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प्रश्न
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.
उत्तर
The magnetic moment associated with the orbital angular momentum is valid with classical mechanics.
The magnetic moment associated with the orbital angular momentum is given as
µl = `-("e"/(2"m")) "l"`
For current i and area of cross-section A, we have the relation:
Magnetic moment
µl = iA ……….(1)
Where,
e = Charge of the electron
r = Radius of the circular orbit
T = Time taken to complete one rotation around the circular orbit of radius r
Orbital angular momentum, l = mvr
L = `"m" xx (2π"r")/"T" xx "r"` ……….(2)
Where,
m = Mass of the electron
v = Velocity of the electron
r = Radius of the circular orbit
Dividing equation (1) by equation (2), we get:
`(µ_"l")/"T" = -("e"/(2"m"))`
µl = `-("e"/(2"m")) "l"`
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