Spin and the Exclusion Principle Modern Ch. 7, Physical Systems, 20
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1 Spin and the Exclusion Principle Modern Ch. 7, Physical Systems, 20 Spin and the Exclusion Principle Modern Ch.7, Physical Systems, 20.Feb EJZReview Hydrogen atom, orbital angular momentum LElectron spin sTotal angular momentum J = S + L= Spin + orbitApplications: 21 cm line, Zeeman effectGood QN and allowed transitionsPauli exclusion principlePeriodic TableLasers
2 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
3 Hydrogen atom: Orbits are not discrete (notice different r scales)
4 Hydrogen atom: Schrödinger solutions depend on new angular momentum quantum numbers Quantization of angular momentum direction for l=2Magnetic field splits l level in (2l+1) values of ml = 0, ±1, ± 2, … ± l
6 Hydrogen atom plus L+S coupling: Hydrogen atom so far: 3D spherical solution to Schrödinger equation yields 3 new quantum numbers:l = orbital quantum numberml = magnetic quantum number = 0, ±1, ±2, …, ±lms = spin = ±1/2Next step toward refining the H-atom model:Spin withTotal angular momentum J=L+swith j=l+s, l+s-1, …, |l-s|
7 Total angular momentum: Multi-electron atoms: J = S+L whereS = vector sum of spins,L = vector sum of angular momentaSpectroscopic notation: L=S P D FAllowed transitions (emitting or absorbing a photon of spin 1)ΔJ = 0, ±1 (not J=0 to J=0) ΔL = 0, ±1Δmj = 0, ±1 (not 0 to 0 if ΔJ=0) ΔS = 0Δl = ±1
8 Discuss state labels and allowed transitions for sodium
9 Magnetic moment of electron Magnetic moment: Bohr magneton models e- as spinning ball (or loop) of chargeWe expectbut Stern-Gerlach experiment shows thatwhere g = …=gyromagnetic ratio(electron is not quite a spinning ball of charge).
10 Application of Zeeman effect: 21-cm line Electron feels magnetic field due to proton magnetic moment (hyperfine splitting).
11 Pauli Exclusion principle Identical fermions have antisymmetric wavefunctions, so electrons cannot share the same energy state.Fill energy levels in up-down pairs:1s2s 2p3s 3p 3d4s 4p 4d 4f…
12 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 wavelengthCoherent: in phase, therefore intensity ~ N2