The cosmic microwave background radiation is light left over from the Big Bang t

Question

The cosmic microwave background radiation is light left over from the Big Bang that has been Doppler-shifted to microwave frequencies by the expansion of the universe. It now fills the universe with 450 photons/cm3 at an average frequency of 160 GHz.

How much energy from the cosmic microwave background, in MeV, fills a small apartment that has 95 m2 of floor space and 2.8-m-high ceilings?

Problem 38.45 Problem 38.45 The cosmic microwave background radiation is lightleft over from the Big Bang mat has been Doppler-hihed to microwave It now fls the by the expansion of the universe. universe with 450 photons/ at an average frequency of 160 GHz. Part A E. 793.611 Submit Incorrect. Try Again: 5 attempts remaining

Explanation / Answer

A = area of floor = 95

h = height = 2.8 m

V = Volume of apartment = A h = 95 x 2.8 = 266 m3 = 266 x 106 cm3

n = number of photons per unit volume = 450

N = total number of photons in apartment = n V = 450 x 266 x 106

f = frequency = 160 x 109 Hz

energy is given as

E = N h f

E = (450 x 266 x 106) (6.63 x 10-34) (160 x 109)

E = 1.27 x 10-11 J

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