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 nth excited state, is :

Options

A. `((e )/( 2m)(n^2 h )/( 2p i))`
B. `((e )/(m ))(nh)/(2pi)`
C. `((e )/(2m ))(Rh )/(2 pi )`
D. `((e )/(m ))(n^2 h )/( 2 pi)`

Answer

C

Explanation

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 ( pi r_(n ) ^(2))`
` I _n = eV_n = ( mz ^2 e^5 )/( 4 epsi_(0)^(2) n^3 h^3 ) , r _n = (n^2 h^2 )/( 4 pi ^2 Kz me^2 ) (k = (1)) /( 4 pi in_0)`
solving we get magnetic moment of the hydrogen atom for ` n^(th)` excited state
` M_n = ((e )/(2m )) (nh )/( 2 pi)`