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NCERT Class XII Chapter
Magnetism and Matter
Questions With Solutions

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Question : 25
Total: 25
The magnetic moment vectors
→
µs
 and
→
µI
 associated with the intrinsic spin angular momentum
→
S
 and orbital angular momentum
→
I
 respectively, of an electron are predicted by quantum theory (and verified experimentally to a high accuracy) to be given by
→
µS
 = - (
e
m
)
→
S
 and
→
µI
 = - (
e
2m
)
→
I
Which of these relations is in accordance with the result expected classically?
Outline the derivation of the classical result.
Solution:  
Out of the two relations given, only one is in accordance with classical physics. This is
→
µ1
 = - (
e
2m
)
→
I
It follows from the definitions of μl and l.
µI = iA = (−
e
T
)πr2 ... (i)
I = mvr = m (
2πr
T
)r ... (ii)
where r is the radius of the circular orbit, which the electron of mass m and charge (– e) completes in time T.
Divide (i) by (ii),
µI
l
 = −
e
T
πr2 ×
T
m2πr2
 = −
e
2m
∴
→
µ1
 = (−
e
2m
)
→
l
Clearly
→
µl
 and
→
l
 will be antiparallel (both being normal to the plane of the orbit)
In contrast,
µS
S
 =
e
m
. It is obtained on the basis of quantum mechanics.
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