13.22 For the $β^{+}$ (positron) emission from a nucleus, there is another competing process known as electron capture (electron from an inner orbit, say, the K–shell, is captured by the nucleus and a neutrino is emitted).

$e^{+}$ + ${}_{Z}^{A}X$ $\to {}_{z - 1}^{A}{Y + v}$

Show that if $β^{+ +}$ emission is energetically allowed, electron capture is necessarily allowed but not vice–versa.

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13.22 Let the amount on energy released during the electron capture process be $Q_{1}$ . The nuclear reaction can be written as:

$e^{+}$ + ${}_{Z}^{A}X$ $\to {}_{z - 1}^{A}{Y + v} + Q_{1}$ ……………………..(1)

Let the amount of energy released during the positron capture process be $Q_{2}$ . The nuclear reaction can be written as:

${}_{Z}^{A}X$ $\to {}_{z - 1}^{A}{Y + e^{+} + v}$ + $Q_{2}$ …………………….(2)

Let us assume

$m_{N} ({}_{Z}^{A}X)$ = Nuclear mass

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Physics Ncert Solutions Class 12th 2023

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