Draw an energy level diagram for a. nonrelativistic

An Introduction to Thermal Physics | 1st Edition | ISBN: 9780201380279 | Authors: Daniel V. Schroeder

Problem 14P Chapter A

An Introduction to Thermal Physics | 1st Edition

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An Introduction to Thermal Physics | 1st Edition | ISBN: 9780201380279 | Authors: Daniel V. Schroeder

An Introduction to Thermal Physics | 1st Edition

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Problem 14P

Draw an energy level diagram for a. nonrelativistic particle confined inside a three-dimensional cube-shaped box, showing all states with energies below 15. (h2/8mL2 ) . Be sure to show each linearly independent state separately, to indicate the degeneracy of each energy level. Does the average number of states per unit energy increase or decrease as E increases?

Step-by-Step Solution:

Solution 14P

Step 1 of 2</p>

The energy for a non relativistic particle in a three dimensional box is

= (

Where, = Planck’s constant , is the mass of the particle, is the length of the cubic box ,\

,,=

All states with energies below 15 are as follows

For () = (1,1,1) the energy of the particle is

=  3

For () = (1,1,2) (1,2,1) (2,1,1) the energy of the particle is

=  6

For () = (1,2,2) (2,1,2) (2,2,1) the energy of the particle iss

=  9

For () = (1,1,3) (1,3,1) (3,1,1) the energy of the particle is

=  11

For () = (2,2,2) the energy of the particle is

=  12

For () = (1,2,3) (1,3,2) (2,1,3) (2,3,1) (3,1,2) (3,2,1) the energy of the particle is

=  14

is as shown in the fig.

Step 2 of 2

Chapter A, Problem 14P is Solved
Textbook: An Introduction to Thermal Physics
Edition: 1st
Author: Daniel V. Schroeder
ISBN: 9780201380279

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