1. Blackbody Radiation
(a) The observable matter in the universe has an average density of about one hydrogen atom per 5 cubic meters of space. Calculate the mass energy density of the observable matter.
(b) The blackbody radiation background of the universe is about 3K. This background is thought to be due to the expansion of the very hot universe after the Big Bang. Calculate the energy density of the 3K cosmic background radiation. Hint: Think StefanBoltzmann and relate the TOTAL FLUX to the temperature. Also, it is important to know that a good starting point is the relationship between energy density and the total radiation flux, S. Specifically,

1
𝑆 𝑑𝑣 = ( ---- 𝜌 𝑑𝑣) c
4

But keep in mind that this is a differential radiation flux per unit frequency (as the math tells you.)
(c) Comparing the results above, would you say that the universe is matter dominated or radiation dominated?
2. Uncertainty
(a) A particle of mass m is confined in a 1-D box of length L. Use the uncertainty relation to estimate the minimum kinetic energy of the particle.
(b) In early days, the atomic nucleus was thought to contain electrons (remember Thomson’s “plum pudding” model.) As supporting evidence, some physicists argued that in nuclear beta decay, electrons were being emitted from the nucleus. Since the energy of a beta particle is typically several hundred keV, would you say that the electrons come from inside the nucleus, based on the uncertainty relation? You may take the nucleus as box of side 10 fm (10x10¯¹⁵ m)

1. Blackbody Radiation (a) The observable matter in the universe h...