Beta Decay — Question 1

Question 1

Beta transformations conserve charge and lepton number

A nucleus ${}^{32}_{15}X$ undergoes beta-minus decay. In a separate process, a nucleus ${}^{22}_{11}Y$ undergoes beta-plus decay. Assign electron lepton number +1 to electrons and electron neutrinos, and -1 to their antiparticles.

1. Write both nuclear decay equations with the correct neutrino species.

2. Check electric charge and electron lepton number in each process.

Question 1 - Solution

Beta transformations conserve charge and lepton number

(a) Method and calculation

$$\boxed{{}^{32}_{15}X\to{}^{32}_{16}D+e^-+\bar\nu_e}.$$$$\boxed{{}^{22}_{11}Y\to{}^{22}_{10}F+e^++\nu_e}.$$

(b) Interpretation and further calculation

$$\beta^-:\quad\boxed{15=16-1,\quad0=(+1)+(-1)}.$$$$\beta^+:\quad\boxed{11=10+1,\quad0=(-1)+(+1)}.$$

Physical check

The mass number stays fixed because a nucleon changes type. The neutrino or antineutrino is necessary for lepton-number, energy and momentum accounting.