This discrepancy between the theoretical conclusion and the experimental
result is called “ULTRAVIOLET CATASTROPHE”. As per the equation, black
body radiates enormously in the shorter wavelength side, but practically black
body chiefly radiates in IR or visible range which is the longer wavelength
region of the spectrum.
This wrong prediction in the radiation emitted by the body is called
In order to explain the energy distribution in the complete spectrum of a
blackbody radiation, Max Ludwig Planck in 1900 put forward the quantum
theory of radiation. For deriving the equation Planck made certain assumption
based on Quantum mechanical consideration.
Assumptions of Quantum theory of radiations are,
1. The walls of the blackbody consist of a very large number of electrical
oscillators. Each oscillator vibrates with a frequency of its own.
2 Energy is absorbed or emitted by a blackbody in a discrete manner, in the
form of small packets called quanta.
3. Each quantum has energy that depends only on the frequency of the
radiation and is given by
E = nh
Where h is a constant known as Plank’s constant = 6.625 x10-34 J-sec and
4. An oscillator may gain or lose energy when it absorbs or emits radiation of
frequency υ given by
υ = ΔE/h
Where, ΔE is the difference in energies of the oscillator before and after
emission or absorption.
Based on the above assumptions, Planck derived an equation which
successfully explained the entire spectrum of blackbody radiation.
The equation is given by
5 h / kT
Planck’s law explains the spectrum of blackbody radiation successfully in both
the shorter wavelength and longer wavelength regions.
Department of Physics