Cavity Radiation - Blackbody Spectrum - Rayleigh Jeans law - Full derivation of Rayleigh-Jeans law

This video presents a detailed discussion of cavity radiation and how it is related to the study of the blackbody spectrum and how it led to the Rayleigh-Jeans law. This video presents a complete derivation of the Rayleigh-Jeans law. In the historical development of quantum mechanics, Planck's radiation law is considered to be the origin of the quantum theory. But the events and experiments leading to the development of quantum theory is equally significant to understand the quantum theory completely and its origins.This video intends to cover this part. This video begins with an introduction to the thermal radiation and blackbodies. Then it moves on to introduce cavity radiation and how a cavity containing a small hole acts as a blackbody emitting blackbody spectrum. The details of how it is actually the surface of the hole in the cavity that acts as the blackbody is discussed in great detail eventually linking the emerging spectrum to the blackbody spectrum.
The video then proceeds to discuss the derivation of the Rayleigh-Jeans law beginning from its basic assumptions and detailed methodology to arrive at the final expression that we know as the Rayleigh-Jeans law. Rayleigh and also Jeans, during the nascent stages of the 20th century gave a classical theory to account for the spectrum observed from blackbody radiation. The methodology employed by Rayleigh and Jeans involved classical ideas from the Electromagnetic theory, the kinetic theory and some geometrical arguments for the assumed shape of the cavity. They began with the assumption that the cavity filled with electromagnetic radiation is composed of standing waves with nodes at the walls of the cavity. The walls of the cavity which are kept at a temperature T is the only temperature defined for the system thereby attributing this as the temperature for the radiation in the cavity. Then a count of the number of waves in a given range of frequencies for the electromagnetic waves present in the cavity was made. This number per unit volume of the cavity was calculated. This factor was multiplied by the average energy per standing wave of the cavity to obtain the energy density of the cavity radiation at temperature T in a given frequency range nu and nu plus d(nu). The standing waves could be considered as a system of large number of similar entities in thermal equilibrium so that classical kinetic theory calculations could be used to arrive at the average energy of kT per wave. Classical kinetic theory makes definite predictions about the average kinetic energy per wave per degree of freedom as half kT where k is the Boltzmann constant. The average total energy of such a system with one degree of freedom is kT (which is twice that of the average kinetic energy) since the system has only one degree of freedom such as a pendulum or a coil spring. This could be applied to the case of the electromagnetic waves in the cavity as their only degree of freedom is their amplitude. Thus the average total energy per wave in the system of electromagnetic standing waves in the cavity is taken to be kT and used in the calculation of Rayleigh-Jeans law. This results in the expression for the energy density of waves forming the radiation in the cavity. Thus the video presents a detailed discussion of all the above ideas and arrives at the final expression of Rayleigh-Jeans law. Then the disagreement of the Rayleigh - Jeans law with the experimental curve obtained for the blackbody spectrum is discussed including the concept of ultraviolet catastrophe. The video comes to a conclusion by indicating that Max Planck who worked on the cavity radiation could come out of the inhibitions of the classical ideas of his day and could propose a groundbreaking assumption that is the cornerstone of a revolutionary quantum theory that led to the birth of modern subject of quantum mechanics.