Q 12-13-012JEE MainAIEEE 2010Medium
A nucleus of mass $M + \Delta m$ is at rest and decays into two daughter nuclei of equal mass $\dfrac{M}{2}$ each. The speed of light is $c$. The binding energy per nucleon for the parent nucleus is $E_1$ and that for the daughter nuclei is $E_2$. Then
Answer: (C) $E_2 > E_1$
The decay happens spontaneously and releases energy $\Delta m\,c^2$, so the products are more tightly bound: the binding energy per nucleon increases, $E_2 > E_1$. (The nucleon number is unchanged, so $E_2 = 2E_1$ is not implied.)
Solution by Sreeraj P, M.Sc Physics