MHT CET202519 Apr 2025Evening ShiftPhysicsAtomic PhysicsActual
Bohr model is applied to a particle of mass m and charge q is moving in a plane under the influence of a transverse magnetic field (B). The energy of the charged particle in the second level will be ( h = Planck's constant )
Options
- AqBh m
- Bq ^2 ~B ^2 ~h ^2 4 ~m
- CqBh 2 ~m
- D2 qBh m
Correct answer
C. qBh 2 ~m
Step-by-step solution
Energy quantization for charged particles in magnetic fields arises from combining Bohr’s angular momentum quantization with magnetic force dynamics. Angular momentum is quantized as L = mvr = n h 2 . The magnetic force provides centripetal acceleration: qvB = mv^2 r , yielding v = qBr m . Substituting into the quantization condition gives m ( qBr m ) r = n h 2 , which simplifies to r^2 = nh 2 qB . The kinetic energy is E = 1 2 mv^2 = q^2B^2r^2 2m . Substituting r^2 yields E = q^2B^2 2m nh 2 qB = qBnh 4 m . For the