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Question : 16
Total: 27
Prove that the magnetic moment of the electron revolving around a nucleus in an orbit of radius r v e v r ∕ 2
Solution:
Proving magnetic moment as
Deducing expression of the magnetic moment of hydrogen atom
The magnetic moment is
m = I A
But current isI =
=
where,T =
A = π r 2
m =
Ï€ r 2 =
But from Bohr's second postulate
m e v r =
=
for n = 1
v r =
Hence the magnetic moment is
m =
=
n = 1
Deducing expression of the magnetic moment of hydrogen atom
The magnetic moment is
But current is
where,
But from Bohr's second postulate
Hence the magnetic moment is
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