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### 6.6 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 *P _{e}*(

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

**Wien Displacement Law**:

$${\lambda}_{max}=\frac{2898\text{\hspace{0.17em}}\mu \text{m}\text{\hspace{0.17em}}\text{K}}{T}$$

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