Cosmology: 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

The correct blackbody temperature implied by the given wavelength can be found using Wien's displacement law, which states that the product of the peak wavelength of blackbody radiation (in meters) and the temperature (in Kelvin) is a constant (2.90 × 10^-3 m∙K). Rearranging this for temperature (T) gives T = (2.90 × 10^-3 m∙K) / (1.06 mm or 1.06 × 10^-3 m), which results in approximately 2.73 K. Since the question asks for a temperature in Celsius and 0°C is equivalent to 273.15 K, a temperature of 2.73 K is equivalent to approximately -270°C.

Cosmology: the Background Microwave Radiation, Discovered in 1965 by Penzias