Wien's displacement law

Also called Wien's law

Wien's law says the peak wavelength a blackbody emits is inversely proportional to its absolute temperature, λmax = b/T, where Wien's constant b = 2.90 x 10^-3 m K. A hotter body peaks at a shorter wavelength.

The AP Physics 2 CED calls it Wien's law, without the word displacement, so both names lead to the same statement. Essential knowledge 15.4.A.3.ii: the peak wavelength emitted by a blackbody, meaning the wavelength at which it emits the greatest amount of radiation per unit wavelength, decreases with increasing temperature.

λmax=bT\lambda_{\max} = \frac{b}{T}

Printed in the Modern Physics group of the AP Physics 2 sheet. The constants table lists Wien's constant as b=2.90×103 mKb = 2.90 \times 10^{-3}\ \mathrm{m \cdot K}, and TT is in kelvin.

Read the word peak precisely. It marks the maximum of intensity per unit wavelength plotted against wavelength (15.4.A.3), not the only wavelength present. A blackbody emits a continuous spectrum, and this law says where that spectrum is tallest.

Inverse, and only inverse. Double the temperature and the peak wavelength halves. A body at 2900 K2900\ \mathrm{K} peaks at (2.90×103)/2900=1.0×106 m(2.90 \times 10^{-3})/2900 = 1.0 \times 10^{-6}\ \mathrm{m}, in the infrared. At 5800 K5800\ \mathrm{K} the peak sits at 5.0×107 m5.0 \times 10^{-7}\ \mathrm{m}, inside the visible band.

It answers a different question from its partner. Wien's law moves the peak sideways along the wavelength axis; the Stefan-Boltzmann law gives the total power leaving the surface. Heating a body does both at once, and a question describing a change of colour wants this one.

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