lecture03_umn

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

Info iconThis preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1

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

View Full DocumentRight Arrow Icon
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 .
Background image of page 2
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
Background image of page 3

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

View Full DocumentRight Arrow Icon
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
Background image of page 4
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 .
Background image of page 5

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

View Full DocumentRight Arrow Icon
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:
Background image of page 6
Image of page 7
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 12/14/2010 for the course CHEM 3502 taught by Professor Staff during the Fall '08 term at Minnesota.

Page1 / 23

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

This preview shows document pages 1 - 7. Sign up to view the full document.

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