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The Boltzmann distribution, also known as the Gibbs or Maxwell-Boltzmann distribution, describes the probability of a particle being in a particular energy state E in a system at thermal equilibrium at absolute temperature T. It’s a fundamental concept in statistical mechanics.

The Rayleigh-Jeans law is an equation that describes the spectral radiance of electromagnetic radiation as a function of frequency for a black body in equilibrium at a given temperature. The law is applicable at long wavelengths (low frequencies) and is particularly accurate for temperatures found in everyday life, but it breaks down at short wavelengths (high frequencies). This failure at short wavelengths led to the ultraviolet catastrophe in classical physics, which was later resolved by Max Planck’s introduction of quantum mechanics.

Classically, we observe and deduce that the energy level is proportional to the frequency squared, then it leads to Rayleigh-Jeans law that intensity is proportional to the temperature.

Compton scattering is a phenomenon observed in the scattering of high-energy photons, primarily X-rays and gamma rays, by electrons. It provides experimental evidence for the particle-like properties of light (or electromagnetic radiation) and is an important concept in the realm of quantum mechanics.