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Lecture Notes for CHEM 3410 - PHYSICAL CHEMISTRY I with Richard at The Richard Stockton College of New Jersey (StoCo)

Notes Information

Material Type:Class Note
Professor:Richard
Class:CHEM 3410 - PHYSICAL CHEMISTRY I
Subject:Chemistry
University:The Richard Stockton College of New Jersey
Term:Spring 2009
Keywords:
  • Natural Sciences
  • Normalization
  • Energy Levels
  • Average Value
  • Probability.
  • Mathematics
  • Potential Energy
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The Richard Stockton College of New Jersey Chemistry Program, School of Natural Sciences and Mathematics PO Box 195, Pomoma, NJ CHEM 3410: Physical Chemistry II | Spring 2009 In-class Practice Problems February 4, 2009 1. A particle is moving in one dimension between x = a and x = b. The potential energy is such that the particle cannot be outside these limits and that the wave function in between is: = Ax (a) Determine the normalization constant A. (b) Calculate the average value of x. 2. An electron is con ned to a 1-D box that is 1 nm long. How many energy levels are there with energy less than 10 eV? How many levels are there between 10 and 100 eV? 3. (a) What is the quantum-mechanical probability of nd the particle in a one-dimensional box in the middle third of the box (between x = a3 and x = 2a3 ) ? Show how this quantity depends on n. You may need to make use of the following integrals and identities: Z sin2(mx)dx = x2 sin(2mx)4m sinA sinB = 2 cos A + B 2 sin A B 2 ...

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