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NCERT Class XII Chapter
Nuclei
Questions With Solutions

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Question : 22
Total: 31
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++
A
‌
Z
X →
A
‌
Z−1
Y+v
Show that if β+ emission is energetically allowed, electron capture is necessarily allowed but not vice-versa.
Solution:  
Let us first consider positron emission.
A
‌
Z
X →
A
‌
Z−1
Y+e+ + v + Q1
The Q value is
Q1 = [m(
A
‌
Z
X)−m(
A
‌
Z−1
Y)−me]c2 ... (i)
Let us now consider electron capture
e−+
A
‌
Z
X →
A
‌
Z−1
Y + v + Q2
The Q value
Q2 = [m(
A
‌
Z
X)+me−m(
A
‌
Z−1
Y)]c2
So , Q2 > Q1
This mean if Q1 > 0 then Q2 > 0 but vice versa is not necessarily allowed.
So, electron capture is not necessary for positron emission.
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