# 6.7: Which wavelength has the greatest spectral irradiance?


The peak of this distribution as a function of wavelength can be found by taking the derivative of Pe(λ) with respect to wavelength, setting the value equal to 0, and solving for the wavelength. The result is the Wien Displacement Law:

$\lambda_{\max }=\frac{2898 \mu \mathrm{m} \mathrm{K}}{T}$

For the sun with a photospheric temperature of about 5780 K, λmax ~ 0.500 μm or 500 nm, which is the color green. However, for Earth with a mid-tropospheric temperature of about 260 K, the peak wavelength is closer to 11 μm, well into the infrared (see below).

Credit: W. Brune

6.7: Which wavelength has the greatest spectral irradiance? is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by William Brune (John A. Dutton: e-Education Institute) via source content that was edited to conform to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.