In the previous lecture we deduced Rayleigh-Jean’s density energy for a Black Body radiation. A Black Body as we understand, is a body that radiates all the energy that it absorbs. But Rayleigh-Jean’s equation allows for the absorption of energy in all frequencies available of e-m waves, and as we saw, since the packed density of energy in an infinitesimal interval of density of frequency, is directly proportional to the frequency to the second power, the equation allows for an infinite density of e-m energy-waves in the Black Body that is counterintuitive. Max Planck, based on experimental data, solved the problem. That the energy density goes no infinity as the frequency increases, is the result of a classical prediction, but the experiment shows that the energy density remains finite for a particular temperature of the body. To solve this discrepancy, Planck considered an alternative by not taking the equipartition of energy (fundamental for the classic theory) in consideration. The classic equipartition of energy, considered that the average kinetic energy of a single molecule, is given by 1/2(kT), where k is the Boltzmann constant, and T is the absolute temperature of the body. The origin of the equipartition law is in the classical kinetic theory called the Boltzmann distribution P(E)=[e^-(E/kT)]/(kT), where P(E)dE gives the probability to find a system with energy between E and E+dE.
Planck concluded that the average energy is a function of the frequency, in contrast to the equipartition energy law, that states that the average energy is independent of the frequency.
In the next video I will develop Planck’s solution to the ultraviolet catastrophe.