Blackbody Radiation

Snapshot from the VRML Blackbody Demo

The equation for blackbody radiation (the Planck equation) is:

F lambda = 2 h c² lambda ^-5 / (exp(hc/k lambda T) - 1).

or, combining the constants:

F lambda = c₁ lambda ^-5 / exp(c₂ / lambda T) - 1),

where c₁ = 2 hc² = 3.7419 × 10^-5 erg cm² s^-1 [ lambda in cm]
and c₂ = hc/k = 1.4288 cm °K.

To allow you to explore the properties of this function and to try to make them a little more tangible to you, we have constructed a VRML (Virtual Reality Markup Language) demonstration which shows you the shape of the function for temperatures ranging from 1000°K to 50000°K for a range of wavelengths from the x-ray through the radio ranges. Lines of a dark reddish color across the model show the location of lines of constant temperature. "Stickpins" on the red side of the distribution give the values of the temperature for 5 of these curves so that you can see the effect of varying the temperature. (The temperature save is linear while the wavelength and intensity scales are logrithmic.) The line running down the ridgeline of the model is computed from the Wien Displacement Law and located the wavelength of the peak emmission as a function of temperature.

Within this VRML "world" you will find items that supply "anchors" or links to World Wide Web pages that derive the approximate forms for the intensities on the blue side of the distribution (the Wien Distribution) and the red side (the Rayleigh-Jeans Distribution) as well as the Wien Displacement Law for the position of the peak of the distribution as a function of temperature and the Stefan-Boltzman Law for the total energy emitted by an object at a given temperature. These links can be activated either through the signposts or the floating buttons. We hope soon to have some interactive exercises available as well.

Unfortunately, at this stage of the development of VRML, not all browsers have the same capabilities. We will try to make recommendations of the best browsers to use for each platform. If your browser supports multiple "cameras," we have supplied 4: a Front view, a Blue side view, a Red side view, and a Top view. These will allow you to quickly switch your viewpoint without having to carefully travel from one point to another. Check your Navigation options to see whether these viewpoints are available to you. In any case, you should be able to walk or fly around the model and to manipulate it but flipping it over and around to see it from different perspectives.

We hope you enjoy this exercise! You may follow the link now to

our VRML Blackbody Model.

Note: The notation exp(x) is another way of writing e^x. In this case I used this form because of the complexity of the term in the exponent, the difficulty of properly creating it in HTML (the language used to write these pages), and the relatively low resolution of computer screens.

Wien Distribution
Rayleigh-Jeans Distribution
Wien Displacement Law
Stefan-Boltzmann Law
Constants

This VRML + HTML package on Blackbody emission was constructed by Karen M. Strom. Contact your local instructor for help if it is used as part of your class.

kstrom@hanksville.org