handout_L15_H2Atom - Lecture 15: The Hydrogen Atom Reading:...

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Lecture 15: The Hydrogen Atom • Reading: Zuhdahl 12.7-12.9 • Outline – The wavefunction for the H atom – Quantum numbers and nomenclature – Orbital shapes and energies H-atom wavefunctions • Recall from the previous lecture that the Hamiltonian is composite of kinetic (KE) and potential (PE) energy. • The hydrogen atom potential energy is given by: e - P + r r 0 V ( r ) = e 2 r H-atom wavefunctions (cont.) • The Coulombic potential can be generalized: e - P + r V ( r ) = Ze 2 r Z • Z = atomic number (= 1 for hydrogen) H-atom wavefunctions (cont.) • The radial dependence of the potential suggests that we should from Cartesian coordinates to spherical polar coordinates. p + e - r = interparticle distance (0 r ) θ = angle from “xy plane” ( π /2 θ - π /2) φ = rotation in “xy plane” (0 φ 2 π ) H-atom wavefunctions (cont.) • If we solve the Schrodinger equation using this potential, we find that the energy levels are quantized: E n =− Z 2 n 2 me 4 8 ε 0 2 h 2 2.178 x 10 18 J
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This note was uploaded on 01/18/2012 for the course CHEM 152A taught by Professor Chiu during the Winter '12 term at University of Washington.

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handout_L15_H2Atom - Lecture 15: The Hydrogen Atom Reading:...

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