final_2010 - Quantity Symbol Value Coulombs Constant 1 4 π...

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Unformatted text preview: Quantity Symbol Value Coulombs Constant 1 4 π o 8 . 98 × 10 9 Nm 2 / C 2 Electron Mass m e 9 . 1 × 10- 31 kg Proton Mass m p 1 . 67 × 10- 27 kg Electron Charge e- 1 . 6 × 10- 19 C Electron Volt eV 1 . 6 × 10- 19 J Permitivity o 8 . 85 × 10- 12 C 2 Nm 2 Magnetic Permeability μ o 4 π × 10- 7 N · A 2 Speed of Light c 3 . × 10 8 m / s Planck’s Constant h 6 . 6 × 10- 34 m 2 kg / s Planck’s Constant/2 π ~ 1 . 05 × 10- 34 m 2 kg / s Integrals Value R ∞-∞ due- αu 2 p π α R ∞-∞ duu 2 e- αu 2 1 2 α p π α R ∞ duu n e- αu n ! α n +1 R du sin 2 ( αu ) u 2- sin(2 αu ) 4 α R du cos 2 ( αu ) u 2 + sin(2 αu ) 4 α R + 1 2- 1 2 duu 2 sin 2 ( nπu )- 6+ n 2 π 2 24 n 2 π 2 n = 2 , 4 , 6 , 8 R + 1 2- 1 2 duu 2 cos 2 ( nπu )- 6+ n 2 π 2 24 n 2 π 2 n = 1 , 3 , 5 , 7 R (cos( θ )) α sin( θ ) dθ- 1 α +1 (cos( θ )) α +1 R (sin( θ )) α cos( θ ) dθ +1 α +1 (sin( θ )) α +1 n ‘ m Φ m ( ϕ ) Θ lm ( θ ) R nl ( r ) Ψ nlm 1 0 1 1 1 √ πa 3 o e- r/a o 1 √ πa 3 o e- r/a o 2 0 1 1 1 √ 32 πa 3 o 2- r a o e- r/ 2 a o 1 √ 32 πa 3 o 2- r a o e- r/ 2 a o 2 1 1 √ 3cos( θ ) 1 √ 96 πa 3 o r a o e- r/ 2 a o 1 √ 32 πa 3 o r a o e- r/ 2 a o cos( θ ) 2 1 ± 1 e ± iϕ q 3 2 sin( θ ) 1 √ 96 πa 3 o r a o e- r/ 2 a o 1 √ 64 πa 3 o r a o e- r/ 2 a o sin( θ ) e ± iϕ For potential V = 1 2 k x 2 the lowest wave functions and energies Ψ = 1 √ πL 1 / 2 e- y 2 / 2 Ψ 1 = 1 √ πL 1 / 2 √ 2 ye- y 2 / 2 Ψ 2 = 1 √ πL 1 / 2 1 √ 2 (2 y 2- 1) e- y 2 / 2 where y ≡ x L L = r ~ Mω o (1) 1. Write down the electronic configuration of atomic iron Z = 26 and the electronic structure of sodium Z = 11....
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final_2010 - Quantity Symbol Value Coulombs Constant 1 4 π...

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