Question

Please answer and explain

15. (4 points) The microwave radiation left over from the Big Bang explosion of the universe has an average energy density of 4*10 J/m. What is the rms value of the electric field from this radiation? Equation (s) to use Final Solution:

Answer 1

T average energy density for CBR = 4 x 10–14 J/m3.
For a region of space where the average energy density = 4 x 10–14 J/m3 the temperature is T(degrees K) =2.73

The energy density in radiation is typically written

u = a T^4

where "a" is called the radiation constant and has the value

a = 7.565767 x 10 ^-16 J m^-3 K^-4

So

u = (7.565767 x 10 ^-16 J m^-3 K^-4)(2.73)^4
u= 4.20245963 × 10-14 m-1 kg s-2 K
This should all be in the infrared region

And the RMS energy density would be

u(RMS) = (.707)(4× 10-14 m-1 kg s-2 K)

u(RMS) = 2.828 x 10 ^-14 J/m3