Question

What is rayleigh-jeans law on black body radiation and 'ultraviolet catastrophe'?

Answer 1

Rayleigh-jeans law:

1. A black body in thermal equilibrium will emit radiation in all frequency ranges, and as the frequency increases, so does the energy of the radiation emission.
2. The black body is a matter that can absorb and emit all energy that comes into contact with it.
3. The greater the intensity, the higher the temperature of the matter.
4. The intensity and energy of the emitted radiation increase as the temperature rises.
5. As the temperature rises, the higher intensity shifts to the lower wavelength side.

Mathematically, this law can be represented as:

$\mathrm{\rho }(\mathrm{\lambda },\mathrm{T})=\frac{2\mathrm{ckbT}}{{\mathrm{\lambda }}^4}$

Here,

$T$ is the temperature.

$\lambda$ is the wavelength.

$c$ is the speed of light in a vacuum.

$k$ is Boltzmann's constant.

Ultraviolet catastrophe:

1. Rayleigh's law predicts infinite intensity as wavelength tends to $0$.
2. Because intensity is a finite quantity, the impossible event of infinite intensity predicted by the wave model of electromagnetic radiation was dubbed the 'ultraviolet catastrophe.'