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

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.

Step 2. Using the density of photons.

$n = \frac{N}{V} n i s t h e d e n s i t y . V = A h A i s t h e a r e a h i s t h e h e i g h t N = n V f_{n e t} = N f_{a v g .} f_{n e t} i s t h e n e t f r e q u e n c y a n d f_{a v g .} i s t h e a v e r a g e f r e q u e n c y . f_{n e t} = n A h f_{a v g .} E_{n e t} = h f_{n e t} E_{n e t} = h n A h f_{a v g .} E_{n e t} = (6.63 \times 10^{- 34}) (450 \times 10^{6}) (A h) (160 \times 10^{9} H z) E_{n e t} = 1.133 \times 10^{- 11} J = 70.72 M e V$