The ratio of angular momentum L of an electron to the magnetic dipole moment m _ orb is ( ' m ' is mass of electron, ' e ' is charge on electron)

Step-by-step solution

An electron with charge e and mass m revolves in a circular orbit of radius r with angular velocity . The orbital magnetic dipole moment arises from the current generated by the orbiting charge. The current is I = e /(2 ) , formed by dividing charge by the orbital period. Multiplying by the orbital area A = r^2 yields the magnetic dipole moment magnitude: m_ orb = e r^2 2 The angular momentum for this point mass system is L = m r^2 , derived from the moment of inertia I_ moment = m r^2 about the axis. The ratio L/m