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Question

In the beta decay of Na24, the combined electron neutrino momentum has a magnitude equal to 4 Mevc. What is the recoil energy of the daughter nucleus, given that its mass is 23.99u ?
Take [c=3×108 m/s,1u=1.66×1027 kg]

A
2.78×104 MeV
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B
3.56×104 MeV
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C
0.72×104 MeV
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D
1.25×104 MeV
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Solution

The correct option is B 3.56×104 MeV
Here, momentum of the electron and neutrino pair is
p=4 MeVc=4×1.6×10133×108
p=2.13×1021 kgms
Also mass of the daughter nucleus is
m=23.99u=23.99×1.66×1027 kg


As parent nucleus decays at rest, so according to conservation of linear momentum, the momentum of daughter nucleus and momentum of electron neutrino pair must be same
If P momentum of daughter nucleus then,
P=p
Now recoil energy Er is
Er = P22m=p22m
(2.13×1021)22×23.99×1.66×1027 J
2.13×2.13×10152×23.99×1.66××1.66×1013 MeV

E=3.56×104 MeV

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