Question

The angular momentum of an electron revolving in a circular orbit is J, What is its magnetic moment?

• A. $\frac{mJ}{2e}$
• B. $\frac{eJ}{2m}$
• C. $\frac{2m}{eJ}$
• D. $\frac{emJ}{2}$

Answer 1

The correct option is B $\frac{eJ}{2m}$

According to Bohr modal of hydrogen like atoms, negatively charged electrons revolves around the positively charged nucleus. This uniform circular motion of electrons is equivalent to a current loop which possesses a magnetic dipole moment =IA

I:- current in the loop

A:-area

Consider an electron revolving anticlockwise around a nucleus in an orbit of radius r with speed v and time period T.

Equivalent current,

I= charge/time

=e/t = e/2πr/v

=ev/2πr

Area of current loop ,A=πr²

So , orbital magnetic moment of electron is=IA

=(ev/2πr). πr²

=evr/2

As J is angular momentum. J=mvr

m- mass of electron

So orbital magnetic moment = eJ/2m