The cosmic microwave background peaks at a wavelength of about 1 mm, and the universe has a temperature of about 3 K. If the microwave background peaked at a wavelength of 10 micrometers, what would its temperature be? (Hint: see Cosmic Calculations 5.1 and 17.1)

Question

Quizplus · Accepted Answer

The relationship between the peak wavelength of blackbody radiation and temperature is given by Wien's displacement law, which states that the product of the peak wavelength and the temperature is a constant. If the peak wavelength decreases from 1 mm to 10 micrometers (a factor of 100), the temperature must increase by the same factor to maintain the constant product. Therefore, the temperature increases from 3 K to 300 K.

The Cosmic Microwave Background Peaks at a Wavelength of About