In the Bohr model an electron moves in a circular orbit around the proton. Considering the orbiting electron to be a circular current loop, the magnetic moment of the hydrogen atom, when the electron is in n^ th excited state, is :

Step-by-step solution

Magnetic moment of the hydrogen atom, when the electron is in n ^ th excited state, i.e., n^ =(n+1) As magnetic moment M _ n = I _ n A = i _ n ( r _ n ^2 ) aligned & i_n=e V_n= m z^2 e^5 4 ₀^2 n^3 h^3 & r_n= n^2 h^2 4 ^2 k z m e^2 (k= 1 4 ₀ ) aligned Solving we get magnetic moment of the hydrogen atom for n ^ th excited state M_ n^ = ( e 2 m ) n h 2