Magnetic moment due to the motion of the electron in nth energy state of hydrogen atom is proportional to …....

Options

A. `n^(-2)`
B. n
C. `n^(2)`
D. `n^(3)`

Answer

B

Explanation

Magnetic moment of a moving electron, which shown in the figure below,

Current, `i=e/T = (eomega)/(2pi) (because omega = (2pi)/T)`
As, magnetic moment,
`M= iA = (eomega)/(2pi) pi R ^(2)`
`rArr M = (ev)/(2R) R ^(2)" " (because omega = v/R)`
`rArr M=(evR)/2 = (eL)/(2m)`
where, `L = mvr and L = (nh)/(2pi)`
So, `M= (enh)/(2pim) rArr M propn`
`because e, h, m` are constant of electron,
Hence, the correct option is (b).