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# lecture03_umn - Lecture 3 The Orbiting Electron Model of...

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Lecture 3 •The Orbiting Electron Model of the Hydrogen Atom •Kinetic Energy of the Hydrogen Atom •Potential Energy of the Hydrogen Atom •The Total Energy of the Bohr Model for the Atom •Wave-particle Duality Chapter 1 of the Book pages 1-25 September 14 2009

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The Orbiting Electron Model of the Hydrogen Atom First decade of the 1900s: it began to become clear that the atomic structure consisted of massive nuclei, composed of protons and neutrons, surrounded by electrons that had comparatively enormous volumes of empty space available to them . Protons and electrons attract one another through the Coulomb force http://hyperphysics.phy-astr.gsu.edu/hbase/forces/funfor.html#c1 Since atoms do not spontaneously annihilate their charged particles in fractions of a second, there must be an opposing force that repels the electrons from the nucleus .
The Planetary Hydrogen Atom •This situation has an obvious analogy (particularly to physicists): •the centrifugal force of an orbiting body that opposes the gravitational force attracting it to a central mass, e.g., a planet . •The total energy of a "planetary" hydrogen atom, assuming the nucleus to be stationary, would derive from two terms : –the kinetic energy of the orbiting electron –the potential energy from the Coulomb attraction

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Kinetic Energy A convenient expression for kinetic energy , usually denoted T (not to be confused with temperature!), is (3-1) where p is momentum (mass•velocity, units of mass•distance/time). This agrees with the other common expression T = (1/2) m v 2 (3-2) For an orbiting body , however, it is usually more convenient not to discuss mass, velocity, and momentum, but rather the analogous quantities, moment of inertia, angular velocity, and angular momentum. Let us visualize the system T = p 2 2 m
r m ! Angular velocity ω is defined as (3-3) so the total velocity is (3-4) and the kinetic energy is (3-5) " = 2 #\$ v = 2 r # = 2 r \$ % 2 = r T = 1 2 m r ( ) 2 The velocity at which mass m is moving is expressed in terms of distance per time . In the case of orbital motion, the particle travels around the circumference of the circle, a distance of 2 π r , once in each orbital frequency, ν .

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Kinetic Energy and Moment of Inertia To make the correspondence between linear and angular formulae more clear, one usually writes (3-6) where I is the "moment of inertia" , which is defined to be equal to mr 2 . Finally, if we recast this equation in the form of eq. 3-1:
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## This note was uploaded on 12/14/2010 for the course CHEM 3502 taught by Professor Staff during the Fall '08 term at Minnesota.

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lecture03_umn - Lecture 3 The Orbiting Electron Model of...

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