Question

A nucleus of mass $M+\Delta m$ is at rest and decays into two daughter nuclei of equal mass of $\frac{M}{2}$ each. The speed of light is c,Then speed of daughter nuclei is?

• A. $c\frac{\Delta m}{M+\Delta m}$
• B. $c\sqrt{\frac{2\Delta m}{M}}$
• C. $c\sqrt{\frac{\Delta m}{M}}$
• D. $c\sqrt{\frac{\Delta m}{M+\Delta m}}$

Answer 1

The correct option is B $c\sqrt{\frac{2\Delta m}{M}}$

Conserving the momentum:
$0=\frac{M}{2}{V}_1-\frac{M}{2}{V}_2$

$V_1=V_2$ .........(1)

$\Delta m{c}^2=\frac{1}{2}.\frac{M}{2}{V}_1^2+\frac{1}{2}.\frac{M}{2}.V_2^2$ ........(2)

$\Delta m{c}^2=\frac{M}{2}{V}_1^2$

$\frac{2\Delta m{c}^2}{M}=V_1^2$

$V_1=c\sqrt{\frac{2\Delta m}{M}}$