For hydrogen-like systems find the magnetic moment ttn corresponding to the motion of an electron along the n-th orbit

Question

For hydrogen-like systems find the magnetic moment μ_n corresponding to the motion of an electron along the n-th orbit and the ratio of the magnetic and mechanical moments μ_n/M_n. Calculate the magnetic moment of an electron occupying the first Bohr orbit.

Answer 1

An electron moving in a circle with a time period T constitutes a current 

I = e/T

and forms a current loop of area πr²  .This is equivalent to magnetic moment,

(In CGS unit μ₁ = μ_B = 9.27 X 10^-21 erg/gauss)