Question

The universe is filled with photons left over from the Big Bang that today have an average energy of about 2 × 10−4 eV (corresponding to a temperature of 2.7 K). As derived in lecture, the number of available energy states per unit volume for photons is ????(????)????????

Answer 1

Answer:

The number of available energy states per unit volume is $4.01\times10^{48}$

Explanation:

Given that,

Average energy  $E=2\times10^{-4}\ eV$

Photon = $4\times10^{-5}\ eV$

We need to calculate the number of available energy states per unit volume

Using formula of energy

$g(\epsilon)d\epsilon=\dfrac{8\pi E^2dE}{(hc)^3}$

Where, E = energy

h = Planck constant

c = speed of light

Put the value into the formula

$g(\epsilon)d\epsilon=\dfrac{8\times\pi\times2\times10^{-4}\times4\times10^{-5}\times1.6\times10^{-19}}{(6.67\times10^{-34}\times3\times10^{8})^3}$

$g(\epsilon)d\epsilon=4.01\times10^{48}$

Hence, The number of available energy states per unit volume is $4.01\times10^{48}$