The background microwave radiation, discovered in 1965 by Penzias and Wilson, has its peak intensity at a wavelength of 1.06 mm. What blackbody temperature does this wavelength imply for the universe? (σ = 5.670 × 10^-8 W/m² ∙ K⁴, Wien displacement law constant is 2.90 × 10^-3 m ∙ K) A) 2.7°C B) -270°C C) 0.0027 K D) 0.00°C E) -2.7°C

Question

Quizplus · Accepted Answer

According to Wien's Law, the peak wavelength of a blackbody radiator is inversely proportional to its temperature. The formula for Wien's displacement constant is:

λmax = b/T

where λmax is the peak wavelength, b is Wien's displacement constant, and T is the temperature in kelvins.

Rearranging this equation, we get:

T = b/λmax

Substituting the values given, we get:

T = (2.90 × 10^-3 m ∙ K) / (1.06 × 10^-3 m) = 2.74 K

This is the temperature of the background microwave radiation, which is equivalent to -270.26°C or -454.47°F. Therefore, the best choice is B.

The Background Microwave Radiation, Discovered in 1965 by Penzias and Wilson