PYQ NEET- Atoms And Nuclei L-8

Question: When an $\alpha$-particle of mass $m$ moving with velocity $\mathrm{v}$ bombards on a heavy nucleus of charge Ze, its distance of closest approach from the nucleus depends on $m$ as#

A) $\frac{1}{m^2}$

B) $\mathrm{m}$

C) $\frac{1}{m}$

D) $\frac{1}{\sqrt{m}}$

Answer: (C) $\frac{1}{m}$#

Sol:#

At closest distance of approach, the kinetic energy of the particle will convert completely into electrostatic potential energy.

Kinetic energy $=\frac{1}{2} m v^2$

Potential energy $=\frac{K Q q}{r}$

$\therefore \frac{1}{2} m v^2=\frac{K Q q}{r}$

$\Rightarrow r \propto \frac{1}{m}$