MHT CET Medical202622 April 2026Morning ShiftPhysicsAtomic PhysicsActual
In the Bohr model, an electron moves in circular orbit around the proton. Considering an orbiting elecrton to be a circular current loop, the magnetic moment of the hydrogen atom, when the electron is in n ^ th state, is
Options
- A( e m ) n^2 h 2
- B( e 2m ) nh 2
- C( e 2m ) n^2 h
- D( e m ) nh 2
Correct answer
B. ( e 2m ) nh 2
Step-by-step solution
The magnetic moment M of a circular current loop is given by M = IA . The current I due to the orbiting electron is I = e T = ev 2 r . The area of the circular loop is A = r^2 . Substituting I and A into the formula for magnetic moment: M = ( ev 2 r )( r^2) = evr 2 Multiplying and dividing by the mass of the electron m : M = e 2m (mvr) = e 2m L According to Bohr's quantization rule, the angular momentum L of the electron in the n^ th state is L = nh 2 . Substituting L into the expression for M : M = ( e 2m ) nh 2 A