Introduction to Black Body Radiation

A black body is a theoretical object that perfectly absorbs all electromagnetic radiation that falls on it. At thermal equilibrium, it emits radiation at the same rate at which it absorbs it. While perfect black bodies don't exist in nature, scientists have created close approximations for study.

One practical approximation of a black body is a hollow cavity with a small opening. When radiation enters through this opening, it undergoes multiple reflections inside the cavity, making the probability of its escape minimal.

The Classical Theory Problem

The classical theory of electromagnetic radiation, known as the Rayleigh-Jeans Law, proposed that the intensity of black body radiation was directly proportional to its frequency. This theory predicted that as frequency increased, the energy emitted would increase without limit.

This prediction led to what became known as the "ultraviolet catastrophe." According to classical physics, a black body would emit an infinite amount of energy at high frequencies - a clear violation of the law of conservation of energy. Experimental results showed this prediction was incorrect, particularly at high frequencies in the ultraviolet region.

Planck's Revolutionary Solution

Max Planck resolved this paradox in 1900 by introducing a radical concept: energy is not continuous but comes in discrete packets called quanta. The energy of a single quantum is given by:

$E = hf$

where:

The total energy of radiation is therefore:

$E = nhf$

where $n$ is an integer known as the quantum number.

Wien's Displacement Law

Wilhelm Wien built upon Planck's work by describing how the peak wavelength of black body radiation varies with temperature. Wien's displacement law states that:

$\lambda_{max} = \frac{b}{T}$

where:

Real-World Applications

Wien's displacement law explains various natural phenomena: