In the first part of the fifth video of ‘Introduction to Quantum Mechanics’, we will discuss the derivation of Planck’s law. In the previous video, we learned what is a black body and how Rayleigh and Jeans, and Wein failed to explain the black body spectrum. They considered blackbody radiation to be made of standing waves inside a cubical box. Using classical statistical mechanics, they calculated the number of modes of vibrations or the number of standing waves inside a frequency interval. They associated average energy to each of the standing waves – kT where k is the Boltzmann’s constant and T is the temperature.
By multiplying this average energy with the number of modes, we get the energy density – the Rayleigh-Jeans law. However, the Rayleigh-Jeans law can only explain the black body spectrum at low frequencies. It blows up at high frequencies. This is known as the Ultraviolet Catastrophe.
The black body radiation spectrum was finally explained by German Physicist Max Planck. He assumed that the standing waves can only have a particular energy, in the multiples of hv where h is the Planck’s constant and v is the frequency. Using this assumption, Max Planck mathematically derived Planck’s radiation law that could easily explain the shape of the black body spectrum. We can also derive the Rayleigh-Jeans Law, Wein’s law, and Stefan’s law from Planck’s radiation law. This will be covered in the second part of the video.