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

A

Explanation

`Bqv=(mv^(2))/r` & `mvr=(nh)/(2pi)`
`PE= -MB=1 AxxB=qxxfxxpi r^(2)B`
`TE=KE+PE=(Bqvr)/2+(qxxomega pi r^(2)B)/(2pi)`
`=(Bqvr)/(2)+(qV)/(2r) r^(2) B=Bqvr=Bqxx(nh)/(2pi m)`