Question

Explain the ultraviolet catastrophe. Discuss the conclusions obtained from Planck’s formula under the conditions of short and long wavelength.

Answer 1

To understand this, first you need to understand what is thermal radiation. I will give a brief intro.

Thermal radiation is the electromagnetic radiation emitted by a body as a result of its temperature.

All bodies emit such radiation to their surroundings and absorb such radiation from them.

When body is at higher temperature than the surroundings, then the rate of emission exceeds the rate of absorption. Usually, most of the radiation is emitted in frequencies outside the visible range. At thermal equilibrium rate of emission becomes equal to rate of absorbtion.

Black body radiation.-

When radiation impinges on a body, it is partly is absorbed and partly is reflected. A black body is the one that absorbs all the radiation coming on it, and therefore emits continuous emission of radiation.

Ultravoilet Catastrophe-

The ultraviolet catastrophe states that, an ideal black body at thermal equilibrium will emit radiation in all frequency ranges, emitting more energy as the frequency increases (or when wavelength decreases). By calculating the total amount of radiated energy (i.e., the sum of emissions in all frequency ranges), it can be shown that a blackbody is likely to release an arbitrarily high amount of energy.

Short and long wavelengths-

At short wavelengths, the spectral radiancy(We define the spectral radiancy RT (ν) such as RT (ν) dν is the energy emitted per unit time in the frequency interval [ν, ν + dν] from a unit area of the surface at temperature T) increases and as we move toward more short wavelengths, the radiancy falls sharply(as in that range the blackbody doesn't emit radiations)

At long wavelengths, the radiancy falls of exponentially.