Question

derive expression for orbital magnetic moment of an electron revolving in circular orbit in an atom​

Answer 1

Answer:

Consider an electron revolving around a nucleus in an atom. Since the electron is a negatively charged particle, so atom will act as a current-carrying loop and its magnetic dipole moment is given by 

M=lA

Where l =current and A =area of cross-section

if r is the radius of orbit then

M=(te)(πr2)

=v2πreπr2=2evr

Sice mvr = angular momentum (L)

So, M=(2me2)L (in vector form), since magnetic dipole moment of the electron and angular momentum are in opposite direction.