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Chapter 38: Q 45 (page 1115)

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 2.5-m-high ceilings?

Short Answer

Expert verified

Energy is equal to 70.72 MeV

Step by step solution

01

Step 1. Given information is :Universe is filled as 450 photons/cm3Average frequency = 160 GHz

We need to find out the energy from the cosmic microwave background, in MeV, that fills a small apartment that has 95 m2 of floor space and 2.5-m-high ceilings.

02

Step 2. Using the density of photons.

n=NVnisthedensity.V=AhAistheareahistheheightN=nVfnet=Nfavg.fnetisthenetfrequencyandfavg.istheaveragefrequency.fnet=nAhfavg.Enet=hfnetEnet=hnAhfavg.Enet=6.63脳10-34450脳106Ah160脳109HzEnet=1.133脳10-11J=70.72MeV

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