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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 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

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**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

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**Hydrogen atom: Orbits are not discrete**

(notice different r scales)

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**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

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**Hydrogen atom examples from Giancoli**

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**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|

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**Total angular momentum:**

Multi-electron atoms: J = S+L where S = vector sum of spins, L = vector sum of angular momenta Spectroscopic notation: L= 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

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**Discuss state labels and allowed transitions for sodium**

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**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 = …=gyromagnetic ratio (electron is not quite a spinning ball of charge).

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**Application of Zeeman effect: 21-cm line**

Electron feels magnetic field due to proton magnetic moment (hyperfine splitting).

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**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 …

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**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

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