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Planck distribution
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Spectrum of thermal radiation.
u(ν) ∝ ν³/(e^{hν/kT}−1)The spectral energy density of blackbody radiation is u(ν) ∝ ν³/(e^{hν/kT} − 1), which cures the ultraviolet catastrophe.
At low frequency it matches Rayleigh–Jeans; at high it falls exponentially.
Led to the birth of quantum physics.
In more detail
Planck's distribution describes the spectrum of blackbody radiation, with energy per mode proportional to frequency divided by an exponential factor. It resolved the ultraviolet catastrophe of classical theory.
Real-world uses
- Estimating temperatures of stars and planets from their spectra.
- Designing infrared sensors using blackbody spectra.
- Astronomers compare observed spectra of stars with the Planck distribution to estimate their surface temperatures.
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Frequently asked questions
What was the ultraviolet catastrophe?
Classical theory predicted infinite energy at high frequencies, which did not match experiments.
How did Planck resolve it?
By proposing that energy is exchanged in discrete packets proportional to frequency.
What did Planck's distribution solve?
It explained the spectrum of blackbody radiation, which classical physics could not describe at short wavelengths.
Related topics in Kinetic Theory & Statistical Physics
Specific heat of solids · Debye model · Photon gas · Random walks · Equation of state of ideal gas in statistical terms · Heat conduction at microscopic level