REED CHEMISTRY 333 - Hydrogen atom (8 pages)

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Hydrogen atom



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Hydrogen atom

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Lecture Notes


Pages:
8
School:
Reed College
Course:
Chemistry 333 - Quantum Mechanics and Molecular Structure
Quantum Mechanics and Molecular Structure Documents

Unformatted text preview:

Hydrogen atom SWE 2 equations Eq 1 hbar2 1 1 B Jsin q N 2 me sin q q q sin2 q b ij 2 yz j zF Q F b Q F k f2 Solution 3D rotor hbar2 l H l 1L 2 me Yl ml lml ml Engel 7 33 Hydrogen atom SWE 2 equations Eq 2 hbar2 1 d 2 d B Jr N HE V HrLLF R b R 2 me r2 d r dr from 3D rotor V r from Coulomb hbar2 1 d 2 d hbar2 e2 B Jr NF B l Hl 1L F R E R 2 me r2 d r dr 2 me r2 4 p e0 r 1 R r eqn gives atom energy Boundary condition R r 0 as r gets large En quantized n l 1 n 1 2 3 En 2 18 10 18 J 13 60 eV me e 4 2 2 2 2 8 e0 h n n n2 Doesn t include Etranslation of CM Properties of En En E En 13 60 1 3 40 2 1 51 3 0 85 4 0 H atom has bound states E 0 free unmoving electron E 0 2 18 10 18 J 13 60 eV me e 4 2 2 2 2 8 e0 h n n n2 2 H atom spectroscopy Rydberg formula for line spectra nm n R J 1 1 2N 2 n m IP H 13 6 eV E1 Isotope effect tiny on line positions Orbitals r R r Y R n l Y l ml n l ml 1 0 0 2 0 1 0 0 1 gn 1 4 3 0 1 2 0 0 1 0 1 2 9 3 Orbitals r n l ml nlm Rnl Ylm 1 0 0 1s R10 s Y00 2 0 0 2s R20 s Y00 2 1 0 2pz R21 pz Y10 2 1 1 2px i 2py R21 p 1 Y1 1 3 0 0 3s R30 s Y00 3 1 0 3pz R31 pz Y10 3 1 1 3px i 3py R31 p 1 Y1 1 3 2 0 3dz2 R32 dz2 Y20 3 2 1 3dxz i 3dyz R32 d 1 Y2 1 3 2 2 3dx2 y2 i 3dxy R32 d 1 Y2 2 Veffective 2 10 18 1 10 18 1 10 18 2 10 18 l 1 n 2 3 4 1 10 R 0 0 l 2 n 3 4 5 10 2 10 10 3 10 10 4 10 10 l 0 n 1 2 3 5 10 10 6 10 10 R 0 0 Centripetal Coulomb hbar2 1 d 2 d hbar2 e2 B Jr NF B l Hl 1L F R E R 2 me r2 d r dr 2 me r2 4 p e0 r 4 R10 radial factor for 1s a0 0 529 1 bohr 0 h2 me e2 R10 3 2 i 1 y z j z R10 2



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