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JEE Main 2021 (20 Jul, Shift 1) · Nuclear Reactions & Q-value

Nuclear Reactions & Q-value question from JEE Main 2021 (20 Jul, Shift 1)

Q14JEE Main 2021 · 20 JUL · SHIFT 1Medium

Nuclear Reactions & Q-value

A nucleus of mass M emits $\gamma$ -ray photon of frequency 'v'. The loss of internal energy by the nucleus is:

[Take 'c' as the speed of electromagnetic wave]

Show answer and solution

Answer: (b)

Internal energy lost $=$ photon energy $+$ recoil kinetic energy of the nucleus.
Recoil: $p = \dfrac{h\nu}{c}$ , $K = \dfrac{p^2}{2M} = \dfrac{h^2\nu^2}{2Mc^2}$
Loss $= h\nu + \dfrac{h^2\nu^2}{2Mc^2} = h\nu\left[1 + \dfrac{h\nu}{2Mc^2}\right]$
So the answer is (b).

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