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 speed of daughter nuclei is

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

Answer 1

Answer: (C)

The decrease in mass $\Delta m$ will appear as the kinetic energy of the two daughter nuclei. Since the two nuclei formed are of equal masses, they will share the available energy equally among themselves. If $v$ is the speed of a daughter nucleus, then $\frac{1}{2}\left(\frac{M}{2}\right)v^{2}=\frac{1}{2}\Delta mc^{2}$
or $v= \, c\sqrt{\frac{2 \Delta m}{M}}$