Question

A nucleus of mass $M+\Delta m$ is at rest and decays into two daughter nuclei of equal mass $\frac{M}{2}$ each. 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 :

• A. $E_2>2E_1$
• B. $E_1>E_2$
• C. $E_2>E_1$
• D. $E_1=2E_2$

Answer 1

The correct option is B $E_1>E_2$

$\begin{array}{c}\text{let}x\to 2y\\ \text{mass}\to M+\Delta m2\times \frac{M}{2}=M\\ \Delta m\text{mass is lost as energy}\\ \Rightarrow \text{energy is released}\\ \Rightarrow \text{energy of}x>\text{energy of y}\\ E_1>E_2\\ \text{option}B\end{array}$