The ratio of angular momentum L to the atomic dipole moment μ i for hydrogen like atoms and ions is

Step-by-step solution

The electron moving with a speed v in the circular Bohr orbit of radius r constitutes a current of magnitude. i = e T . where T is the orbital period of the electron. T = 2 π r / v i = e v 2 π r By definition of atomic dipole moment μ i , its magnitude is given by μ i = i A = e V 2 π r · π r 2 = e v r 2 ∴ Angular momentum, L = m v r ∴ L μ i = 2 m v r e v r = 2 m e =  constant