Spectral energy density at high frequency limit¶

Wien’s approximation, also known as Wien distribution law, describes the spectrum of blackbody thermal radiation. It accurately describes short-wavelength (i.e. high-frequency) spectrum of thermal emission, but fails to do that for long-wavelength (i.e. low-frequency) emission.

Notation:

\(h\) (h) is planck.
\(c\) (c) is speed_of_light.
\(k_\text{B}\) (k_B) is boltzmann_constant.

Conditions:

The black body is isolated from the environment.
\(h \nu \gg k_\text{B} T\), i.e. photon energy is much greater than thermal energy.

Links:

Wikipedia.

spectral_energy_density¶: spectral_energy_density.

Symbol:: w_f
Latex:: \(w_{f}\)
Dimension:: energy/(frequency*volume)

radiation_frequency¶: temporal_frequency of the radiation.

Symbol:: f
Latex:: \(f\)
Dimension:: frequency

equilibrium_temperature¶: Equilibrium temperature of the ensemble.

Symbol:: T
Latex:: \(T\)
Dimension:: temperature

law¶

w_f = 8 * pi * h * f^3 / c^3 * exp(-h * f / (k_B * T))

Latex:: \[w_{f} = \frac{8 \pi h f^{3}}{c^{3}} \exp{\left(- \frac{h f}{k_\text{B} T} \right)}\]