# 6.7: Which wavelength has the greatest spectral irradiance?

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- 3388

The peak of this distribution as a function of wavelength can be found by taking the derivative of * P_{e}*(

*) with respect to wavelength, setting the value equal to 0, and solving for the wavelength. The result is the*

*λ***Wien Displacement Law**:

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

For the sun with a photospheric temperature of about 5780 K, * λ_{max}* ~ 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