Question

The universe is filled with photons left over from the Big Bang that today have an average energy of about 4.9 ✕10-4 (corresponding to a temperature of 2.7 K).
What is the number of available energy states per unit volume for these photons in an interval of 4 ✕10-5eV?

Answer 1

Answer:

The number of available energy is $4.820\times10^{45}$

Explanation:

Given that,

Energy $E=4.9\times10^{-4}\ J$

Temperature = 2.7 K

Energy states per unit volume $dE=4\times10^{-5}\ eV$

We need to calculate the number of available energy

Using formula of energy

$N=g(E)dE$

$N=\dfrac{8\pi\times E^2 dE}{(hc)^3}$

Where, h = Planck constant

c = speed of light

E = energy

Put the value into the formula

$N=\dfrac{8\pi\times(4.9\times10^{-4})^2\times4\times10^{-5}\times1.6\times10^{-19}}{(6.67\times10^{-34}\times3\times10^{8})^3}$

$N=4.820\times10^{45}$

Hence, The number of available energy is $4.820\times10^{45}$