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)