Question

A proton, a deuteron and alpha particle having the same kinetic energy are moving in circular trajectories in a constant magnetic field. $r_p, r_d $ and $r_{\alpha}$ denote respectively the radii of the trajectories of these particles, then

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

Answer 1

Answer: (A)

Radius of the circular path is given by
$r=\frac{mv}{Bq}=\frac{\sqrt{2Km}}{Bq}$
Here, $K$ is the kinetic energy to the particle.
Therefore, $r \propto \frac{\sqrt{m}}{q}$ if $K$ and $5$ are same.
$\therefore r_p : r_d : r_{\alpha}=\frac{\sqrt{1}}{1} : \frac{\sqrt{2}}{1} : \frac{\sqrt{4}}{2}= 1 : \sqrt{2} : 1$
Hence, $f_{\alpha}=r_p < r_d$