12.2.6 UV Catastrophe & Black-Body Radiation

What is Black-Body Radiation?

• A perfect black body is defined as:

A theoretical object that absorbs all of the radiation incident on it and does not reflect or transmit any radiation

• Since a good absorber is also a good emitter, a perfect black body would be the best possible emitter too
• The spectrum of electromagnetic radiation that would be emitted from this hypothetical object is called the black-body spectrum
  • This changes depending on the temperature of the black-body
  • A common example of this is that a cube of metal at room temperature emits invisible infrared radiation
  • When heated to 3000 K, however, it emits a large amount of visible light and we see it glow red, orange or white

A graph showing the spectrum of radiation emitted by a black-body at different temperatures

Each curve is for the same black-body at different temperatures. The peak of each line shows the wavelength of radiation emitted with the most intensity.

• For cooler objects, the wavelength of radiation emitted at the highest intensity is in the infrared range
  • As the object's temperature increases, shorter wavelengths become the most intensely emitted 

What was the Ultra-Violet Catastrophe?

• This dramatically-named event came from a disagreement with experimentally measured black-body spectra and the spectra predicted by classical physics
  • Through experiments with objects very close to being perfect black-bodies, their emission spectra looked much like the diagram above
  • By treating electromagnetic radiation as a wave, however, the spectra were theoretically predicted to emit an infinite amount of ultra-violet as the temperature of the object increased 

Graph showing spectrum from experiment and wave theory's prediction

A big discrepancy between sound experimental data and the currently accepted theory meant that the theory was incorrect and needed to be adapted or completely replaced

• Max Planck addressed this problem by coming up with mathematical descriptions (the details of which you will not be examined on) for the emission and absorption occurring within a black-body 
• In this description, he made his theory fit experimental data
• Oscillators were responsible for emitting electromagnetic radiation, and he assumed the energy emitted was quantised
  • This meant it could only be emitted in integer multiples of these packets (or quanta) of energy
• Therefore, the energy emitted by an oscillator of frequency f  was given as:

• • n  represents the integer multiple of the packet hf
  • h  is Planck's constant and has the value of 6.63 × 10⁻³⁴ J s
• This allowed Planck to develop a theory that explained the observed spectra of almost-perfect black-bodies