Question 537: Atoms & Nuclei

Question

$$
{ }_{82}^{290} X \xrightarrow{\alpha} Y \xrightarrow{e^{+}} Z \xrightarrow{\beta^{-}} P \xrightarrow{e^{-}} Q
$$
In the nuclear emission stated above, the mass number and atomic number of the product $$Q$$ respectively, are

Accepted Answer

To determine the mass number and atomic number of the final product $$Q$$ in the provided nuclear reactions, we need to analyze the impact of each type of decay (alpha, positron emission, beta-minus decay, and electron capture) on the mass number and atomic number of the initial element $$X = { }_{82}^{290} X$$:
1. Alpha decay ($$\alpha$$ decay): In alpha decay, an alpha particle (which is a $$^4_2He$$ nucleus) is emitted. This reduces the mass number by 4 units and the atomic number by 2 units.
$$
{ }_{82}^{290} X \xrightarrow{\alpha} { }_{80}^{286} Y
$$
2. Beta plus decay (positron emission, $$e^{+}$$): During positron emission, a proton in the nucleus is transformed into a neutron, and a positron is emitted. This decreases the atomic number by 1 but does not change the mass number.
$$
{ }_{80}^{286} Y \xrightarrow{e^{+}} { }_{79}^{286} Z
$$
3. Beta-minus decay ($$\beta^{-}$$ decay): In a beta-minus decay, a neutron in the nucleus converts into a proton and an electron (beta particle) and an antineutrino are emitted. This results in an increase in the atomic number by 1, while the mass number remains unchanged.
$$
{ }_{79}^{286} Z \xrightarrow{\beta^{-}} { }_{80}^{286} P
$$
4. Electron capture ($$e^{-}$$ capture): During electron capture, an atomic electron is absorbed by the nucleus, causing a proton to convert into a neutron. This process decreases the atomic number by 1 without altering the mass number.
$$
{ }_{80}^{286} P \xrightarrow{e^{-}} { }_{79}^{286} Q
$$
From the calculations above, the mass number of $$Q$$ is 286, and its atomic number is 79. Comparing these values with the multiple choices:
Option A: Mass number = 280, Atomic number = 81
Option B: Mass number = 286, Atomic number = 80
Option C: Mass number = 288, Atomic number = 82
Option D: Mass number = 286, Atomic number = 81
None of these match exactly, implying an error in the problem or the answer options. Based on the correct atomic number calculations and assuming option D is meant to be atomic number 79, then the corrected choice would have been:
D: Mass number = 286, Atomic number = 79

Answer

280, 81

Answer

286, 80

Answer

288, 82

Answer

286, 81

Atoms & Nuclei

{ }_{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

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