MODERN PHYSICS (LOOSELEAF)
4th Edition
ISBN: 9781119495550
Author: Krane
Publisher: WILEY
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Chapter 10, Problem 12P
To determine
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5. A particle of mass m in a rectangular box with dimensions x, y, z has ground
k² ( 1
1
+
y?
1
state energy E(x, y, z) =
where k is a physical constant. If
+
8m x
the volume of the box is fixed (say V =xyz ), find the values of x, y, and z that
minimize the ground state energy.
In a nanoscale experiment, an atom is confined to an infinitesimally small volume in which its partition function, z, has a value of 6. A second
experiment confines three of these atoms in the same volume. What is the value of Z for this new system?
18
216
06
O24
36
Suppose a system contain four identical particles and five energy levels given by the
relationship, E;= i x 10-20 J, where i = 0 ,1,2,3,4. If the total energy of the system is
Er= 6 €. Find the total number of the microscopic states for the distribution of these
particles over the system energy levels keeping the given system conditions.
Solution
4 identical particles
Energy
(10 Joule)
Macroscopic state
4
Er= 6 €
3
Levels
1
E(10 )
k
1
2
3
4.
7
N!
Wk =
no!n;!n2!n3!n4!
SK = kglnwk
Chapter 10 Solutions
MODERN PHYSICS (LOOSELEAF)
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