Question

A proton, a deuteron and an $\alpha$ - particle having the same kinetic energy are moving in circular trajectories in a constant magnetic field. If $r_{p^{\prime}} r_{d}$ and $r_{\alpha}$ denote respectively the radii of the trajectories of these particles, then

• A. $r_{\alpha} = r_{p} < r_{d}$
• B. $r_{\alpha}>r_{d}>r_{p}$
• C. $r_{\alpha}=r_{d}>r_{p}$
• D. $r_{p}=r_{d}=r_{\alpha}$

Answer 1

Answer: (A)

$r=\frac{m v}{q B}=\frac{\sqrt{2 m K}}{q B} \propto \frac{\sqrt{m}}{q}$