Post on 14-Feb-2016
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Spin and the Exclusion PrincipleModern 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
1
12
( 1) 0,1,2,..., 1
cosz l
l l where l n
L m
EE where E Bohr ground staten l
L
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|
( 1)l l L
1 12 2( 1)s 1
2z ss m
( 1)j j J
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
2 1SJL
Discuss state labels and allowed transitions for sodium
Magnetic moment of electronMagnetic 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).
arg.2
2 2 2Be e
ch e evI area where Itime r
evr eL eShowthatm m
z B sm
z B sg m
Application of Zeeman effect: 21-cm line
Electron feels magnetic field due to proton magnetic moment (hyperfine splitting).
2 BE B
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
…
( , ') ( ', )x x x x
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