L07S10_QM+Orbitals+02-03-10

L07S10_QM+Orbitals+02-03-10 - CHEM 1A L7: "QM...

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Unformatted text preview: CHEM 1A L7: "QM Orbitals" 2/2/2010 Review 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 = h2n2 8mL2 n=2 n=1 4 1 © 2004 M.Kubinec © 2004 M.Kubinec L19-9 L08-1 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∞ L07-2 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∞ L07-3 © 2004 M. Kubinec 1 CHEM 1A L7: "QM Orbitals" 2/2/2010 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 L08-5 © 2004 M.Kubinec H -Atom, One-Electron Ions Onen=1 l = 0 (s) (s ml = 0 n=2 l = 0 (s) (s ml = 0 Radial Node n=2 ml = -1, +1 l = 1 (p) (p ml = 0 z - 2px Angular Node z 2py + z y x + 2pz z 1s + z 2s + - + y x - y y x y L9-5 x x n = 3 l = 0, 1, 2 © A.Pines,M.Kubinec UCB 3s, 3p, 3d Orbitals © A.Pines,M.Kubinec UCB © 2004 M.Kubinec L07-6 L9-6 Quantum Numbers Q.N. n : Principal values orbital property Total nodes =n-1 Energy Shape n: 1, 2, 3 . . . ℓ: 0 (s), 1 (p), 2 (d), n-1 (s), (p), (d), ℓ : Angular Momentum mℓ : Magnetic mℓ: -ℓ, -(ℓ-1),..,0,..,(ℓ-1), ℓ © 2004 M.Kubinec Angular nodes = ℓ Orientation L07-7 © 2004 M. Kubinec 2 CHEM 1A L7: "QM Orbitals" 2/2/2010 H-Atom, One-Electron Ions Onen=1 ℓ = 0 (s) (s mℓ = 0 n=2 ℓ = 0 (s) (s mℓ = 0 Radial Node z 1s + z 2s + - y x y L07-8 x © 2004 M.Kubinec (a) The probability distribution for the hydrogen 1s orbital in threethreedimensional space (b) The probability density of the electron © 2004 M.Kubinec L07-9 Th Three representations of the hydrogen 1s, 2s, and 3s electron © 2004 M.Kubinec L07-10 © 2004 M. Kubinec 3 CHEM 1A L7: "QM Orbitals" 2/2/2010 mℓ = -1, +1 n=2 ℓ = 1 (p ) (p z 2py + mℓ = 0 z - 2px Angular Node z y x + 2pz + y x - y x n = 3 ℓ = 0, 1, 2 © 2004 M.Kubinec 3s, 3p, 3d Orbitals L07-11 ℓ = angular nodes; n-1 = total nodes Representation of the 2p orbitals © 2004 M.Kubinec L07-12 A cross section of the electron probability distribution for a 3p orbital. © 2004 M.Kubinec L07-13 © 2004 M. Kubinec 4 CHEM 1A L7: "QM Orbitals" 2/2/2010 © 2004 M.Kubinec L07-14 Representation of the 3d orbitals © 2004 M.Kubinec L07-15 Representation of the 3d orbitals © 2004 M.Kubinec L07-16 © 2004 M. Kubinec 5 CHEM 1A L7: "QM Orbitals" Representation of the 4f orbitals in terms of their boundary surfaces. 2/2/2010 © 2004 M.Kubinec L07-17 ChemQuiz 7.1 z z Y x Which has the most radial nodes? x + - -+ y A) 4f © 2004 M.Kubinec B) 3d C) 2s L07-18 Lecture Complete © 2004 M.Kubinec L07-20 © 2004 M. Kubinec 6 ...
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