SWELect2ME501F2011 - Purdue University ME 501: Statistical...

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Patterned Border Template 1 Purdue University School of Mechanical Engineering ME 501: Statistical Thermodynamics Lecture 2: Bohr’s Atom, Matter Waves, The Uncertainty Principle, and the Schrödinger Wave Equation Prof. Robert P. Lucht Room 2204, Mechanical Engineering Building School of Mechanical Engineering Purdue University West Lafayette, Indiana Lucht@purdue.edu , 765-494-5623 (Phone) August 24, 2011
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Patterned Border Template 2 Purdue University School of Mechanical Engineering Lecture Topics Bohr’s model of the hydrogen atom. De Broglie’s postulate, matter waves. Heisenberg’s uncertainty principle. The Schrodinger wave equation, the wave function, operators, and expectation values.
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Patterned Border Template 3 Purdue University School of Mechanical Engineering The Classical Atom Consider an electron of charge - e orbiting a massive nucleus of charge + Ze . The electron is orbiting the nucleus at a radius r, with speed v in a circular orbit. The Coulomb attractive force balances the centrifugal force, Incropera, Introduction to Molecular Structure and Thermodynamics m r Ze r e v 2 2 0 2 4  The electron kinetic energy: Tm r ee  1 28 2 2 0 v The potential energy of the electron:  22 2 00 44 rr e Z eZ e VF r d r d r      The total electron energy: 2 0 8 Z e TV r 
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Patterned Border Template 4 Purdue University School of Mechanical Engineering The Classical Atom Total electron energy increases with increasing radius, decreases with decreasing radius r. Electron in circular orbit is accelerating , and from classical EM field theory will radiate EM energy. Thus, classical mechanics and EM field theory predict that the electron will spiral into the nucleus and that the orbit will be unstable. Not the correct picture. (1) Atoms are stable ; electrons and protons do not coalesce. Classical theory predicts that starting from a radius of approximately 0.1 nm, the electron will collapse into the nucleus in 10 -8 sec. (2) As radius r of the electron decreases continuously the orbital frequency will increase continuously. The frequency of the emitted radiation is proportional to the orbital frequency, and therefore will also vary continuously. However, atoms emit only at discrete frequencies (spectral lines).
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Patterned Border Template 5 Purdue University School of Mechanical Engineering The Bohr Atom Bohr theory of the atom is very successful for describing the energy level structure of one-electron atoms (hydrogen, singly-ionized helium, . .). Bohr theory developed from two postulates: (1) Postulate 1: The electron in a hydrogenic atom moves in a discrete orbit with a quantized orbital angular momentum L : (2) Postulate 2: The electron may emit or absorb energy only by undergoing a transition from one discrete orbit (energy level) to another. If E k and E m denote the energies of the two levels, the transition frequency for absorption or emission is given by v ( 1, 2,3,. ...) / 2 e Lm r n n h   km k m h  
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This note was uploaded on 12/26/2011 for the course ME 501 taught by Professor Na during the Fall '10 term at Purdue University-West Lafayette.

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SWELect2ME501F2011 - Purdue University ME 501: Statistical...

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