Question 172: Dual Nature of Matter and Radiation

Question

The recoil speed of a hydrogen atom after it emits a photon in going from n = 5 state to n = 1 state will be :

Accepted Answer

($$\Delta$$E) Releases when photon going from n = 5 to n = 1
$$\Delta$$E = (13.6 $$-$$ 0.54) eV = 13.06 eV.
P
i
= P
f
(By linear momentum conservation)
$$0 = {h \over \lambda } - Mv = {V_{{\mathop{m Re}
olimits} coil}} = {h \over {\lambda M}}$$ ..... (i)
& $$\Delta E = {{hc} \over \lambda } = {{hc} \over {\lambda M}} 	imes M = Mc{V_{{\mathop{m Re}
olimits} coil}}$$
$${V_{{\mathop{m Re}
olimits} coil}} = {{\Delta E} \over {Mc}} = {{13.06 	imes 1.6 	imes {{10}^{ - 19}}} \over {1.67 	imes {{10}^{ - 27}} 	imes 3 	imes {{10}^8}}}$$ = 4.17 m/sec

Answer

4.34 m/s

Answer

2.19 m/s

Answer

3.25 m/s

Answer

4.17 m/s

Dual Nature of Matter and Radiation

The recoil speed of a hydrogen atom after it emits a photon in going from n = 5 state to n = 1 state will be :

Choose the correct answer: