_2H{e^4}} \right)^ + } and doubly ionised lithium {\left( {{}_3L{i^6}} \right)^{ + + }} all have one electron around the nucleus. Consider an electron transition from n=2 to n=1. If the wavelengths of emitted radiation are {\lambda _1},{\lambda _2},{\lambda _3} and {\lambda _4}$ respectively then approximately which one of the following is correct?
Options:
A) 4{\lambda _1} = 2{\lambda _2} = 2{\lambda _3} = {\lambda _4}
B) {\lambda _1} = 2{\lambda _2} = 2{\lambda _3} = {\lambda _4}
C) {\lambda _1} = {\lambda _2} = 4{\lambda _3} = 9{\lambda _4}
D) {\lambda _1} = 2{\lambda _2} = 3{\lambda _3} = 4{\lambda _4}
309
Medium
In a hydrogen like atom electron make transition from an energy level with quantum number $n to another with quantum number \left( {n - 1} \right). If n > > 1,$ the frequency of radiation emitted is proportional to :
Options:
A) {1 \over n}
B) {1 \over {{n^2}}}
C) {1 \over {{n^{{3 \over 2}}}}}
D) {1 \over {{n^3}}}
310
Medium
Assume that a neutron breaks into a proton and an electron. The energy released during this process is : (mass of neutron $ = 1.6725 \times {10^{ - 27}}kg, mass of proton = 1.6725 \times {10^{ - 27}}\,kg, mass of electron = 9 \times {10^{ - 31}}\,kg$ ).
Options:
A) 0.51 MeV
B) 7.10\,MeV
C) 6.30\,MeV
D) 5.4\,MeV
311
Medium
A diatomic molecule is made of two masses ${m_1} and {m_2} which are separated by a distance r. If we calculate its rotational energy by applying Bohr's rule of angular momentum quantization, its energy will be given by: (n$ is an integer)
Options:
A) {{{{\left( {{m_1} + {m_2}} \right)}^2}{n^2}{h^2}} \over {2m_1^2m_2^2{r^2}}}
B) {{{n^2}{h^2}} \over {2\left( {{m_1} + {m_2}} \right){r^2}}}
C) {{2{n^2}{h^2}} \over {\left( {{m_1} + {m_2}} \right){r^2}}}
D) {{\left( {{m_1} + {m_2}} \right){n^2}{h^2}} \over {2{m_1}{m_2}{r^2}}}
312
Medium
Hydrogen atom is excited from ground state to another state with principal quantum number equal to $4.$ Then the number of spectral lines in the emission spectra will be :
Options:
A) 2
B) 3
C) 5
D) 6
313
Medium
Energy required for the electron excitation in $L{i^{ + + }}$ from the first to the third Bohr orbit is :
Options:
A) 36.3 eV
B) 108.8 eV
C) 122.4 eV
D) 12.1 eV
314
Medium
The half life of a radioactive substance is $20 minutes. The approximate time interval \left( {{t_2} - {t_1}} \right) between the time {{t_2}} when {2 \over 3} of it had decayed and time {{t_1}} when {1 \over 3}$ of it had decayed is :
Options:
A) 14$ min
B) 20$ min
C) 28$ min
D) 7$ min
315
Medium
A nucleus of mass $M+\Delta m is at rest and decays into two daughter nuclei of equal mass {M \over 2} each. Speed of light is c. The binding energy per nucleon for the parent nucleus is {E_1} and that for the daughter nuclei is {E_2}.$ Then
Options:
A) {E_2} = 2{E_1}
B) {E_1} > {E_2}
C) {E_2} > {E_1}
D) {E_1} = 2{E_2}
316
Medium
A radioactive nucleus (initial mass number $A and atomic number Z emits 3\,\alpha - particles and 2$ positrons. The ratio of number of neutrons to that of protons in the final nucleus will be
Options:
A) {{A - Z - 8} \over {Z - 4}}
B) {{A - Z - 4} \over {Z - 8}}
C) {{A - Z - 12} \over {Z - 4}}
D) {{A - Z - 4} \over {Z - 2}}
317
Medium
A nucleus of mass $M+\Delta m is at rest and decays into two daughter nuclei of equal mass {M \over 2} each. Speed of light is c.$ The speed of daughter nuclei is
Options:
A) c{{\Delta m} \over {M + \Delta m}}
B) c\sqrt {{{2\Delta m} \over M}}
C) c\sqrt {{{\Delta m} \over M}}
D) c\sqrt {{{\Delta m} \over {M + \Delta m}}}
318
Medium
The transition from the state $n=4 to n=3$ in a hydrogen like atom result in ultra violet radiation. Infrared radiation will be obtained in the transition from :
Options:
A) 3 \to 2
B) 4 \to 2
C) 5 \to 4
D) 2 \to 1
319
Medium
The above is a plot of binding energy per nucleon ${E_b}, against the nuclear mass M;A,B,C,D,E,F correspond to different nuclei. Consider four reactions : \eqalign{ & \left( i \right)\,\,\,\,\,\,\,\,\,\,A + B \to C + \varepsilon \,\,\,\,\,\,\,\,\,\,\left( {ii} \right)\,\,\,\,\,\,\,\,\,\,C \to A + B + \varepsilon \,\,\,\,\,\,\,\,\,\, \cr & \left( {iii} \right)\,\,\,\,\,\,D + E \to F + \varepsilon \,\,\,\,\,\,\,\,\,\,\left( {iv} \right)\,\,\,\,\,\,\,\,\,F \to D + E + \varepsilon ,\,\,\,\,\,\,\,\,\,\, \cr} where \varepsilon is the energy released? In which reactions is \varepsilon $ positive?
Options:
A) (i) and (iii)
B) (ii) and (iv)
C) (ii) and (iii)
D) (i) and (iv)
320
Medium
This question contains Statement- 1 and Statement- 2. Of the four choices given after the statements, choose the one that best describes the two statements: Statement- 1: Energy is released when heavy nuclei undergo fission or light nuclei undergo fusion and Statement- 2: For heavy nuclei, binding energy per nucleon increases with increasing $Z while for light nuclei it decreases with increasing Z.
Options:
A) Statement - $1 is false, Statement - 2$ is true
B) Statement - $1 is true, Statement - 2 is true; Statement - 2 is a correct explanation for Statement - 1
C) Statement - $1 is true, Statement - 2 is true; Statement - 2 is not a correct explanation for Statement - 1
D) Statement - $1 is true, Statement - 2$ is false
321
Medium
Suppose an electron is attracted towards the origin by a force ${k \over r} where 'k' is a constant and 'r' is the distance of the electron from the origin. By applying Bohr model to this system, the radius of the {n^{th}} orbital of the electron is found to be '{r_n}' and the kinetic energy of the electron to be '{T_n}'.$ Then which of the following is true?
Options:
A) {T_n} \propto {1 \over {{n^2}}},{r_n} \propto {n^2}
B) {T_n} independent of n,{r_n} \propto n
C) {T_n} \propto {1 \over n},{r_n} \propto n
D) {T_n} \propto {1 \over n},{r_n} \propto {n^2}
322
Medium
The half-life period of a ratio-active element $X is same as the mean life time of another ratio-active element Y.$ Initially they have the same number of atoms. Then
Options:
A) X and Y$ decay at same rate always
B) X will decay faster than Y
C) Y will decay faster than X
D) X and Y$ have same decay rate initially
323
Medium
Which of the following transitions in hydrogen atoms emit photons of highest frequency ?
Options:
A) n = 1 to n=2
B) n = 2 to n=6
C) n = 6 to n=2
D) n = 2 to n=1
324
Medium
In gamma ray emission from a nucleus
Options:
A) only the proton number changes
B) both the neutron number and the proton number change
C) there is no change in the proton number and the neutron number
D) only the neutron number changes
325
Medium
If ${M_O} is the mass of an oxygen isotope {}_8{O^{17}} , {M_p} and {M_N}$ are the masses of a proton and neutron respectively, the nuclear binding energy of the isotope is
Options:
A) \left( {{M_O} - 17{M_N}} \right){C^2}
B) \left( {{M_O} - 8{M_P}} \right){C^2}
C) \left( {{M_O} - 8{M_P} - 9{M_N}} \right){C^2}
D) {{M_O}{c^2}}
326
Medium
An alpha nucleus of energy ${1 \over 2}m{v^2} bombards a heavy nuclear target of charge Ze$. Then the distance of closest approach for the alpha nucleus will be proportional to
Options:
A) {v^2}
B) {1 \over m}
C) {1 \over {{v^2}}}
D) {1 \over {Ze}}
327
Medium
The energy spectrum of $\beta -particles [ number N(E) as a function of \beta -energy E$ ] emitted from a radioactive source is
Options:
A)
B)
C)
D)
328
Medium
The $'rad'$ is the correct unit used to report the measurement of
Options:
A) the ability of a beam of gamma ray photons to produce ions in a target
B) the energy delivered by radiation to a target
C) the biological effect of radiation
D) the rate of decay of radioactive source
329
Medium
When ${}_3L{i^7} nuclei are bombarded by protons, and the resultant nuclei are {}_4B{e^8}$, the emitted particles will be
Options:
A) alpha particles
B) beta particles
C) gamma photons
D) neutrons
330
Medium
If the binding energy per nucleon in ${}_3^7Li and {}_2^4He nuclei are 5.60 MeV and 7.06 MeV respectively, then in the reaction p + {}_3^7Li \to 2\,{}_2^4He$$ energy of proton must be
Options:
A) 28.24 MeV
B) 17.28 MeV
C) 1.46 MeV
D) 39.2 MeV
331
Medium
The intensity of gamma radiation from a given source is $L. On passing through 36 mm of lead, it is reduced to {{\rm I} \over 8}. The thickness of lead which will reduce the intensity to {{\rm I} \over 2}$ will be
Options:
A) 9mm
B) 6mm
C) 12mm
D) 18mm
332
Medium
The diagram shows the energy levels for an electron in a certain atom. Which transition shown represents the emission of a photon with the most energy?
Options:
A) iv
B) iii
C) ii
D) i
333
Medium
Starting with a sample of pure ${}^{66}Cu,{7 \over 8} of it decays into Zn in 15$ minutes. The corresponding half life is
Options:
A) 15$ minutes
B) 10$ minutes
C) 7{1 \over 2}$ minutes
D) 5$ minutes
334
Medium
A nuclear transformation is denoted by $X\left( {n,\alpha } \right)\matrix{ 7 \cr 3 \cr } Li. Which of the following is the nucleus of element X$ ?
Options:
A) {}_5^{10}B
B) {}^{12}{C_6}
C) {}_4^{11}Be
D) {}_5^9B
335
Medium
If radius of the $\matrix{ {27} \cr {13} \cr } Al nucleus is estimated to be 3.6 fermi then the radius of \matrix{ {125} \cr {52} \cr } \,Te$ nucleus is estimated to be nearly
Options:
A) 8$ fermi
B) 6$ fermi
C) 5$ fermi
D) 4$ fermi
336
Medium
A nucleus disintegrated into two nuclear parts which have their velocities in the ratio of $2:1.$ The ratio of their nuclear sizes will be
Options:
A) {3^{{\raise0.5ex\hbox{\scriptstyle 1}
\kern-0.1em/\kern-0.15em
\lower0.25ex\hbox{\scriptstyle 2}}}}:1
B) 1:{2^{1/3}}
C) {2^{1/3}}:1
D) 1:{3^{{\raise0.5ex\hbox{\scriptstyle 1}
\kern-0.1em/\kern-0.15em
\lower0.25ex\hbox{\scriptstyle 2}}}}
337
Medium
The binding energy per nucleon of deuteron $\left( {{}_1^2\,H} \right) and helium nucleus \left( {{}_2^4\,He} \right) is 1.1 MeV and 7 MeV$ respectively. If two deuteron nuclei react to form a single helium nucleus, then the energy released is
Options:
A) 23.6\,\,MeV
B) 26.9\,\,MeV
C) 13.9\,\,MeV
D) 19.2\,\,MeV
338
Medium
An $\alpha -particle of energy 5 MeV is scattered through {180^ \circ }$ by a fixed uranium nucleus. The distance of closest approach is of the order of
Options:
A) {10^{ - 12}}\,cm
B) {10^{ - 10}}\,cm
C) 1A
D) {10^{ - 15a}}\,cm
339
Medium
In the nuclear fusion reaction $${}_1^2H + {}_1^3H \to {}_2^4He + n given that the repulsive potential energy between the two nuclei is \sim 7.7 \times {10^{ - 14}}J, the temperature at which the gases must be heated to initiate the reaction is nearly [ Boltzmann's Constant k = 1.38 \times {10^{ - 23}}\,J/K$ ]
Options:
A) {10^7}\,\,K
B) {10^5}\,\,K
C) {10^3}\,\,K
D) {10^9}\,\,K
340
Medium
Which of the following cannot be emitted by radioactive substances during their decay ?
Options:
A) Protons
B) Neutrinoes
C) Helium nuclei
D) Electrons
341
Medium
A radioactive sample at any instant has its disintegration rate $5000 disintegrations per minute. After 5 minutes, the rate is 1250$ disintegrations per minute. Then, the decay constant (per minute) is
Options:
A) 0.4 ln2
B) 0.2 ln2
C) 0.1 ln2
D) 0.8 ln2
342
Medium
If the binding energy of the electron in a hydrogen atom is $13.6eV, the energy required to remove the electron from the first excited state of L{i^{ + + }}$ is
Options:
A) 30.6 eV
B) 13.6 eV
C) 3.4 eV
D) 122.4 eV
343
Medium
Which of the following atoms has the lowest ionization potential ?
Options:
A) {}_7^{14}N
B) {}_{55}^{133}\,Cs
C) {}_{18}^{40}\,Ar
D) {}_8^{16}\,O
344
Medium
Which of the following radiations has the least wavelength ?
Options:
A) \gamma $ - rays
B) \beta $ - rays
C) \alpha $ - rays
D) X$ - rays
345
Medium
The wavelengths involved in the spectrum of deuterium $\left( {{}_1^2\,D} \right)$ are slightly different from that of hydrogen spectrum, because
Options:
A) the size of the two nuclei are different
B) the nuclear forces are different in the two cases
C) the masses of the two nuclei are different
D) the attraction between the electron and the nucleus is different in the two cases
346
Medium
A nucleus with $Z=92 emits the following in a sequence: \alpha ,{\beta ^ - },{\beta ^ - },\alpha ,\alpha ,\alpha ,\alpha ,\alpha ,{\beta ^ - },{\beta ^ - },\alpha ,{\beta ^ + },{\beta ^ + },\alpha Then Z$ of the resulting nucleus is
Options:
A) 76
B) 78
C) 82
D) 74
347
Medium
When a ${U^{238}} nucleus originally at rest, decays by emitting an alpha particle having a speed 'u',$ the recoil speed of the residual nucleus is
Options:
A) {{4\mu } \over {238}}
B) - {{4\mu } \over {234}}
C) {{4\mu } \over {234}}
D) - {{4\mu } \over {238}}
348
Medium
At a specific instant emission of radioactive compound is deflected in a magnetic field. The compound can emit $\eqalign{ & \left( i \right)\,\,\,\,\,\,\,electrons\,\,\,\,\,\,\,\,\,\,\,\,\left( {ii} \right)\,\,\,\,\,\,\,protons \cr & \left( {iii} \right)\,\,\,H{e^{2 + }}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( {iv} \right)\,\,\,\,\,\,\,neutrons \cr} $ The emission at instant can be
Options:
A) i, ii, iii
B) i, ii, iii, iv
C) iv
D) ii, iii
349
Medium
If $13.6 eV energy is required to ionize the hydrogen atom, then the energy required to remove an electron from n=2$ is
Options:
A) 10.2 eV
B) 0 eV
C) 3.4 eV
D) 6.8 eV.
350
Medium
If ${N_0} is the original mass of the substance of half-life period {t_{1/2}} = 5 years, then the amount of substance left after 15$ years is
Options:
A) {N_0}/8
B) {N_0}/16
C) {N_0}/2
D) {N_0}/4
351
Easy
The average energy released per fission for the nucleus of { }_{92}^{235} \mathrm{U} is 190 MeV . When all the atoms of 47 g pure { }_{92}^{235} \mathrm{U} undergo fission process, the energy released is \alpha \times 10^{23} \mathrm{MeV}. The value of \alpha is \_\_\_\_ . (Avogadro Number =6 \times 10^{23} per mole)
Options:
352
Medium
An electron in the hydrogen atom initially in the fourth excited state makes a transition to \mathrm{n}^{\text {th }} energy state by emitting a photon of energy 2.86 eV . The integer value of n will be__________.
Options:
353
Medium
A star has $100 \% helium composition. It starts to convert three { }^4 \mathrm{He} into one { }^{12} \mathrm{C} via triple alpha process as { }^4 \mathrm{He}+{ }^4 \mathrm{He}+{ }^4 \mathrm{He} \rightarrow{ }^{12} \mathrm{C}+\mathrm{Q}. The mass of the star is 2.0 \times 10^{32} \mathrm{~kg} and it generates energy at the rate of 5.808 \times 10^{30} \mathrm{~W}. The rate of converting these { }^4 \mathrm{He} to { }^{12} \mathrm{C} is \mathrm{n} \times 10^{42} \mathrm{~s}^{-1}, where \mathrm{n} is _________. [ Take, mass of { }^4 \mathrm{He}=4.0026 \mathrm{u}, mass of { }^{12} \mathrm{C}=12 \mathrm{u}$]
Options:
354
Easy
In an alpha particle scattering experiment distance of closest approach for the $\alpha particle is 4.5 \times 10^{-14} \mathrm{~m}. If target nucleus has atomic number 80 , then maximum velocity of \alpha-particle is __________ \times 10^5 \mathrm{~m} / \mathrm{s} approximately. (\frac{1}{4 \pi \epsilon_0}=9 \times 10^9 \mathrm{SI} unit, mass of \alpha particle =6.72 \times 10^{-27} \mathrm{~kg}$)
Options:
355
Easy
Radius of a certain orbit of hydrogen atom is 8.48 $\mathop A\limits^o. If energy of electron in this orbit is E / x. then x= ________ (Given \mathrm{a}_0=0.529 \mathop A\limits^o, E=$ energy of electron in ground state).
Options:
356
Easy
The shortest wavelength of the spectral lines in the Lyman series of hydrogen spectrum is $915\mathop A\limits^o. The longest wavelength of spectral lines in the Balmer series will be _______ \mathop A\limits^o$.
Options:
357
Easy
If three helium nuclei combine to form a carbon nucleus then the energy released in this reaction is ________ $\times 10^{-2} \mathrm{~MeV}. (Given 1 \mathrm{u}=931 \mathrm{~MeV} / \mathrm{c}^2, atomic mass of helium =4.002603 \mathrm{u}$)
Options:
358
Easy
The disintegration energy $Q for the nuclear fission of { }^{235} \mathrm{U} \rightarrow{ }^{140} \mathrm{Ce}+{ }^{94} \mathrm{Zr}+n is _______ \mathrm{MeV}. Given atomic masses of { }^{235} \mathrm{U}: 235.0439 u ;{ }^{140} \mathrm{Ce}: 139.9054 u, { }^{94} \mathrm{Zr}: 93.9063 u ; n: 1.0086 u, Value of c^2=931 \mathrm{~MeV} / \mathrm{u}$.
Options:
359
Hard
A hydrogen atom changes its state from $n=3 to n=2. Due to recoil, the percentage change in the wave length of emitted light is approximately 1 \times 10^{-n}. The value of n is _______. [Given Rhc =13.6 \mathrm{~eV}, \mathrm{hc}=1242 \mathrm{~eV} \mathrm{~nm}, \mathrm{h}=6.6 \times 10^{-34} \mathrm{~J} \mathrm{~s} mass of the hydrogenatom =1.6 \times 10^{-27} \mathrm{~kg}$]
Options:
360
Medium
A particular hydrogen-like ion emits the radiation of frequency 3 \times 10^{15} \mathrm{~Hz} when it makes transition from n=2 to n=1. The frequency of radiation emitted in transition from n=3 to n=1 is \frac{x}{9} \times 10^{15} \mathrm{~Hz}, when x= ________ .
Options:
361
Easy
The radius of a nucleus of mass number 64 is 4.8 fermi. Then the mass number of another nucleus having radius of 4 fermi is \frac{1000}{x}, where x is _______.
Options:
362
Easy
A nucleus has mass number $A_1 and volume V_1. Another nucleus has mass number A_2 and Volume V_2. If relation between mass number is A_2=4 A_1, then \frac{V_2}{V_1}=$ __________.
Options:
363
Easy
The mass defect in a particular reaction is $0.4 \mathrm{~g}. The amount of energy liberated is n \times 10^7 \mathrm{~kWh}, where n= __________. (speed of light \left.=3 \times 10^8 \mathrm{~m} / \mathrm{s}\right)
Options:
364
Medium
A electron of hydrogen atom on an excited state is having energy $\mathrm{E}_{\mathrm{n}}=-0.85 \mathrm{~eV}$. The maximum number of allowed transitions to lower energy level is _________.
Options:
365
Medium
Hydrogen atom is bombarded with electrons accelerated through a potential difference of $\mathrm{V}, which causes excitation of hydrogen atoms. If the experiment is being performed at \mathrm{T}=0 \mathrm{~K}, the minimum potential difference needed to observe any Balmer series lines in the emission spectra will be \frac{\alpha}{10} \mathrm{~V}, where \alpha=$ __________.
Options:
366
Medium
When a hydrogen atom going from $n=2 to n=1 emits a photon, its recoil speed is \frac{x}{5} \mathrm{~m} / \mathrm{s}. Where x= ________. (Use, mass of hydrogen atom =1.6 \times 10^{-27} \mathrm{~kg}$)
Options:
367
Easy
If Rydberg's constant is $R, the longest wavelength of radiation in Paschen series will be \frac{\alpha}{7 R}, where \alpha=$ ________.
Options:
368
Easy
In a nuclear fission process, a high mass nuclide $(A \approx 236) with binding energy 7.6 \mathrm{~MeV} / Nucleon dissociated into middle mass nuclides (\mathrm{A} \approx 118), having binding energy of 8.6 \mathrm{~MeV} / \mathrm{Nucleon}. The energy released in the process would be ______ \mathrm{MeV}$.
Options:
369
Medium
As per given figure A, B and C are the first, second and third excited energy levels of hydrogen atom respectively. If the ratio of the two wavelengths \left(\right. i.e. \left.\frac{\lambda_{1}}{\lambda_{2}}\right) is \frac{7}{4 n}, then the value of n will be __________.
Options:
370
Easy
The radius of $2^{\text {nd }} orbit of \mathrm{He}^{+} of Bohr's model is r_{1} and that of fourth orbit of \mathrm{Be}^{3+} is represented as r_{2}. Now the ratio \frac{r_{2}}{r_{1}} is x: 1. The value of x$ is ___________.
Options:
371
Easy
A common example of alpha decay is ${ }_{92}^{238} \mathrm{U} \longrightarrow{ }_{90}^{234} \mathrm{Th}+{ }_{2} \mathrm{He}^{4}+\mathrm{Q} Given : { }_{92}^{238} \mathrm{U}=238.05060 ~\mathrm{u}, { }_{90}^{234} \mathrm{Th}=234.04360 ~\mathrm{u}, { }_{2}^{4} \mathrm{He}=4.00260 ~\mathrm{u} and 1 \mathrm{u}=931.5 \frac{\mathrm{MeV}}{c^{2}} The energy released (Q) during the alpha decay of { }_{92}^{238} \mathrm{U}$ is __________ MeV
Options:
372
Medium
A nucleus disintegrates into two nuclear parts, in such a way that ratio of their nuclear sizes is $1: 2^{1 / 3}. Their respective speed have a ratio of n: 1. The value of n$ is __________.
Options:
373
Medium
If 917 $\mathop A\limits^o be the lowest wavelength of Lyman series then the lowest wavelength of Balmer series will be ___________ \mathop A\limits^o $.
Options:
374
Easy
The decay constant for a radioactive nuclide is 1.5 $\times 10^{-5} s^{-1}. Atomic weight of the substance is 60 g mole^{-1}, (N_A=6\times10^{23}). The activity of 1.0 \mug of the substance is ___________ \times 10^{10}$ Bq.
Options:
375
Medium
The ratio of wavelength of spectral lines $\mathrm{H}_{\alpha} and \mathrm{H}_{\beta} in the Balmer series is \frac{x}{20}. The value of x$ is _________.
Options:
376
Easy
A nucleus with mass number 242 and binding energy per nucleon as $7.6~ \mathrm{MeV} breaks into two fragment each with mass number 121. If each fragment nucleus has binding energy per nucleon as 8.1 ~\mathrm{MeV}, the total gain in binding energy is _________ \mathrm{MeV}$.
Options:
377
Medium
Experimentally it is found that $12.8 ~\mathrm{eV} energy is required to separate a hydrogen atom into a proton and an electron. So the orbital radius of the electron in a hydrogen atom is \frac{9}{x} \times 10^{-10} \mathrm{~m}. The value of the x is __________. \left(1 \mathrm{eV}=1.6 \times 10^{-19} \mathrm{~J}, \frac{1}{4 \pi \epsilon_{0}}=9 \times 10^{9} \mathrm{Nm}^{2} / \mathrm{C}^{2}\right. and electronic charge \left.=1.6 \times 10^{-19} \mathrm{C}\right)
Options:
378
Easy
The radius of fifth orbit of the $\mathrm{Li}^{++} is __________ \times 10^{-12} \mathrm{~m}. Take: radius of hydrogen atom = 0.51\,\mathop A\limits^o
Options:
379
Easy
Nucleus A having $Z=17 and equal number of protons and neutrons has 1.2 ~\mathrm{MeV} binding energy per nucleon. Another nucleus \mathrm{B} of Z=12 has total 26 nucleons and 1.8 ~\mathrm{MeV} binding energy per nucleons. The difference of binding energy of \mathrm{B} and \mathrm{A} will be _____________ \mathrm{MeV}$.
Options:
380
Medium
A light of energy $12.75 ~\mathrm{eV} is incident on a hydrogen atom in its ground state. The atom absorbs the radiation and reaches to one of its excited states. The angular momentum of the atom in the excited state is \frac{x}{\pi} \times 10^{-17} ~\mathrm{eVs}. The value of x is ___________ (use h=4.14 \times 10^{-15} ~\mathrm{eVs}, c=3 \times 10^{8} \mathrm{~ms}^{-1}$ ).
Options:
381
Easy
If the binding energy of ground state electron in a hydrogen atom is 13.6\, \mathrm{eV}, then, the energy required to remove the electron from the second excited state of \mathrm{Li}^{2+} will be : x \times 10^{-1} \mathrm{eV}. The value of x is ________.
Options:
382
Easy
For hydrogen atom, $\lambda_{1} and \lambda_{2} are the wavelengths corresponding to the transitions 1 and 2 respectively as shown in figure. The ratio of \lambda_{1} and \lambda_{2} is \frac{x}{32}. The value of x$ is __________.
Options:
383
Medium
A radioactive nucleus decays by two different process. The half life of the first process is 5 minutes and that of the second process is 30 \mathrm{~s}. The effective half-life of the nucleus is calculated to be \frac{\alpha}{11} \mathrm{~s}. The value of \alpha is __________.
Options:
384
Easy
A radioactive element $_{92}^{242}X emits two \alpha-particles, one electron and two positrons. The product nucleus is represented by _{\mathrm{P}}^{234}$Y. The value of P is __________.
Options:
385
Medium
A nucleus disintegrates into two smaller parts, which have their velocities in the ratio 3 : 2. The ratio of their nuclear sizes will be ${\left( {{x \over 3}} \right)^{{1 \over 3}}}. The value of 'x$' is :-
Options:
386
Medium
The wavelength of the radiation emitted is $\lambda_0 when an electron jumps from the second excited state to the first excited state of hydrogen atom. If the electron jumps from the third excited state to the second orbit of the hydrogen atom, the wavelength of the radiation emitted will \frac{20}{x}\lambda_0. The value of x$ is _____________.
Options:
387
Easy
The energy released per fission of nucleus of $^{240}X is 200 MeV. The energy released if all the atoms in 120g of pure ^{240}X undergo fission is ____________ \times 10^{25} MeV. (Given \mathrm{N_A=6\times10^{23}}$)
Options:
388
Medium
Assume that protons and neutrons have equal masses. Mass of a nucleon is $1.6\times10^{-27} kg and radius of nucleus is 1.5\times10^{-15}~\mathrm{A^{1/3}} m. The approximate ratio of the nuclear density and water density is n\times10^{13}. The value of n$ is __________.
Options:
389
Easy
Two radioactive materials A and B have decay constants $25 \lambda and 16 \lambda respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of B to that of A will be "e" after a time \frac{1}{a \lambda}$. The value of a is _________.
Options:
390
Easy
A freshly prepared radioactive source of half life 2 hours 30 minutes emits radiation which is 64 times the permissible safe level. The minimum time, after which it would be possible to work safely with source, will be _________ hours.
Options:
391
Easy
Two lighter nuclei combine to form a comparatively heavier nucleus by the relation given below : ${ }_{1}^{2} X+{ }_{1}^{2} X={ }_{2}^{4} Y The binding energies per nucleon for \frac{2}{1} X and { }_{2}^{4} Y are 1.1 \,\mathrm{MeV} and 7.6 \,\mathrm{MeV} respectively. The energy released in this process is _______________ \mathrm{MeV}$.
Options:
392
Medium
In the hydrogen spectrum, $\lambda be the wavelength of first transition line of Lyman series. The wavelength difference will be "a\lambda'' between the wavelength of 3^{\text {rd }} transition line of Paschen series and that of 2^{\text {nd }} transition line of Balmer series where \mathrm{a}=$ ___________.
Options:
393
Easy
{x \over {x + 4}}$ is the ratio of energies of photons produced due to transition of an electron of hydrogen atom from its (i) third permitted energy level to the second level and (ii) the highest permitted energy level to the second permitted level. The value of x will be ____________.
Options:
394
Medium
A hydrogen atom in its first excited state absorbs a photon of energy x $\times 10-2 eV and excited to a higher energy state where the potential energy of electron is -$1.08 eV. The value of x is ______________.
Options:
395
Easy
The half life of a radioactive substance is 5 years. After x years a given sample of the radioactive substance gets reduced to 6.25% of its initial value. The value of x is ____________.
Options:
396
Medium
\sqrt {{d_1}} and \sqrt {{d_2}} are the impact parameters corresponding to scattering angles 60^\circ and 90^\circ respectively, when an \alpha$ particle is approaching a gold nucleus. For d1 = x d2, the value of x will be ____________.
Options:
397
Medium
A beam of monochromatic light is used to excite the electron in Li+ + from the first orbit to the third orbit. The wavelength of monochromatic light is found to be x $\times 10-$10 m. The value of x is ___________. [Given hc = 1242 eV nm]
Options:
398
Medium
A sample contains 10$-2 kg each of two substances A and B with half lives 4 s and 8 s respectively. The ratio of their atomic weights is 1 : 2. The ratio of the amounts of A and B after 16 s is {x \over {100}}$. The value of x is ___________.
Options:
399
Easy
X different wavelengths may be observed in the spectrum from a hydrogen sample if the atoms are exited to states with principal quantum number n = 6 ? The value of X is ______________.
Options:
400
Medium
The K$\alpha X-ray of molybdenum has wavelength 0.071 nm. If the energy of a molybdenum atoms with a K electron knocked out is 27.5 keV, the energy of this atom when an L electron is knocked out will be __________ keV. (Round off to the nearest integer)[h = 4.14 \times 10-15 eVs, c = 3 \times 108 ms-$1]
Options:
401
Medium
In Bohr's atomic model, the electron is assumed to revolve in a circular orbit of radius 0.5 $\mathop A\limits^o . If the speed of electron is 2.2 \times 166 m/s, then the current associated with the electron will be _____________ \times 10-2 mA. [Take \pi as {{22} \over 7}$]
Options:
402
Medium
A radioactive sample has an average life of 30 ms and is decaying. A capacitor of capacitance 200 $\muF is first charged and later connected with resistor 'R'. If the ratio of charge on capacitor to the activity of radioactive sample is fixed with respect to time then the value of 'R' should be _____________ \Omega$.
Options:
403
Easy
From the given data, the amount of energy required to break the nucleus of aluminium $_{13}^{27}Al is __________ x \times 10-$3 J.Mass of neutron = 1.00866 uMass of proton = 1.00726 uMass of Aluminium nucleus = 27.18846 u(Assume 1 u corresponds to x J of energy)(Round off to the nearest integer)
Options:
404
Easy
The nuclear activity of a radioactive element becomes ${\left( {{1 \over 8}} \right)^{th}}$ of its initial value in 30 years. The half-life of radioactive element is _____________ years.
Options:
405
Easy
A radioactive substance decays to ${\left( {{1 \over {16}}} \right)^{th}}$ of its initial activity in 80 days. The half life of the radioactive substance expressed in days is ____________.
Options:
406
Medium
A particle of mass m moves in a circular orbit in a central potential field U(r) = U0r4. If Bohr's quantization conditions are applied, radii of possible orbitals rn vary with ${n^{{1 \over \alpha }}}, where \alpha$ is ____________.
Options:
407
Medium
The first three spectral lines of H-atom in the Balmer series are given $\lambda1, \lambda2, \lambda3 considering the Bohr atomic model, the wave lengths of first and third spectral lines \left( \frac{\lambda_{1} }{\lambda_{3} } \right) are related by a factor of approximately 'x' \times 10-$1.The value of x, to the nearest integer, is _________.
Options:
408
Medium
A particle of mass 200 MeV/c2 collides with a hydrogen atom at rest. Soon after the collision the particle comes to rest, and the atom recoils and goes to its first excited state. The initial kinetic energy of the particle (in eV) is ${N \over 4}$. The value of N is : (Given the mass of the hydrogen atom to be 1 GeV/c2) ______ .
Options:
409
Medium
The first member of the Balmer series of hydrogen atom has a wavelength of 6561 Å. The wavelength of the second member of the Balmer series (in nm) is:
Options:
410
Medium
A radioactive element having half-life 30 min . is undergoing beta decay. The fraction of radioactive element remains undecayed after 90 min . will be
Options:
A) \frac{1}{2}
B) \frac{1}{4}
C) \frac{1}{8}
D) \frac{1}{16}
411
Medium
The ratio of the total energy of the 2^{\text {nd }} orbit electron for the hydrogen atom (^1\mathrm{H}) to that of a helium ion (\mathrm{He}^+) is :
Options:
A) 4
B) 2
C) \frac{1}{2}
D) \frac{1}{4}
412
Medium
The magnetic moment of electron due to orbital motion is proportional to ( \mathrm{n}= principal quantum number)
Options:
A) n
B) n^2
C) \frac{1}{n}
D) \frac{1}{\mathrm{n}^2}
413
Medium
The frequencies for series limit of Balmer and Paschen series are ' \mathrm{V}_1 ' and ' \mathrm{V}_3 ' respectively. If frequency of first line of Balmer series ' \mathrm{V}_2 ' then the relation between V_1, V_2 and V_3 is
Options:
A) \mathrm{v}_1-\mathrm{v}_3=2 \mathrm{v}_1
B) v_1+v_2=v_3
C) \mathrm{v}_1-\mathrm{v}_2=\mathrm{v}_3
D) v_1+v_3=v_2
414
Medium
A radio active element has rate of disintegration 8000 disintegrations per minute at a particular instant. After four minutes it becomes 2000 disintegrations per minute. The decay constant per minute is
Options:
A) 0.8 \log _{\mathrm{e}} 2
B) 0.6 \log _{\mathrm{e}} 2
C) 0.5 \log _{\mathrm{e}} 2
D) 0.2 \log _{\mathrm{e}} 2
415
Medium
In Paschen series, wavelength of first line is ' \lambda_1 ' and for Brackett series, wavelength of first line is ' \lambda_2 ' then ratio \frac{\lambda_1}{\lambda_2} is
Options:
A) \frac{7}{400}
B) \frac{9}{144}
C) \frac{81}{175}
D) \frac{108}{509}
416
Medium
The ratio of energies of photons produced due to transition of electron of hydrogen atom from its (i) third to 2^{\text {nd }} energy level and (ii) highest energy level to 3^{\text {rd }} level is
Options:
A) 3: 2
B) 5: 4
C) 5: 3
D) 8: 3
417
Medium
In hydrogen atom in its ground state, the first Bohr orbit has radius ' \mathrm{r}_1 '. When the atom is raised to one of its excited states, the electrons orbital velocity becomes one-third. The radius of that orbit is
Options:
A) 2 r_1
B) 3 r_1
C) 4 r_1
D) 9 r_1
418
Medium
A radioactive element has rate of disintegration 9000 disintegration per minute at a particular instant. After two minutes it becomes 3000 disintegration per minute. The decay constant per minute is
Options:
A) 0.5 \log _{\mathrm{c}} 3
B) 0.2 \log _{\mathrm{e}} 3
C) 0.5 \log _{\mathrm{e}} 2
D) 0.2 \log _{\mathrm{e}} 2
419
Medium
In hydrogen atom, transition from the state \mathrm{n}=6 to n=1 results in ultraviolet radiation. Infrared radiation will be obtained in the transition
Options:
A) \mathrm{n}=3 to \mathrm{n}=1
B) \mathrm{n}=4 to \mathrm{n}=2
C) n=6 to n=2
D) n=5 to n=3
420
Medium
A radioactive element { }_{92}^{242} \mathrm{X} emits two \alpha particles, one electron and two positrons. The product nucleus is represented by { }_{\mathrm{p}}^{234} \mathrm{Y}. The value of P is
Options:
A) 87
B) 85
C) 92
D) 96
421
Medium
The activity of radioactive sample is measured as \mathrm{N}_0 counts per minute at time \mathrm{t}=0, and \frac{\mathrm{N}_0}{\mathrm{e}} counts per minute at time \mathrm{t}=3 minute, The activity reduces to half its value in time (in minute)
Options:
A) \frac{1}{3} \log _{\mathrm{e}} 2
B) 3 \log _{\mathrm{e}} 2
C) 3 \log _{10} 2
D) \frac{3}{\log _{10} 2}
422
Medium
In hydrogen atom, the energy of electron in first and third orbit is ' E_1 ' and' E_3 ' respectively. If E_3=x E_1 then the value of x will be
Options:
A) \frac{1}{9}
B) \frac{1}{64}
C) \frac{1}{27}
D) \frac{1}{8}
423
Medium
A radioactive element A decays into radioactive element C by the following processes in succession. \mathrm{A} \rightarrow \mathrm{B}+{ }_2 \mathrm{H}_{\mathrm{e}}^4 ; \mathrm{B} \rightarrow \mathrm{C}+2 \mathrm{e}^{-}Then elements
Options:
A) A and B are isobars.
B) A and C are isobars.
C) A and C are isotopes.
D) A and B are isotopes.
424
Medium
{ }_{88} \mathrm{R}_{\mathrm{a}}^{226} is converted into { }_{82} \mathrm{P}_{\mathrm{b}}^{206} by emission of alpha ( \alpha ) and beta ( \beta ) particles. The number of alpha and beta particles emitted are respectively
Options:
A) 5, 4
B) 4, 5
C) 6, 4
D) 4, 6
425
Medium
Out of the following transitions in hydrogen atom, identify the transition which emits photons of highest frequency.
Options:
A) \mathrm{n}=1 to \mathrm{n}=2
B) \mathrm{n}=2 to \mathrm{n}=1
C) n=2 to n=6
D) n=6 to n=2
426
Medium
Using Bohr's quantization condition, the rotational kinetic energy in the third orbit for a diatomic molecule is ( h= Planck's constant, \mathrm{I}= moment of inertia of diatomic molecule)
Options:
A) \frac{9 h^2}{8 \pi^2 I}
B) \frac{3 \mathrm{~h}^2}{8 \pi^2 \mathrm{I}}
C) \frac{6 h^2}{8 \pi I}
D) \frac{12 h^2}{7 \pi^2 I}
427
Medium
Which of the following transitions in hydrogen atom emit photons of highest frequency? ( \mathrm{n}= principle quantum number)
Options:
A) \mathrm{n}=1 to \mathrm{n}=3
B) \mathrm{n}=2 to \mathrm{n}=4
C) \mathrm{n}=5 to \mathrm{n}=3
D) \mathrm{n}=2 to \mathrm{n}=1
428
Medium
Two radioactive materials A and B having decay constant ' 7 \lambda ' and ' \lambda ' respectively, initially have same number of nuclei. The time taken to have the ratio of number of nuclei of material B to that of A as ' e ' is
Options:
A) \frac{1}{\lambda}
B) \frac{1}{6 \lambda}
C) \frac{1}{7 \lambda}
D) \frac{1}{8 \lambda}
429
Medium
The ratio of angular momentum of an electron in \mathrm{n}^{\text {th }} orbit of hydrogen atom to the velocity of electron in \mathrm{n}^{\text {th }} orbit is proportional to
Options:
A) \mathrm{n}^2
B) \frac{1}{\mathrm{n}^2}
C) \mathrm{n}^3
D) \frac{1}{\mathrm{n}^3}
430
Medium
In hydrogen atom spectrum, when an electron jumps from second excited state to the first excited state, the wavelength of radiation emitted is ' \lambda '. If the electron jumps from the third excited state to the second orbit, the wavelength of radiation emitted will be \frac{20 \lambda}{x}. The value of x is
Options:
A) 18
B) 27
C) 21
D) 36
431
Medium
In hydrogen spectrum, the ratio of wavelengths of the last line of Lyman series and that of the last line of Balmer series is
Options:
A) 1
B) 0.5
C) 0.25
D) 0.2
432
Medium
\begin{aligned} &\text { For the following reaction, the particle ' } \mathrm{x} \text { ' is }{ }_6 \mathrm{C}^{11}\longrightarrow{ }_5 \mathrm{~B}^{11}+\beta+\mathrm{X} \end{aligned}
Options:
A) proton
B) neutrino
C) anti neutrino
D) neutron
433
Medium
The frequency of revolution of an electron in the \mathrm{n}^{\text {th }} orbit of hydrogen atom is
Options:
A) directly proportional to n^2
B) inversely proportional to \mathrm{n}^2
C) directly proportional to n^3
D) inversely proportional to \mathrm{n}^3
434
Medium
If ' \lambda_1 ' and ' \lambda_2 ' are the wavelengths of the first member of the Balmer and Paschen series, in hydrogen atom respectively, then the ratio of respective frequencies, f_1 / f_2, is
Options:
A) 20: 7
B) 27: 5
C) 50: 9
D) 108: 7
435
Medium
The ratio of the wavelength of the last line of Paschen series to that of Balmer series is
Options:
A) \frac{9}{4}
B) \frac{3}{2}
C) \frac{2}{3}
D) \frac{4}{9}
436
Medium
In the second orbit of hydrogen atom, the energy of an electron is ' E '. In the third orbit of helium atom, the energy of the electron will be (atomic number of helium =2)
Options:
A) \frac{4 \mathrm{E}}{9}
B) \frac{4 \mathrm{E}}{3}
C) \frac{16 \mathrm{E}}{9}
D) \frac{16 \mathrm{E}}{3}
437
Medium
Two radioactive substances A and B have decay constants ' 5 \lambda ' and ' \lambda ' respectively. At \mathrm{t}=0, they have the same number of nuclei. The ratio of number of nuclei of A to those of B will be \left(\frac{1}{\mathrm{e}}\right)^2 after a time interval
Options:
A) \frac{1}{42}
B) 4 \lambda
C) 2 \lambda
D) \frac{1}{2 \lambda}
438
Medium
In \mathrm{M}_{\mathrm{O}} is the mass of an oxygen isotope { }_8 \mathrm{O}^{17} and \mathrm{M}_{\mathrm{p}} and \mathrm{M}_{\mathrm{N}} are the mass of proton and mass of neutron respectively, then the nucleus binding energy of the isotope is
Options:
A) \mathrm{M}_{\mathrm{o}} \mathrm{C}^2
B) \left(\mathrm{M}_{\mathrm{o}}-8 \mathrm{M}_{\mathrm{P}}\right) \mathrm{C}^2
C) \mathrm{\left(M_o-17 M_N\right) C^2}
D) \left(\mathrm{M}_{\mathrm{o}}-8 \mathrm{M}_{\mathrm{P}}-9 \mathrm{M}_{\mathrm{N}}\right) \mathrm{C}^2
439
Medium
Frequency of the series limit of Balmer series of hydrogen atom of Rydberg's constant ' R ' and velocity of light ' C ' is
Options:
A) \frac{\mathrm{RC}}{4}
B) RC
C) \frac{4}{\mathrm{RC}}
D) 4 RC
440
Medium
Acceleration of an electron in the first Bohr's orbit is proportional to \mathrm{m}= mass of electron, \mathrm{r}= radius of the orbit, \mathrm{h}= Planck's constant)
Options:
A) \frac{\mathrm{m}^3 \mathrm{r}^3}{\mathrm{~h}^2}
B) \frac{h^2}{m^2 r^3}
C) \frac{\mathrm{h}^2}{\mathrm{mr}^3}
D) \frac{\mathrm{mr}^3}{\mathrm{~h}^2}
441
Medium
In the given reaction ${ }_z \mathrm{X}^A \rightarrow{ }_{z+1} \mathrm{Y}^A \rightarrow{ }_{z-1} \mathrm{~K}^{A-4} \rightarrow{ }_{z-1} \mathrm{~K}^{\mathrm{A}-4}$ radioactive radiations are emitted in the sequence
Options:
A) \alpha, \beta, \gamma
B) \beta, \alpha, \gamma
C) \gamma, \alpha, \beta
D) \beta, \gamma, \alpha
442
Medium
A radioactive substance has half-life of 60 minute. During 3 hour, the amount of substance decayed would be
Options:
A) 8.5 \%
B) 25 \%
C) 12.5 \%
D) 87.5 \%
443
Medium
The ratio of the areas of the electron orbits for the second excited state to the first excited state for the hydrogen atom is
Options:
A) 3: 2
B) 9: 4
C) 16: 81
D) 81: 16
444
Medium
In a hydrogen atom in its ground state, the first Bohr orbit has radius r_1. The electron's orbital speed becomes one-third when the atom is raised to one of its excited states. The radius of the orbit in that excited state is
Options:
A) 3 r_1
B) 4 r_1
C) 9 \pi_1
D) 16 \mathrm{r}_1
445
Medium
The angular momentum of the electron in the third Bohr orbit of hydrogen atom is ' l '. Its angular momentum in the fourth Bohr orbit is
Options:
A) 4 l
B) \frac{4}{3} l
C) \frac{5}{4} l
D) \frac{3}{2} l
446
Medium
The ratio of energies of photons produced due to transition of electron of hydrogen atom from its (a) second to first energy level and (b) highest energy level to second level is
Options:
A) 1: 3
B) 1: 2
C) 3: 1
D) 4: 1
447
Medium
If 'T' is the half life of a radioactive substance then its instantaneous rate of change of activity is proportional to
Options:
A) T
B) T^{-2}
C) T^{+2}
D) T^{-1}
448
Medium
Radius of first orbit in H -atom is ' a_0 ' Then, de-Broglie wavelength of electron in the third orbit is
Options:
A) 3 \pi \mathrm{a}_0
B) 6 \pi \mathrm{a}_0
C) 9 \pi \mathrm{a}_0
D) 12 \pi \mathrm{a}_0
449
Medium
In the Bohr model of hydrogen atom, the centripetal force is furnished by the coulomb attraction between the proton and the electron. If ' r_0 ' is the radius of the ground state orbit, ' m ' is the mass, ' e ' is the charge on the electron and ' \varepsilon_0 ' is the permittivity of vacuum, the speed of the electron is
Options:
A) zero
B) \frac{\mathrm{e}}{\sqrt{\varepsilon_0 \mathrm{r}_0 \mathrm{~m}}}
C) \frac{\mathrm{e}}{\sqrt{4 \pi \varepsilon_0 \mathrm{r}_0 \mathrm{~m}}}
D) \frac{\sqrt{4 \pi \varepsilon_0 \mathrm{r}_0 \mathrm{~m}}}{\mathrm{e}}
450
Medium
If the ionisation energy for the hydrogen atom is 13.6 eV , then the energy required to excite it from the ground state to the next higher state is nearly
Options:
A) 10.2 eV
B) 13.6 eV
C) -10.2 eV
D) -3.4 eV
451
Medium
Using Bohr's model, the orbital period of electron in hydrogen atom in \mathrm{n}^{\text {th }} orbit is ( \mathrm{m}= mass of electron, \mathrm{h}= Planck's constant, \mathrm{e}= electronic charge, \varepsilon_0= permittivity of free space)
Options:
A) \frac{2 \varepsilon_0^2 n^2 h^2}{m e^4}
B) \frac{4 \varepsilon_0^2 \mathrm{n}^2 \mathrm{~h}^2}{\mathrm{me}^2}
C) \frac{4 \varepsilon_0^2 \mathrm{n}^3 \mathrm{~h}^3}{\mathrm{me}^4}
D) \frac{4 \varepsilon_0 \mathrm{n}^2 \mathrm{~h}^2}{\pi \mathrm{me}^2}
452
Medium
The spectral series observed for hydrogen atom found in visible region is
Options:
A) Lyman
B) Balmer
C) Paschen
D) Brackett
453
Medium
In hydrogen atom, if \mathrm{V}_{\mathrm{n}} and \mathrm{V}_{\mathrm{p}} are orbital velocities in \mathrm{n}^{\text {th }} and \mathrm{p}^{\text {th }} orbit respectively, then the ratio \mathrm{V}_{\mathrm{p}}: \mathrm{V}_{\mathrm{n}} is
Options:
A) \mathrm{p}: \mathrm{n}
B) \mathrm{n}: \mathrm{p}
C) \mathrm{p}^2: \mathrm{n}^2
D) \mathrm{n}^2: \mathrm{p}^2
454
Medium
When a hydrogen atom is raised from the ground state to the excited state
Options:
A) potential energy increases and K.E. decreases.
B) potential energy decreases and K.E. increases.
C) both K.E. and potential energy will increase.
D) both K.E. and potential energy decreases.
455
Medium
In hydrogen atom, ratio of the shortest wavelength in the Balmer series to that in the Paschen series is
Options:
A) 9: 4
B) 3: 1
C) 4: 9
D) 1: 3
456
Medium
According to Bohr's theory of hydrogen atom, the ratio of the maximum and minimum wavelength of Lyman series will be
Options:
A) 3: 4
B) 4: 3
C) 2: 5
D) 5: 2
457
Medium
The ratio of minimum wavelengths of Lyman and Balmer series will be
Options:
A) 1.25
B) 0.25
C) 5
D) 10
458
Medium
Half-lives of two radioactive elements A and B are 30 minute and 60 minute respectively. Initially the samples have equal number of nuclei. After 120 minute the ratio of decayed numbers of nuclei of B to that of A will be
Options:
A) 1: 15
B) 1: 4
C) 4: 5
D) 5: 4
459
Medium
For hydrogen atom, ' \lambda_1 ' and ' \lambda_2 ' are the wavelengths corresponding to the transitions 1 and 2 respectively as shown in figure. The ratio of ' \lambda_1 ' and ' \lambda_2 ' is \frac{x}{32}. The value of ' x ' is
Options:
A) 3
B) 9
C) 27
D) 81
460
Medium
The ratio of the radius of the first Bohr orbit to that of the second Bohr orbit of the orbital electron is
Options:
A) 4: 1
B) 2: 1
C) 1: 4
D) 1: 2
461
Medium
A diatomic molecule has moment of inertia ' I ', By applying Bohr's quantization condition, its rotational energy in the \mathrm{n}^{\text {th }} level is [\mathrm{n} \geq 1] [h= Planck's constant]
Options:
A) \frac{1}{\mathrm{n}^2}\left(\frac{\mathrm{~h}^2}{8 \pi^2 \mathrm{I}}\right)
B) \frac{1}{\mathrm{n}}\left(\frac{\mathrm{h}^2}{8 \pi^2 \mathrm{I}}\right)
C) n\left(\frac{h^2}{8 \pi^2 \mathrm{I}}\right)
D) \mathrm{n}^2\left(\frac{\mathrm{~h}^2}{8 \pi^2 \mathrm{I}}\right)
462
Medium
In the uranium radioactive series, the initial nucleus is { }_{92}^{238} \mathrm{U} and that the final nucleus is { }_{82}^{206} \mathrm{~Pb}. When uranium nucleus decays into lead, the number of \alpha-particles and \beta-particles emitted are
Options:
A) 4 \alpha, 5 \beta
B) 5 \alpha, 3 \beta
C) 6 \alpha, 7 \beta
D) 8 \alpha, 6 \beta
463
Medium
If ' \lambda_1 ' and ' \lambda_2 ' are the wavelengths of the first line of the Lyman and Paschen series respectively, then \lambda_2: \lambda_1 is
Options:
A) 3: 1
B) 30: 1
C) 50: 7
D) 108: 7
464
Medium
An electron of stationary Hydrogen atom passes from fifth energy level to ground level. The velocity that the atom acquired as a result of photo emission is ( \mathrm{m}= mass of electron, \mathrm{R}= Rydberg's constant) ( \mathrm{h}= Planck's constant)
Options:
A) \frac{24 \mathrm{Rh}}{25 \mathrm{~m}}
B) \frac{25 \mathrm{Rh}}{24 \mathrm{~m}}
C) \frac{25 \mathrm{~m}}{24 \mathrm{Rh}}
D) \frac{24 \mathrm{~m}}{25 \mathrm{Rh}}
465
Medium
Which of the following statements about the Bohr model of the hydrogen atom is false?
Options:
A) Acceleration of electron in \mathrm{n}=2 orbit is less than that in n=1 orbit.
B) Angular momentum of electron in \mathrm{n}=2 orbit is more than that in n=1 orbit.
C) Kinetic energy of electron in \mathrm{n}=2 orbit is less than that in \mathrm{n}=1 orbit.
D) Potential energy of electron in \mathrm{n}=2 orbit is less than that in n=1 orbit.
466
Medium
The radius of innermost orbit of hydrogen atom is 5.3 \times 10^{-11} \mathrm{~m}. The radius of fourth allowed orbit of hydrogen atom is
Options:
A) 8.48 $\mathop A\limits^o
B) 2.12 $\mathop A\limits^o
C) 4.77 $\mathop A\limits^o
D) 0.53 $\mathop A\limits^o
467
Medium
In the third orbit of hydrogen atom the energy of an electron ' E '. In the fifth orbit of helium (Z=2) the energy of an electron will be
Options:
A) \frac{25 \mathrm{E}}{36}
B) \frac{36 \mathrm{E}}{25}
C) \frac{3 \mathrm{E}}{5}
D) \frac{5 \mathrm{E}}{3}
468
Medium
Ratio of longest wavelength corresponding to Lyman and Balmer series in hydrogen spectrum is
Options:
A) \frac{7}{29}
B) \frac{9}{31}
C) \frac{5}{27}
D) \frac{3}{23}
469
Medium
Half life of radio-active element is 1600 years. The fraction of sample remains undecayed after 6400 years will be
Options:
A) \frac{1}{16}
B) \frac{1}{4}
C) \frac{1}{8}
D) \frac{1}{24}
470
Medium
Frequency of the series limit of Balmer series of hydrogen atom in terms of Rydberg's constant (R) and velocity of light (c) is
Options:
A) 4 \mathrm{Rc}
B) \frac{4}{\mathrm{Rc}}
C) \mathrm{Rc}
D) \frac{\mathrm{Rc}}{4}
471
Medium
If the radius of the first Bohr orbit is '$r' then the de-Broglie wavelength of the electron in the 4^{\text {th }}$ orbit will be
Options:
A) 4 \pi \mathrm{r}
B) 6 \pi \mathrm{r}
C) 8 \pi \mathrm{r}
D) \frac{\pi r}{4}
472
Medium
Magnetic field at the centre of the hydrogen atom due to motion of electron in $\mathrm{n}^{\text {th }}$ orbit is proportional to
Options:
A) \mathrm{n}^4
B) \mathrm{n}^{-3}
C) n^3
D) \mathrm{n}^{-5}
473
Medium
An excited hydrogen atom emits a photon of wavelength $\lambda in returning to ground state. The quantum number n of the excited state is (R=$ Rydberg's constant)
Options:
A) \sqrt{\lambda R(\lambda R-1)}
B) \sqrt{\frac{\lambda R}{(\lambda R-1)}}
C) \sqrt{\frac{(\lambda R-1)}{\lambda R}}
D) \sqrt{\frac{1}{\lambda R(\lambda R-1)}}
474
Medium
When an electron is excited from its 4 th orbit to 5 th stationary orbit, the change in the angular momentum of electron is approximately. (Planck's constant $=h=6.63 \times 10^{-34} \mathrm{~J}-\mathrm{s}$ )
Options:
A) 2 \times 10^{-34} \mathrm{~J}-\mathrm{s}
B) 6.63 \times 10^{-34} \mathrm{~J}-\mathrm{s}
C) 1 \times 10^{-34} \mathrm{~J}-\mathrm{s}
D) 3.14 \times 10^{-34} \mathrm{~J}-\mathrm{s}
475
Medium
A radioactive sample has half-life of 5 years. The percentage of fraction decayed in 10 years will be
Options:
A) 25%
B) 50%
C) 75%
D) 100%
476
Medium
An isotope of the original nucleus can be formed in a radioactive decay, with the emission of following particles.
Options:
A) one $\alpha and one \beta
B) one $\alpha and two \beta
C) one $\alpha and four \beta
D) four $\alpha and one \beta
477
Medium
Two different radioactive elements with half lives '$\mathrm{T}_1' and '\mathrm{T}_2' have undecayed atoms '\mathrm{N}_1' and '\mathrm{N}_2$' respectively present at a given instant. The ratio of their activities at that instant is
Options:
A) \frac{\mathrm{N}_1 \mathrm{~T}_1}{\mathrm{~N}_2 \mathrm{~T}_2}
B) \frac{\mathrm{N}_2 \mathrm{~T}_2}{\mathrm{~N}_1 \mathrm{~T}_1}
C) \frac{\mathrm{N}_1 \mathrm{~T}_2}{\mathrm{~N}_2 \mathrm{~T}_1}
D) \frac{\mathrm{N}_1 \mathrm{~N}_2}{\mathrm{~T}_1 \mathrm{~T}_2}
478
Medium
In Balmer series, wavelength of the $2^{\text {nd }} line is '\lambda_1' and for Paschen series, wavelength of the 1^{\text {st }} line is '\lambda_2', then the ratio '\lambda_1' to '\lambda_2$' is
Options:
A) 5: 128
B) 5: 81
C) 7: 27
D) 9: 132
479
Medium
In Lyman series, series limit of wavelength is $\lambda_1. The wavelength of first line of Lyman series is \lambda_2 and in Balmer series, the series limit of wavelength is \lambda_3. Then the relation between \lambda_1, \lambda_2 and \lambda_3$ is
Options:
A) \lambda_1=\lambda_2+\lambda_3
B) \lambda_2=\lambda_1+\lambda_3
C) \frac{1}{\lambda_1}=\frac{1}{\lambda_2}-\frac{1}{\lambda_3}
D) \frac{1}{\lambda_1}-\frac{1}{\lambda_2}=\frac{1}{\lambda_3}
480
Medium
The wavelength of radiation emitted is '$\lambda_0' when an electron jumps from the second excited state to the first excited state of hydrogen atom. If the electron jumps from the third excited state to the second orbit of the hydrogen atom, the wavelength of the radiation emitted will be \frac{20}{x} \lambda_0. The value of x$ is
Options:
A) 3
B) 9
C) 13
D) 27
481
Medium
According to Bohr's theory of hydrogen atom, the total energy of the electron in the $\mathrm{n}^{\text {th }}$ stationary orbit is
Options:
A) directly proportional to $n
B) inversely proportional to $n
C) directly proportional to $\mathrm{n}^2
D) inversely proportional to $\mathrm{n}^2
482
Medium
Bohr model is applied to a particle of mass '$\mathrm{m}' and charge '\mathrm{q}' moving in a plane under the influence of a transverse magnetic field 'B'. The energy of the charged particle in the \mathrm{n}^{\text {th }} leve will be [\mathrm{h}= Planck's constant ]
Options:
A) \frac{n h q B}{4 \pi \mathrm{m}}
B) \frac{n h q B}{2 \pi m}
C) \frac{\text { nhqB }}{\pi \mathrm{m}}
D) \frac{2 \mathrm{nhqB}}{\pi \mathrm{m}}
483
Medium
The orbital magnetic moment associated with orbiting electron of charge '$e$' is
Options:
A) inversely proportional to angular momentum
B) directly proportional to mass of electron
C) directly proportional to angular momentum
D) inversely proportional to charge on electron
484
Medium
An electron in the hydrogen atom jumps from the first excited state to the ground state. What will be the percentage change in the speed of electron?
Options:
A) 25%
B) 50%
C) 75%
D) 100%
485
Medium
In a radioactive disintegration, the ratio of initial number of atoms to the number of atoms present at time $t=\frac{1}{2 \lambda} is [\lambda=$ decay constant]
Options:
A) \frac{1}{\mathrm{e}}
B) \sqrt{\mathrm{e}}
C) e
D) 2e
486
Medium
The ratio of the velocity of the electron in the first Bohr orbit to that in the second Bohr orbit of hydrogen atom is
Options:
A) 8: 1
B) 2: 1
C) 4: 1
D) 1: 4
487
Medium
The shortest wavelength in the Balmer series of hydrogen atom is equal to the shortest wavelength in the Brackett series of a hydrogen like atom of atomic number $\mathrm{z}. The value of \mathrm{z}$ is
Options:
A) 2
B) 3
C) 4
D) 6
488
Medium
The ratio of longest to shortest wavelength emitted in Paschen series of hydrogen atom is
Options:
A) \frac{144}{63}
B) \frac{25}{9}
C) \frac{9}{25}
D) \frac{63}{144}
489
Medium
The force acting on the electron in hydrogen atom (Bohr' theory) is related to the principle quantum number '$n$' as
Options:
A) \mathrm{n}^4
B) \mathrm{n}^{-4}
C) \mathrm{n}^2
D) \mathrm{n}^{-2}
490
Medium
The wavelength of light for the least energetic photons emitted in the Lyman series of the hydrogen spectrum is nearly [Take $\mathrm{hc}=1240 ~\mathrm{eV} - \mathrm{nm}, change in energy of the levels =10.2 ~\mathrm{eV}$ ]
Options:
A) 150 \mathrm{~nm}
B) 122 \mathrm{~nm}
C) 102 \mathrm{~nm}
D) 82 \mathrm{~nm}
491
Medium
The ratio of wavelengths for transition of electrons from $2^{\text {nd }} orbit to 1^{\text {st }} orbit of Helium \left(\mathrm{He}^{++}\right) and Lithium \left(\mathrm{Li}^{++1}\right) is (Atomic number of Helium =2, Atomic number of Lithium =3$ )
Options:
A) 9: 4
B) 9: 36
C) 4: 9
D) 2: 3
492
Medium
For an electron moving in the $\mathrm{n}^{\text {th }}$ Bohr orbit the deBroglie wavelength of an electron is
Options:
A) \mathrm{n} \pi \mathrm{r}
B) \frac{\pi r}{\mathrm{n}}
C) \frac{\mathrm{nr}}{2 \pi}
D) \frac{2 \pi r}{\mathrm{n}}
493
Medium
If an electron in a hydrogen atom jumps from an orbit of level $n=3 to orbit of level n=2$, then the emitted radiation frequency is (where R = Rydberg's constant, C = Velocity of light)
Options:
A) \frac{3 \mathrm{RC}}{27}
B) \frac{\mathrm{RC}}{25}
C) \frac{8 \mathrm{RC}}{9}
D) \frac{5 \mathrm{RC}}{36}
494
Medium
Using Bohr's model, the orbital period of electron in hydrogen atom in the $\mathrm{n}^{\text {th }} orbit is \left(\varepsilon_0=\right. permittivity of vacuum, \mathrm{h}= Planck's constant, \mathrm{m}= mass of electron, \mathrm{e}=$ electronic charge)
Options:
A) \frac{4 \varepsilon_0 \mathrm{nh}^3}{\mathrm{me}^2}
B) \frac{4 \varepsilon_0 \mathrm{n}^2 \mathrm{~h}^2}{\mathrm{me}^2}
C) \frac{4 \varepsilon_0^2 n^3 h^3}{m e^4}
D) \frac{4 \varepsilon_0^2 \mathrm{n}^2 \mathrm{~h}^3}{m \mathrm{e}^3}
495
Medium
The wave number of the last line of the Balmer series in hydrogen spectrum will be (Rydberg's constant $=10^7 \mathrm{~m}^{-1}$ )
Options:
A) 250 \mathrm{~m}^{-1}
B) 2.5 \times 10^6 \mathrm{~m}^{-1}
C) 0.25 \times 10^9 \mathrm{~m}^{-1}
D) 2.5 \times 10^5 \mathrm{~m}^{-1}
496
Medium
The half life of a radioactive substance is 30 minute. The time taken between 40% decay and 85% decay of the same radioactive substance is
Options:
A) 15 minute
B) 90 minute
C) 60 minute
D) 30 minute
497
Medium
The ratio of energies of photons produced due to transition of electron of hydrogen atom from its (i) second to first energy level and (ii) highest energy level to second energy level is
Options:
A) 6:1
B) 3: 1
C) 12: 1
D) 8: 1
498
Medium
An electron makes a transition from an excited state to the ground state of a hydrogen like atom. Out of the following statements which one is correct?
Options:
A) Kinetic energy, potential energy and total energy decreases
B) Kinetic energy and total energy decreased but potential energy increases
C) Kinetic energy increases but potential energy and total energy decreases
D) Kinetic energy decreases, potential energy increases but total energy remains the same.
499
Medium
The ratio of maximum to minimum wavelength in Balmer series of hydrogen atom is
Options:
A) 36 : 5
B) 3 : 4
C) 9 : 5
D) 5 : 9
500
Medium
Energy of electron in the second orbit of hydrogen atom is $\mathrm{E}. The energy of electron '\mathrm{E}_3' in the third orbit of helium (\mathrm{He})$ atom will be
Options:
A) \mathrm{E}_3=\frac{4 \mathrm{E}}{9}
B) \mathrm{E}_3=\frac{16 \mathrm{E}}{3}
C) \mathrm{E}_3=\frac{16 \mathrm{E}}{9}
D) \mathrm{E}_3=\frac{4 \mathrm{E}}{3}
501
Medium
The shortest wavelength for Lyman series is 912 $\mathop A\limits^o $. The longest wavelength in Paschen series is
Options:
A) 1216 $\mathop A\limits^o
B) 3646 $\mathop A\limits^o
C) 18760 $\mathop A\limits^o
D) 8208 $\mathop A\limits^o
502
Medium
In the Bohr model, an electron moves in a circular orbit around the nucleus. Considering an orbiting electron to be a circular current loop, the magnetic moment of the hydrogen atom, when the electron is in nth excited state, is (e = electronic charge, m$_e$ = mass of the electron, h = Planck's constant)
Options:
A)
\left(\frac{\mathrm{e}}{\mathrm{m}_{\mathrm{e}}}\right) \frac{\mathrm{nh}}{2 \pi}
B)
\mathrm{\left(\frac{e}{m_e}\right) \frac{n^2 h}{2 \pi}}
C)
\mathrm{\left(\frac{e}{2 m_e}\right) \frac{n^2 h}{2 \pi}}
D)
\left(\frac{\mathrm{e}}{2 \mathrm{~m}_{\mathrm{e}}}\right) \frac{\mathrm{nh}}{2 \pi}
503
Medium
The energy of an electron in the excited hydrogen atom is $-3.4 \mathrm{~eV}. Then according to Bohr's theory, the angular momentum of the electron in that excited state is (\mathrm{h}=$ Plank's constant)
Options:
A) \frac{2 \pi}{h}
B) \frac{\mathrm{nh}}{2 \pi}
C) \frac{\mathrm{h}}{\pi}
D) \frac{3 \mathrm{~h}}{2 \pi}
504
Medium
In $n^{\text {th }}$ Bohr orbit, the ratio of the kinetic energy of an electron to the total energy of it, is
Options:
A) 2: 1
B) 1:-1
C) +1: 1
D) -1: 2
505
Medium
If '$E' and 'L' denote the magnitude of total energy and angular momentum of revolving electron in \mathrm{n}^{\text {th }}$ Bohr orbit, then
Options:
A) \mathrm{E} \propto \mathrm{L}^{-1}
B) \mathrm{E} \propto \mathrm{L}
C) \mathrm{E} \propto \mathrm{L}^{-2}
D) \mathrm{E} \propto \mathrm{L}^2
506
Medium
Two radioactive materials $X_1 and X_2 have decay constants '5 \lambda' and '\lambda' respectively. Initially, they have the same number of nuclei. After time 't', the ratio of number of nuclei of X_1 to that of \mathrm{X}_2 is \frac{1}{\mathrm{e}}. Then \mathrm{t}$ is equal to
Options:
A) \frac{\lambda}{2}
B) \frac{\mathrm{e}}{\lambda}
C) \lambda
D) \frac{1}{4 \lambda}
507
Medium
A nucleus breaks into two nuclear parts, which have their velocity ratio $2: 1$. The ratio of their nuclear radii will be
Options:
A) \sqrt{2}
B) \frac{1}{2}
C) \frac{1}{2^{1 / 3}}
D) \frac{1}{\sqrt{2}}
508
Medium
Ratio centripetal acceleration for an electron revolving in 3rd and 5th Bohr orbit of hydrogen atom is
Options:
A) 425 : 18
B) 625 : 81
C) 125 : 27
D) 221 : 36
509
Medium
When an electron in hydrogen atom jumps from third excited state to the ground state, the de-Broglie wavelength associated with the electron becomes
Options:
A) \left(\frac{1}{2}\right)^{\text {th }}
B) \left(\frac{1}{4}\right)^{\text {th }}
C) \left(\frac{1}{8}\right)^{\text {th }}
D) \left(\frac{1}{6}\right)^{\text {th }}
510
Medium
'$\lambda_1' is the wavelength of series limit of Lyman series, '\lambda_2' is the wavelength of the first line line of Lyman series and '\lambda_3' is the series limit of the Balmer series. Then the relation between \lambda_1, \lambda_2 and \lambda_3$ is
Options:
A) \frac{1}{\lambda_1}-\frac{1}{\lambda_2}=\frac{1}{\lambda_3}
B) \frac{1}{\lambda_1}=\frac{1}{\lambda_2}-\frac{1}{\lambda_3}
C) \lambda_2=\lambda_1+\lambda_3
D) \lambda_1=\lambda_2+\lambda_3
511
Medium
A sample of radioactive element contains $8 \times 10^{16}$ active nuclei. The halt-life of the element is 15 days. The number of nuclei decayed after 60 days is
Options:
A) 7.5 \times 10^{16}
B) 2.0 \times 10^{16}
C) 0.5 \times 10^{16}
D) 4.0 \times 10^{16}
512
Medium
The P.E. 'U' of a moving particle of mass 'm' varies with 'x'-axis as shown in figure. The deBroglie wavelength or the particle in the regions $0 \leq x \leq 1 and x > 1 are \lambda_1 and \lambda_2 respectively. II the total energy of the particle is '\mathrm{nE}', then the ratio \lambda_1 / \lambda_2$ is
Options:
A) \sqrt{\frac{n^2}{n-1}}
B) \sqrt{\frac{n-1}{n}}
C) \sqrt{\frac{\mathrm{n}}{\mathrm{n}-1}}
D) \sqrt{\frac{\mathrm{n}(\mathrm{n}-1)}{\mathrm{n}}}
513
Medium
The gyromagnetic ratio of an electron in an hydrogen atom, according to Bohr model is
Options:
A) decreases with the quantum number 'n'.
B) independent of which orbit it is in.
C) negative
D) positive
514
Medium
The electron in hydrogen atom is initially in the third excited state. When it finally moves to ground state, the maximum number of spectral lines emitted are
Options:
A) 3
B) 4
C) 5
D) 6
515
Medium
If the electron in a hydrogen atom moves from ground state orbit to 5th orbit, then the potential energy of the electron
Options:
A) is increased
B) is zero
C) is decreased
D) remains unchanged
516
Medium
The energy levels with transitions for the atom are shown. The transitions corresponding to emission of radiation of maximum and minimum wavelength are respectively
Options:
A) B, C
B) A, C
C) C, D
D) A, D
517
Medium
Using Bohr's model, the orbital period of electron in hydrogen atom in nth orbit is ( \varepsilon_0= permittivity of free space, h= Planck's constant, m= mass of electron and \theta= electronic charge)
Options:
A) \frac{2 \varepsilon_0^2 n^3 h^3}{m e^4}
B) \frac{8 \varepsilon_0^2 n^3 h^3}{m e^4}
C) \frac{2 \varepsilon_0 n^2 h^2}{m e^4}
D) \frac{4 \varepsilon_0^2 n^3 h^3}{m e^4}
518
Medium
A radioactive nucleus emits $4 \alpha-particles and 7 \beta-particles in succession. The ratio of number of neutrons of that of protons, is [A= mass number, Z=$ atomic number]
Options:
A) \frac{A-Z-13}{Z-2}
B) \frac{A-Z-15}{Z-1}
C) \frac{A-Z-13}{Z-1}
D) \frac{A-Z-11}{Z-2}
519
Medium
The ratio of energies of photons produced due to transition of electron of hydrogen atom from its (i) second to first energy level and (ii) highest energy level to second level is respectively
Options:
A) 2.5: 1
B) 3: 1
C) 2: 1
D) 4: 1
520
Medium
Using Bohr's quantisation condition, what is the rotational energy in the second orbit for a diatomic molecule? ($I= moment of inertia of diatomic molecule and, h=$ Planck's constant)
Options:
A) \frac{h}{2 I \pi^2}
B) \frac{h^2}{2 I \pi^2}
C) \frac{h^2}{2 I^2 \pi^2}
D) \frac{h}{2 I^2 \pi}
521
Medium
The ratio of speed of an electron in the ground state in the Bohr's first orbit of hydrogen atom to velocity of light $(c) is ( h= Planck's constant, \varepsilon_0= permittivity of free space, e=$ charge on electron)
Options:
A) \frac{2 \theta^2 \varepsilon_0}{h c}
B) \frac{e^3}{2 \varepsilon_0 h c}
C) \frac{e^2}{2 \varepsilon_0 h c}
D) \frac{2 \varepsilon_0 h c}{e^2}
522
Medium
The force acting on the electrons in hydrogen atom (Bohr's theory) is related to the principle quantum number $n$ as
Options:
A) n^{-4}
B) n^4
C) n^{-2}
D) n^2
523
Medium
If the speed of an electron of hydrogen atom in the ground state is 2.2 \times 10^6 \mathrm{~m} / \mathrm{s}, then its speed in the third excited state will be
Options:
A) 5.5 \times 10^6 \mathrm{~m} / \mathrm{s}
B) 5.5 \times 10^5 \mathrm{~m} / \mathrm{s}
C) 8.8 \times 10^5 \mathrm{~m} / \mathrm{s}
D) 6.8 \times 10^6 \mathrm{~m} / \mathrm{s}
524
Medium
In hydrogen emission spectrum, for any series, the principal quantum number is n. Corresponding maximum wavelength \lambda is ( R= Rydberg's constant)
Options:
A) \frac{R(2 n+1)}{n^2(n+1)}
B) \frac{n^2(n+1)^2}{R(2 n+1)}
C) \frac{n^2(n+1)}{R(2 n+1)}
D) \frac{R(2 n+1)}{n^2(n+1)^2}
525
Medium
When the electron in hydrogen atom jumps from fourth Bohr orbit to second Bohr orbit, one gets the
Options:
A) second line of Balmer series
B) first line of Balmer series
C) first line of Pfund series
D) second line of Paschen series
526
Medium
In Balmer series, wavelength of first line is ' \lambda_1 ' and in Brackett series wavelength of first line is ' \lambda_2 ' then \frac{\lambda_1}{\lambda_2} is
Options:
A) 0.162
B) 0.124
C) 0.138
D) 0.188
527
Medium
Bohr model is applied to a particle of mass ' m ' and charge ' q ' is moving in a plane under the influence of a transverse magnetic field ' B '. The energy of the charged particle in the nth level will be ( h= Planck's constant)
Options:
A) 2 n h q B / \pi \mathrm{m}
B) n h q B / 2 \pi \mathrm{~m}
C) n h q B / 4 \pi \mathrm{~m}
D) n h q B / \pi \mathrm{m}
528
Medium
The angle made by orbital angular momentum of electron with the direction of the orbital magnetic moment is
Options:
A) 120^{\circ}
B) 60^{\circ}
C) 180^{\circ}
D) 90^{\circ}
529
Medium
The wavelength of the first line in Balmer series in the hydrogen spectrum is ' \lambda '. What is the wavelength of the second line in the same series?
Options:
A) \frac{20}{27} \lambda
B) \frac{3}{16} \lambda
C) \frac{5}{36} \lambda
D) \frac{3}{4} \lambda
530
Hard
A particle of mass m is moving around the origin with a constant force F pulling it towards the origin. If Bohr model is used to describe its motion, the radius of the n^{\text {th }} orbit and the particle's speed v in the orbit depend on n as
Options:
A) r \propto n^{2 / 3} ; v \propto n^{1 / 3}
B) r \propto n^{4 / 3} ; v \propto n^{-1 / 3}
C) r \propto n^{1 / 3} ; v \propto n^{1 / 3}
D) r \propto n^{1 / 3} ; v \propto n^{2 / 3}
531
Medium
The spectral series which corresponds to the electronic transition from the levels $n_2=5,6, \ldots to the level n_1=4$ is
Options:
A) Pfund series
B) Brackett series
C) Lyman series
D) Balmer series
532
Medium
Water is used as a coolant in a nuclear reactor because of its
Options:
A) high thermal expansion coefficient
B) high specific heat capacity
C) low density
D) low boiling point
533
Medium
Some energy levels of a molecule are shown in the figure with their wavelengths of transitions. Then :
Options:
A) \lambda_3>\lambda_2, \lambda_1=2 \lambda_2
B) \lambda_3>\lambda_2, \lambda_1=4 \lambda_2
C) \lambda_1>\lambda_2, \lambda_2=2 \lambda_3
D) \lambda_2>\lambda_1, \lambda_2=2 \lambda_3
534
Medium
Select the correct statements among the following : A. Slow neutrons can cause fission in ${ }_{92}^{235} \mathrm{U} than fast neutrons. B. \alpha-rays are Helium nuclei. C. \beta-rays are fast moving electrons or positrons. D. \gamma-rays are electromagnetic radiations of wavelengths larger than \mathrm{X}$-rays. Choose the most appropriate answer from the options given below :
Options:
A) A, B and C only
B) A, B and D only
C) A and B only
D) C and D only
535
Medium
Given below are two statements: Statement I: Atoms are electrically neutral as they contain equal number of positive and negative charges. Statement II: Atoms of each element are stable and emit their characteristic spectrum. In the light of the above statements, choose the most appropriate answer from the options given below.
Options:
A) Both Statement I and Statement II are correct
B) Both Statement I and Statement II are incorrect
C) Statement I is correct but Statement II is incorrect
D) Statement I is incorrect but Statement II is correct
536
Medium
Match List I with List II: List I(Spectral Lines of Hydrogen for transitions from) List II(Wavelengths (nm)) A. $n_2=3 \text { to } n_1=2 I. 410.2 B. n_2=4 \text { to } n_1=2 II. 434.1 C. n_2=5 \text { to } n_1=2 III. 656.3 D. n_2=6 \text { to } n_1=2$ IV. 486.1 Choose the correct answer from the options given below:
Options:
A) A-II, B-I, C-IV, D-III
B) A-III, B-IV, C-II, D-I
C) A-IV, B-III, C-I, D-II
D) A-I, B-II, C-III, D-IV
537
Medium
{ }_{82}^{290} X \xrightarrow{\alpha} Y \xrightarrow{e^{+}} Z \xrightarrow{\beta^{-}} P \xrightarrow{e^{-}} Q In the nuclear emission stated above, the mass number and atomic number of the product Q$ respectively, are
Options:
A) 280, 81
B) 286, 80
C) 288, 82
D) 286, 81
538
Medium
The ground state energy of hydrogen atom is $-13.6 ~\mathrm{eV}$. The energy needed to ionize hydrogen atom from its second excited state will be :
Options:
A) 13.6 ~\mathrm{eV}
B) 6.8 ~\mathrm{eV}
C) 1.51 ~\mathrm{eV}
D) 3.4 ~\mathrm{eV}
539
Medium
The wavelength of Lyman series of hydrogen atom appears in:
Options:
A) visible region
B) far infrared region
C) ultraviolet region
D) infrared region
540
Medium
The angular momentum of an electron moving in an orbit of hydrogen atom is $\mathrm{1.5\left(\frac{h}{\pi}\right)}$. The energy in the same orbit is nearly.
Options:
A) -1.5$ eV
B) -1.6$ eV
C) -1.3$ eV
D) -1.4$ eV
541
Medium
The half life of a radioactive substance is 20 minutes. In how much time, the activity of substance drops to $\left(\frac{1}{16}\right)^{\text {th }}$ of its initial value?
Options:
A) 40 minutes
B) 60 minutes
C) 80 minutes
D) 20 minutes
542
Medium
In hydrogen spectrum, the shortest wavelength in the Balmer series is $\lambda$. The shortest wavelength in the Bracket series is :
Options:
A) 4 \lambda
B) 9 \lambda
C) 16 \lambda
D) 2 \lambda
543
Medium
The radius of inner most orbit of hydrogen atom is $5.3 \times 10^{-11} \mathrm{~m}$. What is the radius of third allowed orbit of hydrogen atom?
Options:
A) 1.06 $\mathop A\limits^o
B) 1.59 $\mathop A\limits^o
C) 4.77 $\mathop A\limits^o
D) 0.53 $\mathop A\limits^o
544
Medium
Let R1 be the radius of the second stationary orbit and R2 be the radius of the fourth stationary orbit of an electron in Bohr's model. The ratio ${{{R_1}} \over {{R_2}}}$ is :
Options:
A) 4
B) 0.25
C) 0.5
D) 2
545
Medium
Given below are two statements Statement I : The law of radioactive decay states that the number of nuclei undergoing the decay per unit time is inversely proportional to the total number of nuclei in the sample. Statement II : The half of a radionuclide is the sum of the life time of all nuclei, divided by the initial concentration of the nuclei at time t = 0. In the light of the above statements, choose the most appropriate answer from the options given below :
Options:
A) Statement I is incorrect but statement II is correct
B) Both statement I and statement II are correct
C) Both statement I and statement II are incorrect
D) Statement I is correct but statement II is incorrect
546
Medium
At any instant, two elements X1 and X2 have same number of radioactive atoms. If the decay constant of X1 and X2 are 10 $\lambda and \lambda respectively, then the time when the ratio of their atoms becomes {1 \over e}$ respectively will be :
Options:
A) {1 \over {5\lambda }}
B) {1 \over {11\lambda }}
C) {1 \over {9\lambda }}
D) {1 \over {6\lambda }}
547
Medium
The ratio of Coulomb's electrostatic force to the gravitational force between an electron and a proton separated by some distance is 2.4 $\times 1039. The ratio of the proportionality constant, K = {1 \over {4\pi {\varepsilon _0}}} to the gravitational constant G is nearly (Given that the charge of the proton and electron each = 1.6 \times 10-19 C, the mass of the electron = 9.11 \times 10-31 kg, the mass of the proton = 1.67 \times 10-$27 kg) :
Options:
A) 10
B) 1020
C) 1030
D) 1040
548
Medium
The graph which shows the variation of the de Broglie wavelength ($\lambda$) of a particle and its associated momentum (p) is
Options:
A)
B)
C)
D)
549
Medium
In the given nuclear reaction, the element X is ${}_{11}^{22}Na \to X + {e^ + } + v
Options:
A) {}_{11}^{23}Na
B) {}_{10}^{23}Ne
C) {}_{10}^{22}Ne
D) {}_{12}^{22}Mg
550
Medium
Let T1 and T2 be the energy of an electron in the first and second excited states of hydrogen atoms, respectively. According to the Bohr's model of an atom, the ratio T1 : T2 is
Options:
A) 1 : 4
B) 4 : 1
C) 4 : 9
D) 9 : 4
551
Medium
A nucleus of mass number 189 splits into two nuclei having mass number 125 and 64. The ratio of radius of two daughter nuclei respectively is
Options:
A) 1 : 1
B) 4 : 5
C) 5 : 4
D) 25 : 16
552
Medium
A nucleus with mass number 240 breaks into two fragments each of mass number 120, the binding per nucleon of unfragmented nuclei is 7.6MeV while that of fragments is 8.5MeV. The total gain in the Binding Energy in the process is :
Options:
A) 216MeV
B) 0.9MeV
C) 9.4MeV
D) 804MeV
553
Medium
The half life of a radioactive nuclide is 100 hours. The fraction of original activity that will remain after 150 hours would be :
Options:
A) {2 \over {3\sqrt 2 }}
B) {1 \over 2}
C) {1 \over {2\sqrt 2 }}
D) {2 \over 3}
554
Medium
A radioactive nucleus $_Z^AX \to {}_{Z - 1}B \to {}_{Z - 3}C \to {}_{Z - 2}D$, where Z is the atomic number of element X. The possible decay particles in the sequence are :
Options:
A) \beta-, \alpha, \beta$+
B) \alpha, \beta-, \beta$+
C) \alpha, \beta+, \beta-
D) \beta+, \alpha, \beta-
555
Medium
When a uranium isotope $_{92}^{235}U is bombarded with a neutron, it generates _{36}^{89}Kr$ three neutrons and :
Options:
A) {}_{40}^{91}Zr
B) {}_{36}^{101}Kr
C) {}_{36}^{103}Kr
D) {}_{56}^{144}Ba
556
Medium
For which one of the following, Bohr model is not valid?
Options:
A) Singly ionised helium atom (He+)
B) Deuteron atom
C) Singly ionised neon atom (Ne+)
D) Hydrogen atom
557
Medium
The energy equivalent of 0.5 g of a substance is :
Options:
A) 4.5 \times {10^{13}}J
B) 1.5 \times {10^{13}}J
C) 0.5 \times {10^{13}}J
D) 4.5 \times {10^{16}}J
558
Medium
\alpha $-particale consists of :
Options:
A) 2 electrons, 2 protons and 2 neutrons
B) 2 electrons and 4 protons only
C) 2 protons only
D) 2 protons and 2 neutrons only
559
Medium
The total energy of an electron in an atom in an orbit is –3.4 eV. Its kinetic and potential energies are, respectively.
Options:
A) 3.4 eV, – 6.8 eV
B) 3.4 eV, 3.4 eV
C) – 3.4 eV, – 3.4 eV
D) – 3.4 eV, – 6.8 eV
560
Medium
The ratio of kinetic energy to the total energy of an electron in a Bohr orbit of the hydrogen atom, is
Options:
A) 1 : 1
B) 1 : -1
C) 2 : -1
D) 1 : -2
561
Medium
For a radioactive material, half-life is 10 minutes. If initially there are 600 number of nuclei, the time taken (in minutes) for the disintegration of 450 nuclei is
Options:
A) 20
B) 10
C) 30
D) 15
562
Medium
Radioactive material 'A' has decay constant '8 $\lambda ' and material 'B' has decay constant '\lambda $'. Initially they have same number of nuclei. After what time, the ratio of number of nuclei of material 'B' to that 'A' will be e ?
Options:
A) {1 \over {7\lambda }}
B) {1 \over {8\lambda }}
C) {1 \over {9\lambda }}
D) {1 \over {\lambda }}
563
Medium
The ratio of wavelengths of the last line of Balmer series and the last line of Lyman series is
Options:
A) 1
B) 4
C) 0.5
D) 2
564
Medium
The half-life of a radioactive substance is 30 minutes. The time (in minutes) taken between 40% decay and 85% decay of the same radioactive substance is
Options:
A) 15
B) 30
C) 45
D) 60
565
Medium
If an electron in a hydrogen atom jumps from the 3rd orbit to the 2nd orbit, it emits a photon of wavelength $\lambda $. When it jumps from the 4th orbit to the 3rd orbit, the corresponding wavelength of the photon will be
Options:
A) {{16} \over {25}}\lambda
B) {9 \over {16}}\lambda
C) {{20} \over 7}\lambda
D) {{20} \over {13}}\lambda
566
Medium
When an $\alpha $-particle of mass m moving with velocity v bombards on a heavy nucleus of charge Ze, its distance of closest approach from the nucleus depends on m as
Options:
A) {1 \over {{m^2}}}
B) m
C) {1 \over m}
D) {1 \over {\sqrt m }}
567
Medium
Given the value of Rydberg constant is 107 m$-$1, the wave number of the last line of the Balmer series in hydrogen spectrum will be
Options:
A) 0.25 $ \times 107 m-$1
B) 2.5 $ \times 107 m-$1
C) 0.025 $ \times 104 m-$1
D) 0.5 $ \times 107 m-$1
568
Medium
A nucleus of uranium decays at rest into nuclei of thorium and helium. Then
Options:
A) The helium nucleus has more momentum than the thorium nucleus.
B) The helium nucleus has less kinetic energy than the thorium nucleus.
C) The helium nucleus has more kinetic energy than the thorium nucleus.
D) The helium nucleus has less momentum than the thorium nucleus.
569
Medium
In the spectrum of hydrogen, the ratio of the longest wavelength in the Lyman series to the longest wavelength in the Balmer series is
Options:
A) {{27} \over 5}
B) {5 \over {27}}
C) {4 \over 9}
D) {9 \over 4}
570
Medium
Consider 3rd orbit of He+ (Helium), using non-relativistic approach, the speed of electron in this orbit will be [given K = 9 $ \times 109 constant, Z = 2 and h (Planck's Constant) = 6.6 \times 10-$34 J s]
Options:
A) 0.73 $ \times $ 106 m/s
B) 3.0 $ \times $ 108 m/s
C) 2.92 $ \times $ 106 m/s
D) 1.46 $ \times $ 106 m/s
571
Medium
If radius of the ${}_{13}^{27} Al nucleus is taken to be RAl, then the radius of {}_{53}^{125}$Te nucleus is nearly
Options:
A) {3 \over 5}{R_{Al}}
B) {\left( {{{13} \over {53}}} \right)^{1/3}}{R_{Al}}
C) {\left( {{{53} \over {13}}} \right)^{1/3}}{R_{Al}}
D) {5 \over 3}{R_{Al}}
572
Medium
Hydrogen atom in ground state is excited by a monochromatic radiation of $\lambda = 975 \mathop A\limits^ \circ $. Number of spectral lines in the resulting spectrum emitted will be
Options:
A) 3
B) 2
C) 6
D) 0 10
573
Medium
The binding energy per nucleon of and nuclei are 5.60 MeV and 7.06 MeV respectively. In the nuclear reaction ${}_3^7Li + {}_1^1H \to {}_2^4He + _2^4He + Q$ the value of energy Q released is
Options:
A) 19.6 MeV
B) -$ 2.4 MeV
C) 8.4 MeV
D) 17.3 MeV
574
Medium
A radioactive X with a half life 1.4 $ \times $ 109 years decays to Y which is stable. A sample of the rock from a cave was found to contain X and Y in the ratio 1 : 7. The age of the rock is
Options:
A) 1.96 $ \times $ 109 years
B) 3.92 $ \times $ 109 years
C) 4.20 $ \times $ 109 years
D) 8.40 $ \times $ 109 years
575
Medium
\alpha -particles, \beta -particles and \gamma $-rays are all having same energy. Their penetrating power in a given medium in increasing order will be
Options:
A) \gamma , \alpha , \beta
B) \alpha , \beta , \gamma
C) \beta , \alpha , \gamma
D) \beta , \gamma , \alpha
576
Medium
An electron in hydrogen atom makes a transition n1 $ \to $ n2 where n1 and n2 are principal quantum numbers of the two states . Assuming Bohr's model to be valid, the time period of the electron in the initial state is eight times that in the final state. The possible values of n1 and n2 are
Options:
A) n1 = 6 and n2 = 2
B) n1 = 8 and n2 = 1
C) n1 = 8 and n2 = 2
D) n1 = 4 and n2 = 2
577
Medium
How does the Binding Energy per nucleon vary with the increase in the number of nucleons ?
Options:
A) Decrease continuously with mass number.
B) First decreases and then increases with increase in mass number.
C) First increases and then decreases with increase in mass number.
D) increases continuously with mass number.
578
Medium
Ratio of longest wave lengths corresponding to Lyman and Balmer series in hydrogen spectrum is
Options:
A) {7 \over {29}}
B) {9 \over {31}}
C) {5 \over {27}}
D) {3 \over {23}}
579
Medium
A certain mass of Hydrogen is changed to Helium by the process of fusion. The mass defect in fusion reaction is 0.02866 u. The energy liberated per u is (given 1 u = 931 MeV)
Options:
A) 6.675 MeV
B) 13.35 MeV
C) 2.67 MeV
D) 26.7 MeV
580
Medium
The half life of a radioactive isotope 'X' is 20 years. It decays to another element 'Y' which is stable. The two elements 'X' and 'Y' were found to be in the ratio 1 : 7 in a sample of a given rock. The age of the rock is estimated to be
Options:
A) 80 years
B) 100 years
C) 40 years
D) 60 years
581
Medium
The transition from the state n = 3 to n = 1 in a hydrogen like atom results in ultraviolet radiation. Infrared radiation will be obtained in the transition from
Options:
A) 2 $ \to $ 1
B) 3 $ \to $ 2
C) 4 $ \to $ 2
D) 4 $ \to $ 3
582
Medium
The half life of a radioactive nucleus is 50 days. The time invertal (t2 $- t1) between the time t2 when {2 \over 3} of it has decayed and the time t1 when {1 \over 3}$ of it had decayed is
Options:
A) 30 days
B) 50 days
C) 60 days
D) 15 days
583
Medium
A mixture consists of two radioactive materials A1 and A2 with half lives of 20 s and 10 s respectively. Initially the mixture has 40 g of A1 and 160 g of A2. The amount of the two in the mixture will become equal after
Options:
A) 60 s
B) 80 s
C) 20 s
D) 40 s
584
Medium
An electron of a stationary hydrogen atom passes from the fifth energy level to the ground level. The velocity that the atom acquired as a result of photon emission will be
Options:
A) {{24hR} \over {25m}}
B) {{25hR} \over {24m}}
C) {{25m} \over {24hR}}
D) {{24m} \over {25hR}}
585
Medium
If the nuclear radius of 27Al is 3.6 fermi, the approximate nuclear radius of 64Cu in fermi is
Options:
A) 2.4
B) 1.2
C) 4.8
D) 3.6
586
Medium
Electron in hydrogen atom first jumps from third excited state to second excited state and then from second excited to the first excited state. The ratio of the wavelengths $\lambda 1 : \lambda $2 emitted in the two cases is
Options:
A) {7 \over 5}
B) {27 \over 20}
C) {27 \over 5}
D) {20 \over 7}
587
Medium
An electron in the hydrogen atom jumps from excited state n to the ground state. The wavelength so emitted illuminates a photosensitive material having work function 2.75 eV. If the stopping potential of the photoelectron is 10 V, then the value of n is
Options:
A) 2
B) 3
C) 4
D) 5
588
Medium
Two radioactive nuclei P and Q, in a given sample decay into a stable nucleus R. At time t = 0. number of P species are 4 N0 and that of Q are N0. Half -life of P (for conversion to R) is 1 minute where as that of Q is 2 minutes. Initially there are no nuclei of R present in the sample. When number of nuclei of P and Q are equal, the number of nuclei of R present in the sample would be
Options:
A) 2 N0
B) 3 N0
C) {{9{N_0}} \over 2}
D) {{5{N_0}} \over 2}
589
Medium
Out of the following which one is not a possible energy for a photon to be emitted by hydrogen atom according to Bohr's atomic model?
Options:
A) 0.65 eV
B) 1.9 eV
C) 11.1 eV
D) 13.6 eV
590
Medium
Fusion reaction takes place at high temperature because
Options:
A) nuclei break up at high temperature
B) atoms get ionised at high temperature
C) kinetic energy is high enough to overcome the coulomb repulsion between nuclei
D) molecules break up at high temperature
591
Medium
A nucleus ${}_n^mX emits one \alpha particle and two \beta $ particles. The resulting nucleus is
Options:
A) {}_{n - 4}^{m - 6}Z
B) {}_n^{m - 6}Z
C) {}_n^{m - 4}X
D) {}_{n - 2}^{m - 4}Y
592
Medium
A radioactive nucleus of mass M emits a photon of frequency $v$ and the nucleus recoils. The recoil energy will be
Options:
A) Mc2 $- hv
B) h2$\upsilon $2/2Mc2
C) zero
D) h$v
593
Medium
The power obtained in a reactor using U235 disintegration is 1000 kW. The mass decay of U235 per hour is
Options:
A) 10 microgram
B) 20 microgram
C) 40 microgram
D) 1 microgram
594
Medium
The half life of a radioactive isotope X is 50 years. It decays to another element Y which is stable. The two elements X and Y were found to be in the ratio of 1 : 15 in a sample of a given rock. The age of the rock was estimated to be
Options:
A) 150 years
B) 200 years
C) 250 years
D) 100 years
595
Medium
The wavelength of the first line of Lyman series for hydrogen atom is equal to that of the second line of Balmer series for a hydrogen like ion. The atomic number Z of hydrogen like ion is
Options:
A) 3
B) 4
C) 1
D) 2
596
Medium
The decay constant of a radio isotope is $\lambda . If A1 and A2 are its activities at times t1 and t2 respectively, the number of nuclei which have decayed during the time (t1 -$ t2)
Options:
A) A1t1 $-$ A2t2
B) A1 $-$ A2
C) (A1 $- A2)/\lambda
D) \lambda ({A_1} - {A_2})
597
Medium
The binding energy per nucleon in deuterium and helium nuclei are 1.1 MeV and 7.0 MeV, respectively. When two deuterium nuclei fuse to form a helium nucleus the energy released in the fusion is
Options:
A) 23.6 MeV
B) 2.2 MeV
C) 28.0 MeV
D) 30.2 MeV
598
Medium
The activity of a radioactive sample is measured as N0 counts per minute at t = 0 and N0/e counts per minute at t = 5 minutes. The time (in minutes) at which the activity reduces to half its value is
Options:
A) {\log _e}{2 \over 5}
B) {5 \over {{{\log }_e}2}}
C) 5log102
D) 5loge 2
599
Medium
The energy of a hydrogen atom in the ground state is $-$ 13.6 eV. The energy of a He+ ion in the first excited state will be
Options:
A) -$ 13.6 eV
B) -$ 27.2 eV
C) -$ 54.4 eV
D) -$ 6.8 eV
600
Medium
The mass of a ${}_3^7Li Li nucleus is 0.042 u less than the sum of the masses of all its nucleons. The binding energy per nucleon of {}_3^7Li$ nucleus is nearly
Options:
A) 46 MeV
B) 5.6 MeV
C) 3.9 MeV
D) 23 MeV
601
Medium
The energy of a hydrogen atom in the ground state is $-$ 13.6 eV. The energy of a He+ ion in the first excited state will be
Options:
A) -$ 13.6 eV
B) -$ 27.2 eV
C) -$ 54.4 eV
D) -$ 6.8 eV
602
Medium
An alpha nucleus of energy ${1 \over 2}$ mv2 bombards a heavy nuclear target of charge Ze. Then the distance of closest approach for the alpha nucleus will be proportional to
Options:
A) {1 \over {Ze}}
B) v2
C) {1 \over m}
D) {1 \over {{v_4}}}
603
Medium
The number of beta particles emitted by a radioactive substance is twice the number of alpha particles emitted by it. The resulting daughter is an
Options:
A) isomer of parent
B) isotone of parent
C) isotope of parent
D) isobar of parent
604
Medium
The ionization energy of the electron in the hydrogen atom in its ground state is 13.6 eV. The atoms are excited to higher energy levels to emit radiations of 6 wavelengths, Maximum wavelength of emitted radiation corresponds to the transition between
Options:
A) n = 3 to n = 1 states
B) n = 2 to n = 1 states
C) n = 4 to n = 3 states
D) n = 3 to n = 2 states
605
Medium
In a Rutherford scattering experiment when a projectile of charge z1 and mass M1 approaches a target nucleus of charge z2 and mass M2, the distance of closest approach is r0. The energy of the projectile is
Options:
A) directly proportional to z1z2
B) inversely proportional to z1
C) directly proportional to mass M1
D) directly proportional to M1 $ \times $ M2
606
Medium
In the nuclear decay given below ${}_Z^AX \to {}_{Z + 1}^AY \to {}_{Z - 1}^{A - 4}B{}^ * \to {}_{Z - 1}^{A - 4}B,$ the particles emitted in the sequence are
Options:
A) \gamma , \beta , \alpha
B) \beta , \gamma , \alpha
C) \alpha , \beta , \gamma
D) \beta , \alpha , \gamma
607
Medium
If M(A; Z), Mp and Mn denote the masses of the nucleus ${}_Z^AX,$ proton and neutron respectively in units of u (1 u = 931.5 MeV/c2) and BE represents its bonding energy in MeV, then
Options:
A) M(A, Z) = ZMp + (A $- Z)Mn -$ BE
B) M(A, Z) = ZMp + (A $-$ Z)Mn + BE/c2
C) M(A, Z) = ZMp + (A $- Z)Mn -$ BE/c2
D) M(A, Z) = ZMp + (A $-$ Z)Mn + BE
608
Medium
Two radioactive materials X1 and X2 have decay constants $5\lambda and \lambda $ respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of X1 to that X2 will be 1/e after a time
Options:
A) 1/4$\lambda
B) e/$\lambda
C) \lambda
D) {1 \over 2}\lambda
609
Medium
The ground state energy of hydrogen atom is $-$ 13.6 eV. When its electron is in the first excited state, its excitation energy is
Options:
A) 10.2 eV
B) 0
C) 3.4 eV
D) 6.8 eV
610
Medium
Two nuclei have their mass numbers in the ratio of 1 : 3. The ratio of their nuclear densities would be
Options:
A) {\left( 3 \right)^{1/3}}:1
B) 1 : 1
C) 1 : 3
D) 3 : 1
611
Medium
The total energy of electron in the ground state of hydrogen atom is $-$ 13.6 eV. The kinetic energy of an electron in the first excited state is
Options:
A) 6.8 eV
B) 13.6 eV
C) 1.7 eV
D) 3.4 eV.
612
Medium
If the nucleus ${}_{13}^{27}Al has a nuclear radius of about 3.6 fm, them {}_{32}^{125}Te$ would have its radius approximately as
Options:
A) 9.6 fm
B) 12.0 fm
C) 4.8 fm
D) 6.0 fm
613
Medium
A nucleus ${}_Z^AX$ has mass represented by M(A, Z). If Mp and Mn denote the mass of proton and neutron respectively and B.E. the binding energy in MeV, then
Options:
A) B.E. = [ZMp + (A $- Z)Mn -$ M(A, Z)]c2
B) B.E. = [ZMp + AMp $-$ M(A, Z)]c2
C) B.E. = M(A, Z) $- ZMp - (A -$ Z)Mn
D) B.E. = [M(A, Z) $- ZMp - (A -$ Z)Mn]c2
614
Medium
In a mass spectrometer used for measuring the masses of ions, the ions are initially accelerated by an electric potential $V and then made to describe semicircular paths of radius R using a magnetic field B. If V and B are kept constant, the ratio \left( {{{ch\arg e\,\,on\,\,\,the\,\,ion\,\,} \over {mass\,\,of\,\,the\,\,ion}}} \right)$ will be proportional to
Options:
A) 1/R2
B) R2
C) R
D) 1/R
615
Medium
In a radioactive decay process, the negatively charged emitted $\beta $-particles are
Options:
A) the electrons produced as a result of the decay of neutrons inside the nucleus
B) the electrons produced as a result of collisions between atoms
C) the electrons orbitting around the nucleus
D) the electrons present inside the nucleus
616
Medium
Two radioactive substances A and B have decay constants 5$\lambda and \lambda $ respectively. At t = 0 they have the same number of nuclei. The ratio of number of nuclei of A to those of B will be (1/e)2 after a time interval
Options:
A) 4\lambda
B) 2\lambda
C) 1/$2\lambda
D) 1/$4\lambda
617
Medium
The radius of germanium (Ge) nuclide is measured to be twice the radius of ${}_4^9$Be. The number of nucleons in Ge are
Options:
A) 72
B) 73
C) 74
D) 75
618
Medium
Ionization potential of hydrogen atom is 13.6 eV. Hydrogen atoms in the ground state are excited by monochromatic radiation of photon energy 12.1 eV. According to Bohr's theory, the spectral lines emited by hydrogen will be
Options:
A) one
B) two
C) three
D) four
619
Medium
In a radioactive material the activity at time t1 is R1 and at a later time t2, it is R2. If the decay constant of the material is $\lambda $, then
Options:
A) R1 = R2
B) R1 = R2e$-\lambda (t1-$t2)
C) R1 = R2e$\lambda (t1-$t2)
D) R1 = R2(t2/t1).
620
Medium
The binding energy of deuteron is 2.2 MeV and that of ${}_2^4He is 28 MeV. If two deuterons are fused to form one {}_2^4$He then the energy released is
Options:
A) 30.2 MeV
B) 25.8 MeV
C) 23.6 MeV
D) 19.2 MeV
621
Medium
Energy levels A, B and C of a certain atom corresponding to increasing values of energy i.e. EA < EB < EC. If $\lambda 1, \lambda 2 and \lambda $3 are wavelengths of radioations corresponding to transitions C to B, B to A and C to A respectively, which of the following relations is correct?
Options:
A) {\lambda _3} = {\lambda _1} + {\lambda _2}
B) {\lambda _3} = {{{\lambda _1}{\lambda _2}} \over {{\lambda _1} + {\lambda _2}}}
C) {\lambda _1} + {\lambda _2} + {\lambda _3} = 0
D) {\lambda _3}^2 = {\lambda _1}^2 + {\lambda _2}^2
622
Medium
Fission of nuclei is possible because the binding energy per nucleon in them
Options:
A) increases with mass number at low mass numbers
B) decreases with mass number at low mass numbers
C) increases with mass number at high mass numbers
D) decreases with mass number at high mass numbers.
623
Medium
In any fission process the ratio mass of fission products mass of parent nucleus is
Options:
A) equal to 1
B) greater than 1
C) less than 1
D) depends on the mass of the parent nucleus.
624
Medium
Which one of the following pairs of nuclei are isotones ?
Options:
A) 34Se74, 31Ga71
B) 38Sr84, 38Sr86
C) 42Mo92, 40Zr92
D) 20Ca40, 16S32
625
Medium
The total energy of an electron in the first excited state of hydrogen atom is about $-$ 3.4 eV. Its kinetic energy in this state is
Options:
A) 3.4 eV
B) 6.8 eV
C) -$ 3.4 eV
D) -$ 6.8 eV
626
Medium
In the reaction ${}_1^2H + {}_1^3H \to {}_2^4He + {}_0^1n, if the binding energies of {}_1^2 H, {}_1^3H and {}_2^4$He are respectively a, b and c (in MeV), then the energy (in MeV) released in this reaction is
Options:
A) a + b + c
B) a + b $-$ c
C) c $- a -$ b
D) c + a $-$ b
627
Medium
The half life of radian is about 1600 years. Of 100 g of radium existing now, 25 g will remain unchanged after
Options:
A) 4800 years
B) 6400 years
C) 2400 years
D) 3200 years
628
Medium
The Bohr model of atoms
Options:
A) Assumes that the angular momentum of electrons is quantized.
B) Uses Einstein's photoelectric equation.
C) Predicts continuous emission spectra fror atoms.
D) Predicts the same emission spectra for all types of atoms.
629
Medium
If in a nuclear fusion process the masses of the fusing nuclei be m1 and m2 and the mass of the resultant nucleus be m3, then
Options:
A) m3 = m1 + m2
B) m3 = $\left| {{m_1} - {m_2}} \right|
C) m3 < (m1 + m2)
D) m3 > (m1 + m2)
630
Medium
A nucleus represented by the symbol ${}_Z^AX$ has
Options:
A) Z neutrons and A $-$ Z protons
B) Z protons and A $-$ Z neutrons
C) Z protons and A neutrons
D) A protons and Z $-$ A neutrons
631
Medium
If M(A; Z), Mp and Mn denote the masses of the nucleus ${}_Z^AX,$ proton and neutron respectively in units of u (1 u = 931.5 MeV/c2) and BE represents its bonding energy in MeV, then
Options:
A) M(A, Z) = ZMp + (A $- Z)Mn -$ BE
B) M(A, Z) = ZMp + (A $-$ Z)Mn + BE/c2
C) M(A, Z) = ZMp + (A $- Z)Mn -$ BE/c2
D) M(A, Z) = ZMp + (A $-$ Z)Mn + BE
632
Medium
The mass number of a nucleus is
Options:
A) always less than its atomic number
B) always more than its atomic number
C) sometimes equal to its atomic number
D) sometimes less than and sometimes more than its atomic number
633
Medium
The mass of proton is 1.0073 u and that of neutron is 1.0087 u (u = atomic mass unit). The binding energy of ${}_2^4 He is (Given helium nucleus mass \approx $ 4.0015 u.)
Options:
A) 0.0305 J
B) 0.0305 erg
C) 28.4 MeV
D) 0.061 u
634
Medium
A sample of radioactive element has a mass of 10 g at an instant t = 0. The approximate mass of this element in the sample after two mean lives is
Options:
A) 1.35 g
B) 2.50 g
C) 3.70 g
D) 6.30 g
635
Medium
The volume occupied by an atom is greater than the volume of the nucleus by a factor of about
Options:
A) 101
B) 105
C) 1010
D) 1015
636
Medium
Solar energy is mainly caused due to
Options:
A) burning of hydrogen in the oxygen
B) fission of uranium present in the Sun
C) fusion of protons during synthesis of heavier elements
D) gravitational contraction
637
Medium
An electron is moving round the nucleus of a hydrogen atom in a circular orbit of radius r. The Coulomb force $\overrightarrow F $ between the two is
Options:
A) K{{{e^2}} \over {{r^2}}}\widehat r
B) - K{{{e^2}} \over {{r^3}}}\widehat r
C) K{{{e^2}} \over {{r^3}}}\widehat r
D) - K{{{e^2}} \over {{r^2}}}\widehat r
638
Medium
A nuclear reaction given by ZXA $ \to z+1YA + -1e0 + \overline v $ represents
Options:
A) \beta $-decay
B) \gamma $-decay
C) fusion
D) fission
639
Medium
In which of the following systems will the radius of the first orbit (n = 1) be minimum ?
Options:
A) doubly ionized lithium
B) singly ionized helium
C) deuterium atom
D) hydrogen atom
640
Medium
A deutron is bombarded on 8O16 nucleus then $\alpha $-particle is emitted. The product nucleus is
Options:
A) 7N13
B) 5B10
C) 4Be9
D) 7N14
641
Medium
A sample of radioactive element containing 4 $ \times $ 1016 active nuclei. Half life of element is 10 days, then number of decayed nuclei after 30 days
Options:
A) 0.5 $ \times $ 1016
B) 2 $ \times $ 1016
C) 3.5 $ \times $ 1016
D) 1 $ \times $ 1016
642
Medium
Which of the following are suitable for the fusion process ?
Options:
A) light nuclei
B) heavy nuclei
C) element lying in the middle of the periodic table
D) middle elements, which are lying on binding energy curve.
643
Medium
Energy released in nuclear fission is due to
Options:
A) some mass is converted into energy
B) total binding energy of fragments is more than the binding energy of parantal element
C) total binding energy of fragments is less than the binding energy of parental element
D) total binding energy of fragments is equal to the binding energy of parental element.
644
Medium
Mn and Mp represent the mass of neutron and proton respectively. An element having mass M has N neutrons and Z protons, then the correct relation will be
Options:
A) M < {N $ \cdot Mn + Z \cdot $ Mp}
B) M > {N $ \cdot Mn + Z \cdot $ Mp}
C) M = {N $ \cdot Mn + Z \cdot $ Mp}
D) M = N {Mn + Mp}
645
Medium
The interplanar distance in a crystal is 2.8 $ \times 10-$8 m. The value of maximum wavelength which can be diffracted
Options:
A) 2.8 $ \times 10-$8 m
B) 5.6 $ \times 10-$8 m
C) 1.4 $ \times 10-$8 m
D) 7.6 $ \times 10-$8 m
646
Medium
Half life of a radioactive element is 12.5 hour and its quantity is 256 g. After how much time its quantity will remain 1 g?
Options:
A) 50 hrs
B) 100 hrs
C) 150 hrs
D) 200 hrs
647
Medium
X(n, $\alpha ) {}_3^7$Li, then X will be
Options:
A) {}_5^{10}$ B
B) {}_5^9$ B
C) {}_5^{11}$ Be
D) {}_2^4$ He.
648
Medium
Which rays contain (positive) charged particles ?
Options:
A) \alpha $-rays
B) \beta $-rays
C) \gamma $-rays
D) X-rays
649
Medium
The energy of hydrogen atom in nth orbit is En then the energy in nth orbit of singly ionised helium atom will be
Options:
A) 4En
B) En/4
C) 2En
D) En/2
650
Medium
Maximum frequency of emission is obtained for the transition
Options:
A) n = 2 to n = 1
B) n = 6 to n = 2
C) n = 1 to n = 2
D) n = 2 to n = 6.
651
Medium
The life span of atomic hydrogen is
Options:
A) fraction of one second
B) one year
C) one hour
D) one day
652
Medium
The relation between $\lambda and T1/2 as (T1/2 \to $ half life)
Options:
A) T1/2 = ${{\ln 2} \over \lambda }
B) T1/2 ln2 = $\lambda
C) T1/2 = ${1 \over \lambda }
D) ($\lambda $ + T1/2) = ln2
653
Medium
When an electron does transition from n = 4 to n = 2, then emitted line spectrum will be
Options:
A) first line of Lyman series
B) second line of Balmer series
C) first line of Balmer series
D) second line of Paschen series.
654
Medium
Nuclear fission is best explained by
Options:
A) liquid droplet theory
B) Yukawa $\pi $-meson theory
C) independent particle model of the nucleus
D) proton-proton cycle.
655
Medium
For the given reaction, the particle X is $_6{C^{11}} \to {}_5{B^{11}} + {\beta ^ + } + X
Options:
A) neutron
B) anti neutrino
C) neutrino
D) proton
656
Medium
The ratio of minimum wavelengths of Balmer and Paschen series of hydrogen atom will be
Options:
A) 1: 4
B) 4: 9
C) 9: 4
D) 4: 1
657
Medium
The activity of a radioactive sample is measured as No counts per minute at $t=0 and \mathrm{N}_0 / \mathrm{e} counts per minute at t=6 \mathrm{~min}$. The time (in minutes) at which the activity reduces to half its value is.
Options:
A) \left(\log _e 2\right) / 6
B) 6 / \log _e 2
C) 6 \log _0 2
D) 6 \log _e 2
658
Medium
The wavelength of $k_\alpha-line characteristic X-rays emitted by an element is 0.32 \mathop A\limits^o. The wavelength of the k_\beta$-line emitted by the same element will be
Options:
A) 0.32 $\mathop A\limits^o
B) 0.39 $\mathop A\limits^o
C) 0.49 $\mathop A\limits^o
D) 0.27 $\mathop A\limits^o
659
Medium
A radioactive element $X convents into another stable element Y. Half-life of X is 2 hrs. Initially only X is present. After time t, the ratio of atoms of X and Y is found to be 1: 4, then t$ in hours is
Options:
A) 2
B) 4
C) between 4 and 6
D) 6
660
Medium
A nuclide at rest emits an \alpha-particle. In this process
Options:
A) \alpha$-particle moves with large velocity and the nucleus remains at rest.
B) Both $\alpha$-particle and nucleus move with equal speed in opposite directions.
C) Both move in opposite directions except $\alpha$-particle with greater speed.
D) Both move in opposite direction with greater velocity of $\alpha$-particle.
661
Medium
The half-life period of a radioactive element $x is same as the mean life time of another radioactive element y$. Initially, both of them have the same number of atoms. Then,
Options:
A) x and y$ have the same decay rate initially
B) x and y$ decay at the same rate always
C) y will decay at a faster rate than x
D) x will decay at a faster rate than y
662
Medium
Polonium has a half-life of 140 days. If we take $20 \mathrm{~g}$ of polonium initially then the amount of it that remains after 280 days is
Options:
A) 2.5 g
B) 5 g
C) 10 g
D) 15 g
663
Medium
According to Bohr model of hydrogen atom, only those orbits are permissible which satisfy the condition
Options:
A) m v=n h
B) \frac{m v^2}{r}=n\left(\frac{h}{2 \pi}\right)
C) m v r=n\left(\frac{h}{2 \pi}\right)
D) m v r^2=n\left(\frac{h}{2 \pi}\right)
664
Medium
The Rutherford scattering experiment proves that an atom consists of
Options:
A) a sphere of positive charge in which electrons are embedded like seeds of water-melon
B) a sphere of negative charge in which protons are embedded like seeds of water-melon
C) a sphere of electron cloud in which the positive charge in placed at the centre of the sphere
D) a sphere of neutral charge
664
Total Questions
126
Easy
529
Medium
9
Hard
Study Tips
Before You Start
- • Review the chapter concepts thoroughly
- • Keep a notebook for important formulas
- • Practice similar problems from your textbook
- • Time yourself to improve speed
After Practice
- • Review all incorrect answers carefully
- • Watch video solutions for difficult questions
- • Make notes of common mistakes
- • Practice similar questions again later