According to the Rayleigh-Jeans’ Law,
where B is the power emitted let unit area per unit solid angle per unit wavelength for a given wavelength and temperature, T is the temperature of the body, lambda is the wavelength of radiation emitted by the body, and k is Boltzmann’s constant. This classical physics equation can be used to determine how much energy per second is emitted from a body due to its temperature.
The Rayleigh-Jeans Law is derived by first considering the classical equation E=½kT, where E is the average energy per degree or freedom per particle in a body. The derivation of that equation is a standard A-Level derivation.
In classical physics, every degree of freedom will have equal energy. By some clever geometry, Eq 1 can be derived from summing all the possible E=½kT states.
Rayleigh-Jeans Law works at low temperatures, and accurately predicts the spectral radiance of a body, but at high temperatures it breaks down and makes predictions such as an infinite intensity of ultraviolet radiation.
What is interesting is that Max Planck solved the ultraviolet catastrophe in 1900, but the problem didn’t acquire the name ‘ultraviolet catastrophe‘ until 1911 when Paul Ehrenfest used the term in a letter he wrote to Albert Einstein. I find that interesting. Max Plank solved the problem over a decade before it had even been given its catchy name.
Max Plank solved the problem over a decade before it had even been given its catchy name
Max Planck solved the ultraviolet catastrophe by challenging the assumption that all vibrational modes with a body were possible, and that energy was a continuum shared between an infinite number of modes. Instead, Max Planck proposed that only certain discreet vibrational modes were possible, corresponding to a discrete array of possible wavelengths of electromagnetic radiation emitted from a body.
I’ll share video about the mathematics of this when I get a chance to record it.
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