Class 12 Physics
CBSE and UP Board
Magnetism and Matter
Chapter-5 Exercise 5.25
Additional Exercise
NCERT Solutions for Class 12 Physics Chapter 5 Question 25
The magnetic moment vectors µs and µl associated with the intrinsic spin angular momentum S and orbital angular momentum l, respectively, of an electron are predicted by quantum theory (and verified experimentally to a high accuracy) to be given by: µs = –(e/m) S, µl = –(e/2m)l Which of these relations is in accordance with the result expected classically? Outline the derivation of the classical result.
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Out of the two relations given, only one is in accordance with classical physics.
The magnetic momemtum vector which as a result of orbital Angular Moment is given by ,
μl=−e/2m l
It follows from the definitions ofμl and l.
μl=iA=(−e/T)πr2 …(i)
Angular momentum, l=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), μl/l=[(−e/T)πr2 ]/(m(2πr/T)r )=−e/2m
∴μl=(−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.