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NCERT Class XII Chapter
Nuclei
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Question : 14 of 31
Marks: +1, -0
The nucleus 1023Ne^{23}_{10}\mathrm{Ne} decays by β\beta^{-} emission. Write down the β\beta^{-} decay equation and determine the maximum kinetic energy of the electrons emitted. Given that:
m (1023Ne)(^{23}_{10}\mathrm{Ne}) = 22.994466 amu, m (1123Na)(^{23}_{11}\mathrm{Na}) = 22.989770 amu
Solution:  
The β\beta^{-} decay of 1023Ne^{23}_{10}\mathrm{Ne} may be explained as
1023Ne^{23}_{10}\mathrm{Ne}1123Na+10e+νˉ+Q^{23}_{11}\mathrm{Na} + ^{0}_{-1}\mathrm{e} + \bar{\nu} + Q
The expression or the kinetic energy released may be written as
Q = [m(1023Ne)m(1123Na)me]c2\left[ m(^{23}_{10}\mathrm{Ne}) - m(^{23}_{11}\mathrm{Na}) - m_e \right] c^2 = [m(1023Ne)m(1123Na)]c2\left[ m(^{23}_{10}\mathrm{Ne}) - m(^{23}_{11}\mathrm{Na}) \right] c^2
≈ [22.994466 – 22.989770] × 931.5 MeV
≈ 0.004696 × 931.5 MeV = 4.374 MeV
As 1123Na^{23}_{11}\mathrm{Na} is massive, the kinetic energy released is mainly shared by electron-positron pair. When the neutrino carries no energy, the electron has a maximum kinetic energy equal to 4.374 MeV.
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