In the Bohr atom model the electrons move around the nucleus in circular orbits. Obtain an expression the magnetic moment `(mu)` of the electron in a Hydrogen atom in terms of its angular momentum L.

Explanation

Consider an electron of charge e, moves with constant speed v in a circular orbit of radius 'r' in Hydrogen atom as shown in fig.
The current constitute by revolving electron in circular motion around a nucleus, `I = (e)/(T)`.
Time period of orbiting electron , `T = (2pi r)/(v) rArr I = (e)/((2pi r)/(v)) = (ev)/(2pi r)` orbital magnetic moment, `mu = IA = I(pi r^(2))`
`rArr mu = (ev)/(2pi r)(pi r^(2)) = (evr)/(2)`
`mu = (e)/(2m)(m v r)` [`because` Multiplying and dividing with 'm' on right side]
`:. mu = (e)/(2m)` L where L = mvr = angular momentum.