constant

wien displacement constant

Wien's displacement constant, relating peak wavelength to temperature
Value
\(b = 2.897771955 \times 10^{-3}\)metre kelvin
8 related articles · 2 formulas

Description

Wien's displacement constant is the proportionality factor in Wien's displacement law, which states that the wavelength at which a black body emits the most intense radiation is inversely proportional to its absolute temperature. In other words, hotter objects glow with peak emission at shorter wavelengths — a red-hot object is cooler than a white-hot one, which is cooler than a blue-white one. The constant has a value of approximately 2.898 × 10⁻³ meter·kelvin, and it links the macroscopic property of temperature to the microscopic distribution of thermal radiation.

History

Wilhelm Wien derived the displacement law in 1893, before Planck's full quantum theory of black-body radiation. It was a key step toward quantum mechanics, and Wien received the Nobel Prize in Physics in 1911 for his work on thermal radiation.

How it works

The law emerges from the Planck radiation formula, which describes the spectrum of electromagnetic radiation emitted by an ideal black body. By taking the derivative of the spectral radiance with respect to wavelength and setting it to zero, one finds the wavelength of maximum emission. That wavelength, λ_max, equals the constant divided by the temperature T: λ_max = b / T. The constant b encapsulates fundamental physical constants — Planck's constant, the speed of light, and Boltzmann's constant — in a single numerical value.

In practice

It is used in astronomy to estimate the surface temperature of stars from their color, and in infrared thermography to calibrate thermal imaging cameras.

Fun fact

The constant means that a star like the Sun, with a surface temperature of about 5,800 K, peaks in the visible spectrum, while the cosmic microwave background at 2.7 K peaks in the microwave region.

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Formulas

$$\lambda_{\rm max} = \frac{b}{T}$$
The peak wavelength of blackbody radiation is inversely proportional to temperature.
What is in the formula
lambda_maxvariableWavelength at which blackbody emission is maximum — wavelength metre
TvariableAbsolute temperature of the blackbody — temperature kelvin
bconstantWien's displacement constant, relating peak wavelength to temperature — wien displacement constant = 2.897771955e-3 metre kelvin
$$\lambda_{\text{max}} T = b$$
Peak wavelength of blackbody radiation is inversely proportional to temperature.
What is in the formula
\lambda_{\text{max}}variableWavelength of maximum spectral radiance — wavelength metre
TvariableAbsolute temperature of the blackbody — temperature kelvin
bvariableWien's displacement constant — wien displacement constant metre kelvin
bconstantWien's displacement constant, relating peak wavelength to temperature — wien displacement constant = 2.897771955e-3 metre kelvin

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