Thermal de Broglie Wavelength - Massless Particles

Massless Particles

For a massless particle, the thermal wavelength may be defined as:

where c is the speed of light. As with the thermal wavelength for massive particles, this is of the order of the average wavelength of the particles in the gas and defines a critical point at which quantum effects begin to dominate. For example, when observing the long-wavelength spectrum of black body radiation, the "classical" Rayleigh–Jeans law can be applied, but when the observed wavelengths approach the thermal wavelength of the photons in the black body radiator, the "quantum" Planck's law must be used.

The massless thermal wavelength is derived from the more general definition of the thermal wavelength due to Yan (Yan 2000) described below.