Question

An electron excites from first orbit to the second orbit of a hydrogen atom. By what factor will the magnetic dipole moment of the revolving electron change? Show calculations.

Answer 1

Magnetic dipole moment is given by = M = IA

Current = I = Charge/Time period = = e × v/2πr

Area = A = πr² 

(r = radius of orbit, v = speed of electron in that orbit) 

Thus, 

M = e × v/2πr × πr² = evr/2 

M = evr/2 

We know mvr = nh/2π 

Therefore, M = enh/4πm

\(i.e. M ∝ n\)

So, when the electron excites to the second orbit the magnetic dipole moment becomes 2 times that in the first orbit.