# PlanckRadiationLaw

PlanckRadiationLaw[temperature,λ]

returns the spectral radiance for the specified temperature and wavelength λ.

PlanckRadiationLaw[temperature,f]

returns the spectral radiance for the specified temperature and frequency f.

PlanckRadiationLaw[temperature,property]

returns the value of the property for the specified temperature.

PlanckRadiationLaw[temperature,{λ1,λ2}]

returns the integrated result of the spectral radiance over the wavelength range λ1 to λ2.

PlanckRadiationLaw[temperature,{f1,f2}]

returns the integrated result of the spectral radiance over the frequency range f1 to f2.

# Details

• Inputs temperature, λ, and f should be Quantity objects.
• Properties include:
•  "Color" color of the peak wavelength "MaxFrequency" peak frequency "MaxWavelength" peak wavelength "MeanFrequency" average frequency "MeanWavelength" average wavelength "SpectralPlot" plot of spectral radiance versus wavelength
• Spectral radiance is returned in SI units.

# Examples

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## Basic Examples(2)

Find the spectral radiance:

Determine spectral radiance by frequency:

Examine the shape of spectral radiance at Quantity[100,"DegreesCelsius"]:

Find the average wavelength:

Discover the color of the peak wavelength:

## Scope(3)

Explore all the properties of PlanckRadiationLaw:

Find the peak wavelength for 6000 K and its color:

Determine the peak frequency at 6000 K:

Find the integrated spectral radiance over wavelength or frequency:

## Applications(5)

Calculate the maximum radiance as a function of wavelength:

Calculate the maximum radiance as a function of frequency:

Note that the peak values do not correspond to the same wavelength of light:

Examine how the spectral radiance varies as a function of frequency:

Use the directional temperature, corrected for relativistic effects, to see how the peak for spectral radiance is shifted to longer wavelengths for an object moving at relativistic speeds:

Demonstrate Wien's displacement law, that the peak wavelength is inversely proportional to the temperature:

Find the radiant exitance by approximating the integral of Planck's law by integrating the dominant part of the spectrum and using Lambert's cosine law to derive the angular factor for a point on the black body's surface:

Divide by the fourth power of the temperature to find the StefanBoltzmann constant:

## Properties & Relations(1)

The formula used by PlanckRadiationLaw is the same as presented by FormulaData:

## Neat Examples(2)

Compare Planck's radiation law to Wien's distribution law:

Compare Wien's distribution law to the RayleighJeans law and Planck's radiation law:

In a micrometer-sized box, quantum effects cause the minimum frequency possible to be the following:

Plot the energy density within this box, accounting for the finite size effect relative to a blackbody in an infinite cavity:

Wolfram Research (2014), PlanckRadiationLaw, Wolfram Language function, https://reference.wolfram.com/language/ref/PlanckRadiationLaw.html (updated 2016).

#### Text

Wolfram Research (2014), PlanckRadiationLaw, Wolfram Language function, https://reference.wolfram.com/language/ref/PlanckRadiationLaw.html (updated 2016).

#### CMS

Wolfram Language. 2014. "PlanckRadiationLaw." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2016. https://reference.wolfram.com/language/ref/PlanckRadiationLaw.html.

#### APA

Wolfram Language. (2014). PlanckRadiationLaw. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/PlanckRadiationLaw.html

#### BibTeX

@misc{reference.wolfram_2023_planckradiationlaw, author="Wolfram Research", title="{PlanckRadiationLaw}", year="2016", howpublished="\url{https://reference.wolfram.com/language/ref/PlanckRadiationLaw.html}", note=[Accessed: 01-October-2023 ]}

#### BibLaTeX

@online{reference.wolfram_2023_planckradiationlaw, organization={Wolfram Research}, title={PlanckRadiationLaw}, year={2016}, url={https://reference.wolfram.com/language/ref/PlanckRadiationLaw.html}, note=[Accessed: 01-October-2023 ]}