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Unformatted text preview: Chem 120A The Hydrogen Atom, Part 1 03/08/06 Spring 2006 Lecture 20 READING: Engel: Ch 9 In the last lecture we saw how the separation of variables technique could be used to find solutions to the 2D Particle in a Box. Now we will use this same technique to solve for the 3D Hydrogen Atom. We will use separation of variables in two different ways. First we will separate the wavefunction into a component which determines the external energy of the particle and a component which determines the internal energy (the internal structure is what we are really interested in). Next we will take the wavefunction which de scribes the internal structure and separate it into a part which depends on the radial distance of the electron from the nucleus (the radial part of the wavefunction) and a part which depends on the angular coordinates in space (the angular component of the wavefunction). Hydrogenic atoms consist of a nucleus at a point, r 1 which has charge +Ze (Z is the number of protons and e is the elementary charge = 1 . 602 × 10 19 Coulombs) and an electron of charge e at a point r 2 (see Figure 1). Hydrogenic atoms have only one electron (e.g. He + , Li 2 + , O 7 + ). For more than one electron the results will be quite different. Hydrogenic atoms have spherical symmetry, so it will become natural for us to use spherical coordinates ( r , θ , φ ) to describe the system. The Hamiltonian for a Hydrogenic atom is: ˆ H = ¯ h 2 2 m 1 ∇ 2 1 ¯ h 2 2 m 2 ∇ 2 2 Ze 2 4 πε r (1) where m 1 is the nuclear mass, m 2 is the electron mass and r is the magnitude of separation between the nucleus and the electron =  r 1 r 2  Chem 120A, Spring 2006, Lecture 20 1 ∇...
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This note was uploaded on 09/29/2009 for the course CHEM 120A taught by Professor Whaley during the Spring '07 term at Berkeley.
 Spring '07
 Whaley
 Physical chemistry, Atom, pH

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