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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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