L06S10_QuantumHAtom+02-01-10 (1)

L06S10_QuantumHAtom+02-01-10 (1) - CHEM 1A L6:...

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Unformatted text preview: CHEM 1A L6: "Quantum H-Atom" 1/31/2010 Weekly Review Sessions Thursday 5-7 p.m. 51 Pimentel Hall Greg Dallinger DropDrop-in Office Hours Mondays to Fridays 10-3 10See schedule posted at the door Location: 12B Latimer Hall © 2004 M.Kubinec L6-1 Lab 3: This Week! •Review and Discussion © 2004 M.Kubinec L6-2 Summary Particles and Waves Momentum Matter Particle Photon (yellow) (yellow) e(v ~ 105 m sec-1) DeBroglie (nm) ~ 600 ~6 ~ 0.06 ~ 6x10-26 L8-3 Ψ: Ψ 2 ~ Probability v 2 e- p=mv p=mv Particle h p= h=6.62 x 10-34 Js Wave Duality h = p L6-4 Na (80K, v~300 m sec-1) Baseball (170g, v~40 m sec-1) © A.Pines,M.Kubinec,UCB © 2002 A.Pines,M.Kubinec, UC Discrete, Quantized States Standing Waves Ψ(x) E n 3 2 1 Nodes 2 1 0 L6-11 Absorption and Emission Spectra ΔE=h Excited States + + + - Ground State © 2002 A.Pines,M.Kubinec, UC + © 2004 M.Kubinec © A.Pines,M.Kubinec,UCB L6-3 L8-7 © 2004 M. Kubinec 1 CHEM 1A L6: "Quantum H-Atom" 1/31/2010 Discrete, Quantized States Standing Waves Ψ(x) E n 3 2 1 Nodes 2 1 0 L6-4 Excited States States + + + - Ground State © 2004 M.Kubinec + An electron as a standing wave around the nucleus © 2004 M.Kubinec L6-5 Absorption and Emission Spectra Electronic Transtions v ΔE = hν © 2004 M.Kubinec L6-6 © 2004 M. Kubinec 2 CHEM 1A L6: "Quantum H-Atom" 1/31/2010 ChemQuiz© 6.1 Shown is an energy– energy– level scheme and the emission spectrum. Which line arises from 3 1? 3 2 1 A B C E C) C L6-7 A) A © 2004 M.Kubinec B) B ChemQuiz© 6.2 To which energy-level scheme does the emission spectrum correspond? A) © 2004 M.Kubinec B) C) L6-9 Absorption and Emission Spectra Review ΔE=h © A.Pines,M.Kubinec,UCB L8-7 Wave Functions Energy: - h2 d2 Ψ(x) = ET Ψ(x) 8π2m dx2 2 nπ nπ x A sin L 8π2m L Ψ(x) Ψ2(x) En 16 n=4 h2 = ET Ψ(x) n=3 9 En = © 2004 M.Kubinec h2n2 8mL2 n=2 n=1 4 © 2004 M.Kubinec L08-11 1 L19-9 © 2004 M. Kubinec 3 CHEM 1A L6: "Quantum H-Atom" 1/31/2010 Ψ(x) = A sin 2π x known momentum () h de Broglie relation: mv = p = Uncertainty Principle Ψ2(x) = intensity or probability x uncertainty in position Ψ(x) = ΣAi sin 2π x i i uncertainty in momentum © 2004 M.Kubinec Δx Δp ≥ h/4π h/4 L08-12 known position x Quantum Mechanics Schrödinger equation: - h2 d2 Ψ(x) + V(x) Ψ(x) = ET Ψ(x) 8π2m dx2 Kinetic Potential Total H Ψ(x) = ET Ψ(x) © 2004 M.Kubinec L08-13 Wave Functions Energy: Ψ(x) = ET Ψ(x) 8π2m dx2 h2 d2 nπ nπ 2 A sin L x 8π2m L h2 = ET Ψ(x) n=4 Ψ(x) Ψ2(x) En 16 n=3 9 En = h2n2 8mL2 n=2 n=1 4 1 © 2004 M.Kubinec L08-14 © 2004 M. Kubinec 4 CHEM 1A L6: "Quantum H-Atom" 1/31/2010 Orbital Energies n : Principal Q. N. -Z 2 n2 n ∞ 3 n: 1, 2, 3 . . . Ionized E 0 -R∞ -R∞ 4 9 En = R∞ R∞ 2 = 2.18 x 10-18 J = 3.29 x1015 Hz N0R∞ = 1312 kJmol-1 © 2004 M.Kubinec 1 Ground -R∞ L08-15 ChemQuiz© 6.3 H To which ion does the E-Level diagram ‘X’ correspond ? 2 1 4 3 2 X -R∞ 4 -R∞ A) H © 2004 M.Kubinec B) He + C) Li 2+ 1 L08-16 ChemQuiz© 6.4 Which transition in + He has the same wavelength as n = 2 1 in H? ∞ 3 2 Ionized -R∞ -R∞ 4 9 A) 2 1 © 2004 M.Kubinec B) 4 1 C) 4 2 1 Ground -R∞ L08-18 © 2004 M. Kubinec 5 CHEM 1A L6: "Quantum H-Atom" 1/31/2010 Energy of Transitions En= - Z2 n2 R∞ R∞ = 2.18 x 10-18J NAR∞ = 1312 kJmol-1 ΔE= -Z2R∞ 1 nf2 1 ni2 ni ΔE = h nf L08-20 © 2004 M.Kubinec Lecture Complete © 2004 M.Kubinec L08-21 © 2004 M. Kubinec 6 ...
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This note was uploaded on 04/24/2010 for the course CHEM 1A taught by Professor Nitsche during the Spring '08 term at University of California, Berkeley.

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