Discussion Forum



1)

An electron, a proton and an alpha particle having the same kinetic energy are moving in circular orbits of radii re,rp,rα is repectively, in a unifrom magnetic field B. The relation between re,rp, rα is>>


A) $r_{e}\gt r_{p}= r_{\alpha}$

B) $r_{e}\lt r_{p}= r_{\alpha}$

C) $r_{e}\lt r_{p}\lt r_{\alpha}$

D) $r_{e}\lt r_{\alpha}\lt r_{p}$

Answer:

Option B

Explanation:

From  $Bqv=\frac{mv^{2}}{r},$ we have

    $r=\frac{mv}{Bq}=\frac{\sqrt{2mK}}{Bq}$

     where,K is the kinetic energy

 As,  kinetic energies of particles are same ;

  $r\propto \frac{\sqrt{m}}{q}$

=   $r_{e}:r_{p}:r_{\alpha}=\frac{\sqrt{m}_{e}}{e}:\frac{\sqrt{m_{p}}}{e}:\frac{\sqrt{4m_{p}}}{2e}$

 Clearly,  $r_{p}=r_{\alpha} $ and $r_{e}$ , is least [ $\because m _{e}<m_{p}$ ]

  So,    $r_{p} =r_{\alpha}>r_{e}$