InterviewSolution
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InterviewSolution
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The magnetic moment vectors `vecmu_s` and `vecmu_l` associated with the intrinsic spin angular momentum `vecS` and orbital angular momentum `vecl` respectively, of an electron are predicted by quantum theory (and verified experimentally to a high accuracy to be given by `vecmu_s=-(e/m)vecS` and `vecmu_l=-((e)/(2m))vecl` Which of these relations is in accordance with the result expected classically? Outline the derivation of the classical result. |
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Answer» Out of the two relations given only one is in accordance with classical physics. This is `vec(mu)_(1) = -((e)/(2m))vec(l)` It follows from the definitions of `mu_(1)` and l. `mu = iA = ((-e)/(T)) pi r^(2)`. `l = m v r = m((2pir)/(T))r` Where r is the radius of the circular orbi which the electron of mass m and charge (-e) completes in time T. Divide (i) by (ii) `(mu_(1))/(l) = (-e)/(T) pi r^(2) xx (T)/(m^(2) pi r^(2)) = (-e)/(2m)` `vec(mu)_(1) = ((-e)/(2m))vec(l)` Clearly `vec(mu)_(1)` and `vec(l)` will be antiparallel (both being normal to the plane of the orbit) In contrast `(mu_(s))/(s) = (e)/(m)`. It is obtained on the basis of quantum mechanics. |
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