Question

An electron of mass m revolves around a nucleus of charge + ze. Show that it behaves like a tiny magnetic dipole. Hence prove that the magnetic moment associated with it is expressed as u=e/3 ml, where l is the orbital angular momentum of the electron. Give the significance of negative sign

Answer 1

║⊕ANSWER⊕║

• When electron revolves around a nucleus, it creates circular current around it. In this way, it is equivalent to a current carrying coil.
• So, it behaves as a tiny magnetic dipole.

• We know that a current carrying coil behaves like a magnetic dipole having dipole moment equal to i A, where i is current and A is area of the coil.

• e is charge of electron. Angular momentum of electron is, L =mr2ω

• Substituting the above in equation. (i), we get,

• Here negative sign indicates µ is directs away from L.