Alpha Decay — Question 1

Question 1

Alpha emission changes both charge and nucleon number

A hypothetical parent ${}^{220}_{86}X$ emits an alpha particle and leaves daughter Y. The daughter later emits one beta-minus particle; neglect any delayed nucleon emission.

1. Write the alpha-decay equation and find the neutron numbers before and after it.

2. Find A, Z and neutron number of the nucleus after the subsequent beta-minus decay.

Question 1 - Solution

Alpha emission changes both charge and nucleon number

(a) Method and calculation

$$\boxed{{}^{220}_{86}X\to{}^{216}_{84}Y+{}^4_2\mathrm{He}}.$$$$\boxed{N_X=220-86=134,\quad N_Y=216-84=132}.$$

(b) Interpretation and further calculation

$$\beta^-:\ n\to p+e^-+\bar\nu_e\Rightarrow\boxed{A=216,\quad Z=85}.$$$$\boxed{N=216-85=131}.$$

Physical check

Alpha emission removes two protons and two neutrons. Beta-minus emission converts one neutron into one proton while preserving nucleon number.