Black-body radiation

Ultraviolet Catastrophe

Wein (1889)

\(E=\sigma T^4\), Stefan-Boltzman Law. \(\sigma=5.67\cdot10^8\). \(U(\nu,T)=A\nu^3\exp(-\beta\nu/T)\) black_body_spectrum.png

Planck (1900)

Oscillators \(\nu\) are quantized by energy such that \(E=n\hbar\nu\), \(n\in\mathbb{N}\).

  • \(U(\nu,T)=\frac{8\pi\nu^2}{c^3}\frac{\hbar\nu}{\exp(\hbar\nu/(k_BT))-1}\)

Author: Christian Cunningham

Created: 2024-05-30 Thu 21:19

Validate