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CBSE Class 12 Physics 2019 Outside Delhi Set 1 Paper

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Question : 16 of 27
Marks: +1, -0
Prove that the magnetic moment of the electron revolving around a nucleus in an orbit of radius r with orbital speed v is equal to evr2. Hence using Bohr's postulate of quantization of angular momentum, deduce the expression for the magnetic moment of hydrogen atom in the ground state.
Solution:  
Proving magnetic moment as
evr
2

Deducing expression of the magnetic moment of hydrogen atom
The magnetic moment is
m=IA
But current is I=
e
T
=
ev
2πr

where, T=
2πr
v
and the area, A=πr2
m=
ev
2πr
π
r2
=
evr
2

But from Bohr's second postulate
mevr=
nh
2π
=
h
2π
for n=1
vr=
nh
2πme

Hence the magnetic moment is
m=
e
2
h
2πme
=
eh
4πme
(Here n=1 )
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