Spin and the Exclusion Principle Modern Ch. 7, Physical Systems, 20

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Spin and the Exclusion Principle Modern Ch. 7, Physical Systems, 20 Spin and the Exclusion Principle Modern Ch.7, Physical Systems, 20.Feb.2003 EJZ Review Hydrogen atom, orbital angular momentum L Electron spin s Total angular momentum J = S + L= Spin + orbit Applications: 21 cm line, Zeeman effect Good QN and allowed transitions Pauli exclusion principle Periodic Table Lasers

Hydrogen atom : Bohr model We found rn = n2 r1, En = E1/n2, where the “principle quantum number” n labels the allowed energy levels. Discrete orbits match observed energy spectrum

Hydrogen atom: Orbits are not discrete (notice different r scales)

Hydrogen atom: Schrödinger solutions depend on new angular momentum quantum numbers Quantization of angular momentum direction for l=2 Magnetic field splits l level in (2l+1) values of ml = 0, ±1, ± 2, … ± l

Hydrogen atom examples from Giancoli

Hydrogen atom plus L+S coupling: Hydrogen atom so far: 3D spherical solution to Schrödinger equation yields 3 new quantum numbers: l = orbital quantum number ml = magnetic quantum number = 0, ±1, ±2, …, ±l ms = spin = ±1/2 Next step toward refining the H-atom model: Spin with Total angular momentum J=L+s with j=l+s, l+s-1, …, |l-s|

Total angular momentum: Multi-electron atoms: J = S+L where S = vector sum of spins, L = vector sum of angular momenta Spectroscopic notation: L=0 1 2 3 S P D F Allowed transitions (emitting or absorbing a photon of spin 1) ΔJ = 0, ±1 (not J=0 to J=0) ΔL = 0, ±1 Δmj = 0, ±1 (not 0 to 0 if ΔJ=0) ΔS = 0 Δl = ±1

Discuss state labels and allowed transitions for sodium

Magnetic moment of electron Magnetic moment: Bohr magneton models e- as spinning ball (or loop) of charge We expect but Stern-Gerlach experiment shows that where g = 2.0023…=gyromagnetic ratio (electron is not quite a spinning ball of charge).

Application of Zeeman effect: 21-cm line Electron feels magnetic field due to proton magnetic moment (hyperfine splitting).

Pauli Exclusion principle Identical fermions have antisymmetric wavefunctions, so electrons cannot share the same energy state. Fill energy levels in up-down pairs: 1s 2s 2p 3s 3p 3d 4s 4p 4d 4f …

LASER = Light Amplification by Stimulated Emission of Radiation Pump electrons up into metastable excited state. One transition down stimulates cascade of emissions. Monochromatic: all photons have same wavelength Coherent: in phase, therefore intensity ~ N2