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

Question

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

Tardigrade Admin · Accepted Answer

Radius of the circular path is given by

r = \frac{m v}{Bq} = \frac{2 K m}{Bq}

Here,

K

is the kinetic energy to the particle.
Therefore,

r \propto \frac{m}{q}

if

K

and

5

are same.

∴ r_{p} : r_{d} : r_{α} = \frac{1}{1} : \frac{2}{1} : \frac{4}{2} = 1 : 2 : 1

Hence,

f_{α} = r_{p} < r_{d}

Q. 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 $r_{α}$ denote respectively the radii of the trajectories of these particles, then

$r_{α} = r_{p} < r_{d}$

$r_{α} > r_{p} < r_{d}$

$r_{α} = r_{p} > r_{d}$

$r_{p} = r_{d} = r_{α}$

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

rα​=rp​<rd​

rα​>rp​<rd​

rα​=rp​>rd​

rp​=rd​=rα​

Radius of the circular path is given by r=Bqmv​=Bq2Km​​ Here, K is the kinetic energy to the particle. Therefore, r∝qm​​ if K and 5 are same. ∴rp​:rd​:rα​=11​​:12​​:24​​=1:2​:1 Hence, fα​=rp​<rd​

Q. 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 $r_{α}$ denote respectively the radii of the trajectories of these particles, then

$r_{α} = r_{p} < r_{d}$

$r_{α} > r_{p} < r_{d}$

$r_{α} = r_{p} > r_{d}$

$r_{p} = r_{d} = r_{α}$