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. `n((hqB)/(2pim))`
B. `n((hqB)/(4pim))`
C. `n((hqB)/(8pim))`
D. `n((hqB)/(pim))`

Answer

B

Explanation

Particle of mass m and charge q moving in a magnetic field B with velocity v and having radius r.
`(mv^2)/r =qvB`
Bohr model, `mvr=(nh)/(2pi)`….(i)
`(mv)/(qB)=r`….(ii)
Put the equation (i) in equation (ii)
`(m^2v^2)/(qB)=(nh)/(2pi)`
`mv^2=(nh qB)/(2pim)`
`1/2mv^2=n((hqB)/(4pim))`
K.E.=`n((hqB)/(4pim))`
Energy of charged particle in the `n^(th)` level .