Blackbody radiation: What is the wavelength of peak emission for a black body at 37°C? (c = 3.0 × 10⁸ m/s, Wien displacement law constant is 2.9 × 10^-3 m ∙ K, σ = 5.67 × 10^-8 W/m² ∙ K⁴)

Question

Quizplus · Accepted Answer

We can use Wien's displacement law, which states that the product of the wavelength corresponding to the peak emission and the temperature of the black body is a constant, given by Wien's displacement law constant. Mathematically, this can be written as:
λ_max*T = constant = 2.9 × 10^-3 m ∙ K
Plugging in the given temperature of 37°C (which is 310 K), we get:
λ_max = (2.9 × 10^-3 m ∙ K) / 310 K
λ_max = 9.4 × 10^-6 m
Converting this to micrometers (µm), we get:
λ_max = 9.4 µm
Therefore, the wavelength of peak emission for a black body at 37°C is 9.4 µm, which corresponds to choice B.

Blackbody Radiation: What Is the Wavelength of Peak Emission for a Black