Question

A nucleus of mass $M+△m$ 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 $c\sqrt{\frac{2△m}{M}}$

• A. True
• B. False

Answer 1

The correct option is A True

True. Total momentum and energy need to be conserved for a nuclear reaction.

Earlier the parent nucleus was at rest,

So,

Since the masses of the daughter nuclei are the same, the will move with the same speed (v, say) in mutually opposite directions.

Now, Kinetic energy = change in rest energy

$\Rightarrow \frac{1}{2}\left(\frac{M}{2}\right)\times v^2\times 2=\left(\right(M+△m)-\frac{M}{2}\times 2)\times c^2$
$\Rightarrow \frac{1}{2}M{v}^2=△m{c}^2\Rightarrow v=\sqrt{\frac{2△m}{M}}c$