Show that the ratio of the magnetic dipole moment to the angular momentum (l = mvr) is a universal constant for hydrogen-like atoms and ions. Find its value.
Magnetic dipole moment = ni A
Angular momentum = mvr = nh2π
Since the ratio of magnetic dipole moment, and angular momentum is independent of 'Z'.
Hence it is a universal constant
Ratio = e5×m×πr2 n224 ϵ0h3n3×2πnh