Question

4. Orbital Magnetic Moment - In the derivation of the orbital magn etic dipole moment in the notes, we assumed a single electron orbiting a nucleus to obtain the magnetic moment. From a quantum mechanical point of view this is strange because the electron's position is uncertain. Instead of the single charge consider the cases below. Follow the analysis th rough and determine if a different result would have been obtained for the magnetic moment. Consider the electrons charge and mass broken in half with each half orbiting the nucleus. Would the magnetic moment change? a. b. Now consider both the charge and the mass of the electron evenly distributed all along the circumference (with a mass per unit length of m./2r and a charge per unit length of q/2tr). Would the magnetic moment change? How do your answers help justify how the magnetic dipole of the spinning electron was calculated? C.

Answer 1

We know that if epsilon change is revolving around nucleolus then magnetic moment cm is given by - so m = IA = qA/T = qV/2 pi r pi r^z M < = qvr/2 If q = 0 so M = ev r/2 \r\n If charge is divided in to 2 equal parts by charge an by mass, so - m = e/2 vr/2 + c/2 vr/2 m = ev r/2 so no change If charge per unit length is a/2 pi r and mass per unit length is me/2 pi r so a = q/2 pi r times 2 pi r = q so m = qvr/2 or evr/2 so no change we have calculated it by - m = evr/2