If one were to apply Bohr model to a particle of mass `'m'` and charge `'q'` moving in a plane under the influence of a mgentic filed `'B'`, the energy of the cahrged particle in the `n^(th)` level will be :-

Options

A. 2nhq B/`pi` m
B. nhq B/`2pi` m
C. nhq B/`4pi` m
D. nhq B/`pi` m

Answer

C

Explanation

For a particle moving in a magnetic field, then applied two forces are equal.
centripetal force `(F_(c))` = magnetic force `(F_(m))`
`rArr(mv^(2))/r=qvB`
`rArrmv^(2)=qB(vr)` ….(i)
Also, from Bohr's model,
`mvr=(nh)/(2pi)`
`thereforevr=(nh)/(2pim)` ....(ii)
From Eq. (i) and (ii), we get
`mv^(2)=(nh)/(2pim)dotqB` ....(iii) Energy of the electron moving in nth orbit,
`E=1/2dotmv^(2)=1/2dot(nhqB)/(2pim)` (using Eq. (iii)
`rArrE=(nhqB)/(4pim)`
Hence, the energy of the charged particle in the nth level will be `(nhqB)/(4pim)`