The Earth has a surface temperature of 300 K.The wavelength at which the Earth is brightest is 10 microns.The dayside of Mercury is brightest at 4 microns.Which of the following is closest to the temperature on the dayside of Mercury?

Question

Quizplus · Accepted Answer

According to Wien's displacement law, the wavelength at which a blackbody emits the most radiation is inversely proportional to its temperature. Thus, for a blackbody emitting most strongly at 10 microns (like the Earth), we have:

λ_max = b/T
where b is Wien's displacement constant. Solving for T, we find:

T = b/λ_max = 2.898 x 10^-3 m K / 10 x 10^-6 m = 289.8 K

For a blackbody emitting most strongly at 4 microns (like the dayside of Mercury), we have:

λ_max = b/T
Solving for T, we find:

T = b/λ_max = 2.898 x 10^-3 m K / 4 x 10^-6 m = 724.5 K

Therefore, the closest choice is 750 K.

The Earth Has a Surface Temperature of 300 K