An electron in the ground state of hydrogen atom is revolving in a circular orbit of radius R . The orbital magnetic moment of the electron is ( m = mass of electron, h = Planck's constant, e = electronic charge )

Step-by-step solution

(A) In ground state ( n =1) according to Bohr's theory: mvR = h 2 or v = h 2 mR Now time period, T = 2 R v = 2 R h / 2 mR = 4 ² mR ² ~h Magnetic moment, M = iA Where, I = charge time period = e 4 ² mR ² ~h = eh 4 ² mR ² and A = R ² M = ( R ² ) ( eh 4 ² mR ² ) or M = eh 4 m Direction of magnetic moment M is perpendicular to the plane of orbit.