Question

Show that the magnetic moment of an atom is M = \(\frac { 1 }{ 2 }\)eωr², where e the charge of an electron, ω – the angular speed of electron and r – the radius of electron orbit.

Answer 1

The electrons are revolving around the nucleus of an atom. If ‘e’ is the charge of an electron and T its period of revolution, then
Current I = \(\frac { e }{ T }\) = \(\frac { eω }{ 2π }\).
Since T = \(\frac { 2π }{ ω }\), ω is the angular velocity.
If A = πr², is the area of the orbit of radius ‘r’, then a magnetic moment of the atom,
M = IA = \(\frac { eω }{ 2π }\).πr² = \(\frac { 1 }{ 2 }\)eωr².