Thermal radiation is electromagnetic radiation generated by the thermal motion of charged particles in matter. All matter with a temperature greater than absolute zero emits thermal radiation.
Kirchhoff's Law of thermal radiation states that for an arbitrary body in thermal equilibrium with its surroundings, its emissivity is equal to its absorptivity.
e_lambda / a_lambda = E_lambda (Blackbody)
In simpler terms, good absorbers of a particular wavelength are also good emitters of that same wavelength at the same temperature.
A perfect blackbody is an idealized physical body that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence.
When a blackbody is heated, it emits radiation. The spectral distribution of this radiation (how much energy is emitted at each wavelength) was experimentally determined by Lummer and Pringsheim.
Classical physics attempted to explain the blackbody spectrum using two different approaches:
Derived using thermodynamics, it worked well for short wavelengths (high frequencies) but failed to match the experimental data at long wavelengths.
Based on the principle of equipartition of energy, it assumed radiation in a cavity consists of standing waves. It matched experimental results at long wavelengths but failed spectacularly at short wavelengths.
The Ultraviolet Catastrophe was a prediction of the Rayleigh-Jeans law that an ideal blackbody at thermal equilibrium would emit radiation with infinite power as the wavelength approaches zero (the ultraviolet range).
This was a major failure of classical physics because it contradicted the Law of Conservation of Energy and experimental observations, which showed that emission power actually drops to zero at very short wavelengths.
In 1900, Max Planck solved the blackbody radiation problem by introducing a revolutionary hypothesis:
Where h is Planck's constant (6.626 x 10^-34 J·s) and n is an integer (1, 2, 3...).
By applying statistical mechanics to these quantized oscillators, Planck derived the correct formula for the energy density of blackbody radiation:
This formula perfectly matches the experimental blackbody spectrum across all wavelengths.
Planck's Law is the "master equation" from which all other radiation laws can be derived:
Developed by Meghnad Saha, this formula relates the ionization state of a gas to its temperature and pressure.
It is used in astrophysics to determine the temperatures and chemical compositions of stellar atmospheres by analyzing the absorption lines in stellar spectra. It provides a qualitative idea of how thermal ionization occurs in high-temperature environments like stars.
Tip: If asked to "deduce" Wien's or Rayleigh-Jeans from Planck's, clearly show the limit conditions (e.g., "For lambda approaching infinity..."). This is a high-scoring part of the derivation!