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?
Question
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?
Solution
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.
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