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 $r_p,r_d$ and $r_{\alpha }$ denote respectively the radii of the trajectories of these particles, then

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

Given that $K_p=K_d=K_{\alpha }=K$(Say)
We know that $m_p=m,m_d=2m$ and $m_{\alpha }=4m$ and $q_p=e,q_d=e$ and $q_{\alpha }=2e$
Further $r=\frac{\sqrt{2mK}}{qB}\Rightarrow r_p=\frac{\sqrt{2mK}}{eB},r_d=\frac{\sqrt{2\left(2m\right)K}}{eB}=\sqrt{2}{r}_p$
and $r_{\alpha }=\frac{\sqrt{2\left(4m\right)K}}{\left(2e\right)B}=r_p.$ Hence $r_{\alpha }=r_p<r_d$