Blackbody radiation: a whole curve, not one quantum

The experiment measures a distribution

A small hole in a cavity held at one temperature approximates an ideal source: its equilibrium radiation depends on the temperature, not on the details of a particular glowing surface. A spectral measurement asks how much radiation arrives in each band. It does not record the energy of individual emission events.

The apparatus still matters. Turning a detector’s electrical signal into a radiance depends on the aperture geometry, the spectral bandwidth, the thermometer calibration, stray radiation and the detector response. Only after those are controlled can the data be compared with a universal law; the apparent color of a hot object is not enough.

Read the evidence: M. Planck (1901), On the Law of Distribution of Energy in the Normal Spectrum — English transcription NIST SP 250-43, Radiance Temperature Calibrations — spectral radiance and instrument response

Wien’s two laws make different claims

The displacement law says how the spectrum shifts with temperature. Wien’s distribution law claims more: the intensity along the whole curve. When the distribution law fails in one range, that does not overturn every result that bears Wien’s name.

Measurements forced the change. In the introduction to his 1901 paper, Planck cites long-wavelength measurements by Lummer and Pringsheim, and especially by Rubens and Kurlbaum, as showing that the earlier distribution did not hold in general. His later Nobel lecture recalls the same pressure from infrared data. The problem at the time was a proposed curve that disagreed with measured radiation, not only a prediction that was later called a catastrophe.

Read the evidence: M. Planck (1901), On the Law of Distribution of Energy in the Normal Spectrum — English transcription M. Planck (1920), The Genesis and Present State of Development of the Quantum Theory — Nobel lecture

Say which spectrum you mean before comparing peaks

In modern notation, the expression below gives the spectral radiance per unit frequency of an ideal blackbody in equilibrium, in vacuum. Frequency is in hertz and temperature in kelvin; radiance is in watts per square metre per steradian per hertz. The constants are Planck’s constant, the vacuum speed of light and Boltzmann’s constant.

A spectrum per unit wavelength counts radiation in wavelength intervals instead. Relabeling the horizontal axis does not convert the vertical scale. So the peak of the per-wavelength curve generally does not sit at the wavelength that corresponds to the peak of the per-frequency curve. A peak means something only when the convention is stated.

B_\nu(T)=\frac{2h\nu^3}{c^2}\frac{1}{e^{h\nu/(k_{\mathrm B}T)}-1}

Read the evidence: NIST SP 250-43, Radiance Temperature Calibrations — spectral radiance and instrument response

The limiting cases show where the laws differ

At frequencies well below the thermal energy divided by Planck’s constant, expanding the exponential gives the Rayleigh–Jeans limit. At high frequencies, dropping the one subtracted in the denominator gives the Wien approximation. Both are limits of the same expression, not separate curves chosen by eye.

The classical equipartition spectrum keeps rising at high frequency, and its total diverges when it is extended to all frequencies. Planck’s expression suppresses that tail. But Wien’s approximation already worked at short wavelengths, so a test has to reach the range where the candidate laws actually differ. A good match where they agree cannot tell them apart.

Planck’s energy elements were only the start of the photon story

Planck’s counting argument shares finite energy elements among resonators. That step did not yet contain the later picture of free light quanta in scattering. In his retrospective lecture, Planck himself describes how a light quantum propagates as a conceptual question still unresolved at that time.

The Compton article follows energy and momentum transfer in a different apparatus. An equilibrium spectrum and a scattering wavelength shift test different parts of a theory. This article traces the historical evidence. The blackbody Lab is a separately developed simulator, and this article neither introduces nor validates it.