A proton, a deuteron and an α - particle having the same kinetic energy are moving in circular trajectories in a constant magnetic field. If rp prime rd and rα denote respectively the radii of the trajectories of these particles, then

Question

A proton, a deuteron and an α - particle having the same kinetic energy are moving in circular trajectories in a constant magnetic field. If rp prime rd and rα denote respectively the radii of the trajectories of these particles, then (A) rα = rp < rd (B) rα>rd>rp (C) rα=rd>rp (D) rp=rd=rα

Tardigrade Admin · Accepted Answer

r=(m v/q B)=(√2 m K/q B) propto (√m/q)

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

$r_{α} = r_{p} < r_{d}$

$r_{α} > r_{d} > r_{p}$

$r_{α} = r_{d} > r_{p}$

$r_{p} = r_{d} = r_{α}$

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

Q. A proton, a deuteron and an α - particle having the same kinetic energy are moving in circular trajectories in a constant magnetic field. If rp′​rd​ and rα​ denote respectively the radii of the trajectories of these particles, then

rα​=rp​<rd​

rα​>rd​>rp​

rα​=rd​>rp​

rp​=rd​=rα​