Question

Proton, deuteron and alpha particle of the same kinetic energy are moving in circular field. The radii of proton, deuteron and alpha particle are respectively $r_p$, $r_d$ and $r_{\alpha }$. Which one of the following relations is correct?

• A. $r_{\alpha }=r_p=r_d$
• B. $r_{\alpha }=r_p<r_d$
• C. $r_{\alpha }>r_d>r_p$
• D. $r_{\alpha }=r_d<r_d$

Answer 1

The correct option is B $r_{\alpha }=r_p<r_d$

We know that for proton, deuteron and alpha particle, mass ratio is 1:2:4 and charge ratio is 1:1:2.

$r=\frac{\sqrt{2mk}}{Bq}$
which implies that $r\propto \frac{\sqrt{m}}{q}$

This results in : $r_{\alpha }=r_p<r_d$