Question

Obtain an expression for orbital magnetic moment of an electron rotating about the nucleus in an atom.

Answer 1

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=IA

where I= current and A= area of cross section

if r is the radius of orbit then

M=(e/t)(pi r^2)

=(ev/2pi r)(pi r^2) =evr/2 =mevr/2m

Since mvr= angular momentum(L)

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

Answer 2

Explanation:

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