A uniform magnetic field `B` exists in a region. An electrons projected perpendicular to the field goes in a circle. Assuming Bohr's quantization rule for angular momentum, calculate
(a) the smallest possible radius of the electrons
(b) the radius of the nth orbit and
(c) the minimum possible speed of the electron.

Explanation

(a) To move in circle, necessary centripetal force is provided by magnetic force.
`(mv^(2))/(r )=Bev`
`v=(ber)/(m)`
`mvr=(nh)/(2pi)`
`m(Ber)/(m)r=(nh)/(2pi)`
`r^(2)=(nh)/(2pieB)`
(b) `v=(Be)/(r ) r`
`v_(n)=(Be)/(m)r_(n)=(Be)/(m)sqrt((nh)/(2pieB))`
`=sqrt((heB)/(2pim^(2))`