## Blackbody Radiation

Section 2

#### The Planck Distribution Formula

The Planck distribution formula describes the energy density of blackbody
radiation at a particular temperature and frequency.

The
area of the light blue region is the value of the integral of the Planck
distribution function between the start and end frequencies. It is the integrated
energy density in this range.

**Section 2 Exercises:**

- The default parameters for this page correspond to those given in Example
4-6, page 118 in the text. The function u( f ) in the text field below the graph
is plotted. Is this the same as equation 4-19 (see also equation 9.55
in Thornton & Rex) in the text? Check the result of the example.
- Using five different temperatures below 30,000K, derive a relation between
f
_{max} and T. The temperature can be changed in the text
field and then registered
by pressing the "Do Integral" button. Coordinates in
the graph may be found by left-clicking. Compare your result with the
Wien displacement law.
- Using five different temperatures below 8000K, determine the relationship
between the integral over "all" frequencies and the temperature. Is it a fourth power of the
temperature dependence? The
upper limit of integration should be no larger than 2.0E+15 Hz.
- For the visible range, compare the integrated energy densities for the Sun
and Sirius A.

This exercise was written by Dan Boye.

**© 2000 by Prentice-Hall, Inc. A Pearson Company**