The human eye is most sensitive to 560 nm (green) light. What is the temperature (K) of a black body that would radiate most intensely at this wavelength?

To solve this problem, we can use Wien's Displacement Law, which states that the wavelength of the peak emission of a black body is inversely proportional to its temperature. The formula for this law is:

λ_max * T = b

where:

• λ_max is the wavelength at which the emission is highest,
• T is the absolute temperature of the black body,
• b is Wien's constant, approximately equal to 2.898 x 10^-3 m*K.

We want to find T, so we rearrange the formula to:

T = b / λ_max

Given that λ_max = 560 nm = 560 x 10^-9 m and b = 2.898 x 10^-3 m*K, we substitute these values into the formula to get:

T = 2.898 x 10^-3 m*K / 560 x 10^-9 m = 5175 K

So, the temperature of a black body that would radiate most intensely at 560 nm is approximately 5175 K.