Question

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 magnetic field 'b', the energy of the charged particle in the nth level will be

Answer 1

Hello dear,

● Answer-
E = nhqB/4πm

● Explanation-
For a particle moving in magnetic field-
Centripetal force = Magnetic force
mv^2/r = qvB
mv2 = qvBr ...(1)

Also for Bohr's model,
mvr = nh/2π
vr = nh/2πm ...(2)

Putting (2) in eqn.(1),
mv^2 = qB(nh/2πm)

Energy of particle moving in nth orbit is-
E = mv^2/2
E = qB(nh/2πm)/2
E = nhqB/4πm

Energy of particle moving in nth orbit is is nhqB/4πm .

Hope this is useful...