Frimus said:I recommend a textbook by Barbara Ryden https://www.amazon.com/dp/1107154839/?tag=pfamazon01-20. In section "2.5 Cosmic Microwave Background" she makes calculations you are asking about and comes to a conclusion that "...there are about 411 CMB photons per cubic centimeter of the universe at the present day."
Chalnoth said:This link might help:
https://en.m.wikipedia.org/wiki/Photon_gas
If you want to drive the result yourself, use E=hv for the energy of a photon of a given frequency to do the appropriate integral.
I'm not sure what level the question is being asked. The photon gas wiki page has the number of photons per volume as a function of temperature directly. You could just use that formula and get the answer straight away.rano jojo said:Thank you, but i how i can get the frequency and then how i can find the number of the photons? just i am confused
Use E=mc^2 n another relation in which uses T of this relation~rano jojo said:i know that the total energy density of a blackbody radiation is
E= 4 segma/C * T^4
so how i can use this to find the number of the CMB photons in 0.25 litre?
The number of CMB photons in 0.25-litre can be estimated by using the formula:
N = (8πkT³/3h³c³)V,
where N is the number of photons, k is the Boltzmann constant, T is the temperature of the CMB (2.7 K), h is the Planck constant, c is the speed of light, and V is the volume (0.25-litre).
Estimating the number of CMB photons in a given volume is important for understanding the density and energy of the CMB radiation, which is a crucial element in the study of the early universe and the theory of the Big Bang.
Yes, the number of CMB photons can change over time due to the expansion of the universe. As the universe expands, the photons get stretched and their energy decreases, leading to a decrease in their number density.
The estimation of the number of CMB photons in a given volume is based on the assumptions of a uniform temperature and a blackbody spectrum of the CMB radiation. Therefore, the accuracy of the estimation depends on the validity of these assumptions.
The number of CMB photons in a given volume can also be affected by the presence of other sources of radiation, such as stars and galaxies, which can contribute to the overall energy density of the universe. Additionally, the presence of dark matter and dark energy can also affect the number of CMB photons through their effects on the expansion rate of the universe.