13.22 For the (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).
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Show that if emission is energetically allowed, electron capture is necessarily allowed but not vice–versa.
13.22 For the (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).
+
Show that if emission is energetically allowed, electron capture is necessarily allowed but not vice–versa.
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1 Answer
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13.22 Let the amount on energy released during the electron capture process be . The nuclear reaction can be written as:
+ …………………….(1)
Let the amount of energy released during the positron capture process be . The nuclear reaction can be written as:
+ …………………….(2)
Let us assume
= Nuclear mass of
= Atomic mass of
= Nuclear mass of
= Atomic mass of
= mass of the electron
c = speed of light
Q-value of the electron capture reaction is given as:
= [= [
= [ …&hel
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Q = [4 *4.0026 – 15.9994] *931.5 MeV
Q = 10.2 MeV
-(1)
for B,
for B,
-(2)
The reaction is X²? → Y¹²? + Z¹²?
Binding energies per nucleon are: X=7.6 MeV, Y=8.5 MeV, Z=8.5 MeV.
Gain in binding energy (Q) = (Binding energy of products) - (Binding energy of reactants)
Q = (120 × 8.5 + 120 × 8.5) - (240 × 7.6) MeV
Q = (2 × 120 × 8.5) - (240 × 7.6) MeV = 2040 - 1824 = 216 MeV.
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