## Blackbody Sources

A hot material, such as an electrically-heated filament in a light bulb, emits a continuum spectrum of light. This light is called blackbody radiation. The spectrum is approximated by Planck's radiation law for blackbody radiators:

and is the light power as a function of light frequency, , k is the Boltzmann constant, T is temperature in K, h is Planck's constant, and c is the speed of light.

The most common incandescent lamps and their wavelength ranges are:
tungsten filament lamp (a.k.a. a light bulb) : 350 nm - 2.5 µm
glowbar : 1 - 40 µm
Nernst glower : 400 nm - 20 µm

Tungsten lamps are used in visible and near-infrared (NIR) absorption spectroscopy and the glowbar and Nernst glower are used for infrared spectroscopy.

The following figure shows an example of the light distribution of a heated object at four different temperatures. A light bulb operates at approximately 4000 K, so you can see that it emits mostly at longer wavelengths and decreases through the visible region.

Three spreadsheets are provided that differ only in transforming the x axis in wavelength, frequency, or energy (wavenumbers).

To use the spreadsheets simply enter one to four temperatures (in K) in the shaded cells. To see curves for a different range of x values, refill the column of 200 current values on the Raw Data worksheet with new values.

## Self-study Exercises

• Using a calculator or your own spreadsheet formulas, fill in the blank spaces in the following table.