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Last modified: November 20, 2021 ✓

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 orbital 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.