Rayleigh–Jeans law at low frequencies

E31549

approximation classical limit of Planck’s law physical law

The Rayleigh–Jeans law at low frequencies is the classical approximation for blackbody radiation that accurately describes the long-wavelength, low-energy limit of Planck’s radiation spectrum.

Observed surface forms (1)

Surface form	Occurrences
Rayleigh–Jeans law	2

Statements (46)

Predicate	Object
instanceOf	approximation ⓘ classical limit of Planck’s law ⓘ physical law ⓘ
accuratelyDescribes	long-wavelength tail of blackbody spectrum ⓘ
appliesTo	long wavelengths ⓘ low frequencies ⓘ low photon energies ⓘ
associatedWith	ultraviolet catastrophe when extrapolated to high frequencies ⓘ
assumes	classical electromagnetic field ⓘ continuous energy spectrum ⓘ electromagnetic modes have energy kT per degree of freedom ⓘ
context	thermodynamic equilibrium of radiation in a cavity ⓘ
contrastWith	Wien’s law at high frequencies ⓘ
dependsOn	absolute temperature T ⓘ frequency ν ⓘ wavelength λ ⓘ
derivedFrom	classical statistical mechanics ⓘ equipartition theorem ⓘ
describes	spectral radiance of blackbody radiation ⓘ
domain	blackbody radiation ⓘ
failsAt	high frequencies ⓘ short wavelengths ⓘ
field	classical electrodynamics ⓘ statistical physics ⓘ thermal radiation ⓘ
formulaInFrequencyForm	B_ν(T) = (2ν²kT)∕c² ⓘ
formulaInWavelengthForm	B_λ(T) = (2ckT)∕λ⁴ ⓘ
historicalRole	motivated development of quantum theory ⓘ
implies	energy density of radiation grows without bound with frequency in classical theory ⓘ
isApproximationOf	Planck radiation law ⓘ surface form: Planck’s law of blackbody radiation
isClassicalLimitOf	Planck radiation law ⓘ surface form: Planck’s radiation law
isValidInLimit	hν ≪ kT ⓘ λ ≫ hc∕kT ⓘ
namedAfter	James Jeans ⓘ Lord Rayleigh ⓘ
predicts	spectral radiance proportional to temperature T ⓘ spectral radiance proportional to λ⁻⁴ in wavelength domain ⓘ spectral radiance proportional to ν² in frequency domain ⓘ
relatesQuantity	spectral radiance per unit frequency ⓘ spectral radiance per unit wavelength ⓘ
usedFor	approximating cosmic microwave background spectrum at low frequencies ⓘ
usedIn	microwave regime analysis ⓘ radio astronomy ⓘ
usesConstant	Boltzmann constant ⓘ surface form: Boltzmann constant k speed of light c ⓘ
validFor	hν∕kT ≪ 1 ⓘ

Referenced by (3)

Full triples — surface form annotated when it differs from this entity's canonical label.

Lord Rayleigh → knownFor → Rayleigh–Jeans law at low frequencies ⓘ

this entity surface form: Rayleigh–Jeans law

Planck radiation law → reducesTo → Rayleigh–Jeans law at low frequencies ⓘ

Wien displacement law → relatedTo → Rayleigh–Jeans law at low frequencies ⓘ

this entity surface form: Rayleigh–Jeans law