Blackbody+Radiation

=Blackbody Radiation=

Theory
A blackbody is an idealized object that perfectly emits and radiates radiation. Blackbodies were first modeled by Rayleigh and Jeans who built a model that predicted as the frequency increased the radiation intensity would approach infinity.

Rayleigh Jean model for intensity as a function of temperature:

Where I is radiation intensity, T is the object’s temperature in Kelvin, υ is frequency, kb is Boltzmann’s constant and c the speed of light.

Since the area of an intensity vs. frequency graph shows the energy radiated, then any blackbody who emitted at high frequencies would be emitting every larger amounts of energy. Indeed, it was experimentally shown that the Rayleigh Jean model was only accurate for small frequencies.

While working the conundrum, Plank realized that if energy, like mass, was quantized then the Rayleigh Jean model needed a second term. Plank, modified the model to:

(Where h is planks’ constant)

The additional term approaches 1 as the frequency approaches 0, which implies that it does not contradict the Rayleigh Jean model. What it changes is that as the frequency gets larger, the second term gets much smaller. Because an exponential function grows at a faster rate then a power for large frequencies Plank’s model approaches zero, solving the infinite energy problem.

Example Graph

Below is the blackbody radiation for an object at a constant temperature: The observed light color depends on the intensity of the relative abundance of each frequency.

Application
One of the most important applications of blackbody theory is our ability to determine the temperature of a far away object (i.e. star) based on what frequencies of light it emits. Blackbody radiation also allows infrared imaging.

Links
Blackbody Spectrum Simulation: http://phet.colorado.edu/en/simulation/blackbody-spectrum Deeper Blackbody Theory: [] Brief history of quantum mechanics (with Blackbody): []