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:

1. \(h\) (h) is planck.

2. \(c\) (c) is speed_of_light.

3. \(k_\text{B}\) (k_B) is boltzmann_constant.

Conditions:

1. The black body is isolated from the environment.

2. \(h \nu \gg k_\text{B} T\), i.e. photon energy is much greater than thermal energy.

Links:

1. 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:

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