Lecture 3

Blackbody Radiation and the Ultraviolet Catastrophy

I. "Cavity Radiation" = Laboratory Example of an Ideal Thermal Radiator = Black Body Radiator

A.  Black body radiators emit a continuous spectrum with characteristics described by Wien's &  Stefan-Boltzmann laws (see lecture 2) (these laws were inferred by observations of  black body spectra, not derived from theory)
1.  Wien's law:  lmax= constant/T  (lmax=wavelength of the intensity peak; T=absolute temperature of  black body)
2.  Stefan-Boltzmann law:  P/A = sT4(P/A=total radiated power per unit area; T=absolute temperature of  black body)
B. When classical theory is used to calculate the form of a black body spectrum it fits the observations at longer wavelengths, however it diverges exponentally from the observed spectrum at short wavelengths and predicts the non-sensical result that as the wavelength approaches zero the intensity approaches infinity!
1.  the above described breakdown of classical theory for predicting the black body spectrum was called the ultraviolet catastrophy
2.  the classical model assumes the light is radiated from tiny oscillators in the material which can oscillate with a continuous range of energies
3.  Max Plank realized that if the oscillators were constrained to only oscillate at specific energies with a set energy difference between them, the predicted spectrum matched the observed black body spectrum

II. The Plank Curve, a Revolution Begins

A.  Plank's idea of constraining the oscillator energies to discrete values (later called quantizing the energies) was one of the first steps in the road to the theory now known as quantum mechanics or quantum theory
1.  Plank found that to calculate the correct black body spectrum the oscillator energies had to be constrained to discrete values with the energy difference between the discrete values given by:  DE = hf  (DE = energy difference, f = frequency of oscillator, h = Plank's constant = 6.626 x 10-34J s)
2.  Plank's constant was of fundamental importance in the development of quantum theory which describes the quantization of light and matter
B.  The calculated spectrum that resulted from quantizing the oscillors fit the black body spectrum perfectly and is called the Plank curve; both Wien's and the Stefan-Boltzmann laws can be derived from the Plank curve (dervied from theory)