31x_Lecture26_Hatom-orbitals-Aufbau

31x_Lecture26_Hatom-orbitals-Aufbau - Hydrogen Atom...

Info iconThis preview shows pages 1–10. Sign up to view the full content.

View Full Document Right Arrow Icon
WEM 2008 Hydrogen Atom Orbitals Multi-electron Atoms!
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
H atom wavefunctions – the atomic orbitals: Ground State MDF 2007, WEM 2008 o r/a 1s 3 o 1 Ae A a ψ= π 1s orbital a o = 0.529 Å the Bohr radius normalization constant spherical polar coordinates The wavefunction is the probability amplitude. The probability is the absolute valued squared of the wavefunction. o 2 2r/a 2 1s Ae This is roughly the probability of finding the electron a distance r from the nucleus on a line where the nucleus is at r = 0 (more precise in two pages) r (Å) ψ 0.2 0.4 0.6 0.8 1 1.2 1.4 0.5 1 1.5 2 1 2 2.5 3 1 r (Å) ψ 2 note different scale
Background image of page 2
The 2s Hydrogen orbital (n=?, l=?, m=?) o 2 2 r/2a 2s o B(2 r/a )e  ψ=  Absolute value of the wavefunction squared – probability distribution. o r/2a o 3 o 1 B(2 r/a )e B 42a = π When r = 2a o , this term goes to zero. There is a “node” in the wave function. normalization constant a o = 0.529, the Bohr radius 2 4 6 8 0.1 0.2 0.3 0.4 0.5 1 2 3 4 0.05 0.15 0.25 ψ ψ 2 r (Å) r (Å) node node MDF 2007, WEM 2008
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
1s – no nodes 2s – 1 node 3s – 2 nodes The nodes are radial nodes. Radial distribution functions. Probability of finding electron a distance r from the nucleus in any direction ( ). 22 4 r dr πψ Representing s orbitals - = 0 MDF 2007, WEM 2008
Background image of page 4
Each 2p orbital has one angular node. o r/2a 2p,z o (r / a )e cos ψθ “Dumbbell” shape, oriented along each axis MDF 2007, WEM 2008 Example: The 2p orbitals = 1
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
3d orbitals = 2 Each 3d orbital has two angular nodes. d xy d xz d yz d x 2 -y 2 d z 2 MDF 2007, WEM 2008
Background image of page 6
A family picture: (Chem Connections) MORE IMAGES/VISUALIZATIONS
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Many electron atoms are based on hydrogen atom Can solve H atom problem exactly because one electron. Get energies, E n 4 quantum numbers – n, , m, s s, p, d, f orbitals In H atom, energy only depends on principal quantum number, n. But for many electron atoms – can’t solve Schrödinger eqn exactly. Still get s, p, d, and f orbitals Now, energy levels depend on two Q – numbers, n and . Copyright - Michael D. Fayer, 2004, W. E. Moerner, 2009 Note: ONE-electron, “hydrogenic” atoms (e.g. O +7 ) already solved - just H with Z ≠1 2 H n 2 ZR E n =
Background image of page 8
Energy Level Diagram for Multi-electron Atoms (not to scale) 5s 5p 5d 5f 4s 4p 4d 4f 3s 3p 3d 2s 2p 1s 6s 6p 7s Order of energy levels 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f 1 st trans series 2 nd trans series 3 rd
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 10
This is the end of the preview. Sign up to access the rest of the document.

This document was uploaded on 01/12/2011.

Page1 / 26

31x_Lecture26_Hatom-orbitals-Aufbau - Hydrogen Atom...

This preview shows document pages 1 - 10. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online