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Zeeman Effect
-------------
The magnetic dipole moment is given by:
μ = IA
The torque on the dipole moment is given by:
τ = μ x B
The torque tends to line up the magnetic dipole moment with
the magnetic field because this represents the lowest energy
configuration.
The potential energy associated with the dipole moment is
U(θ) = -μ.B
Therefore, the change in energy between the up and down
state is:
ΔE = 2μB
The magnetic dipole moment for the electron is:
μe = -eL/2m
Therefore the energy becomes:
E = eBL/2m
For the oribital angular momentum in the z-direction,
L = ml. Thus we can write:
E = ehBml/2m
= μBmlB
Where μB is the Bohr Magneton = eh/2m
This gives a displacement in the energy levels such that
ΔE = mlμBB
This splitting of the levels is referred to as the ZEEMAN EFFECT.
Similarly, for the spin angular momentum MS = ±1/2h.
Thus, we can write:
E = ehBmS/2m
= μBmSB
In general, the Zeeman effect is the result of both the orbital and
spin angular momenta. Thus, we can write:
ΔE = (e/2m)(L + gS).B = gLμBmJB
Where g is the spin g-factor ~ 2 and gL is the LANDE g-factor
The Lande g-factor is a geometric factor that compensates for
the fact that the S and L vectors are both precessing around
the magnetic field in generally different directions.