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

Question

An electron , a proton and an alpha particle having the same kinetic energy are moving in circular orbits of radii re, rp, rα respectively in a uniform magnetic field B. The relation between re, rp, rα is : (A) re > rp = rα (B) re < rp = rα (C) re < rp < rα (D) re < rα < rp

Tardigrade Admin · Accepted Answer

r=(√2 m k/q B) (rα/rp)=(√2 mα/qα) × (qp/√2 mp) [mα=4 mp qα=2 qp] =1 Mass of electron is least and charge qe=e So, re< rp=rα

Q. An electron , a proton and an alpha particle having the same kinetic energy are moving in circular orbits of radii $r_{e}, r_{p}, r_{α}$ respectively in a uniform magnetic field $B$ . The relation between $r_{e}, r_{p}, r_{α}$ is :

$r_{e} > r_{p} = r_{α}$

$r_{e} < r_{p} = r_{α}$

$r_{e} < r_{p} < r_{α}$

$r_{e} < r_{α} < r_{p}$

$r = \frac{2 mk}{qB}$
$\frac{r _{α}}{r _{p}} = \frac{2 m _{α}}{q _{α}} \times \frac{q _{p}}{2 m _{p}}$
$[m_{α} = 4 m_{p} q_{α} = 2 q_{p}]$
$= 1$
Mass of electron is least and charge $q_{e} = e$
So, $r_{e} < r_{p} = r_{α}$

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

re​>rp​=rα​

re​<rp​=rα​

re​<rp​<rα​

re​<rα​<rp​