Hand written solution required

Advanced Physics Suppose the Hubble constant were not 22 but 13.0 km/s per million lig ht-years. Then what would the critical density {in kg/m3} be? (For H = 22 km/s per million light-years, the critical density is 9.6 X 1027 kg/m3.) kg/m The CMB contains roughly 400 million photons per m3. The energy of each photon depends on its wavelength. Calculate the typical wavelength of a CMB photon. Hint The CMB is blackbody radiation at a temperature of 2.73 K. According to Wien's law, the peak wavelength in nanometers is given by Amax = 3x106 T (a) Calculate the wavelength at which the CMB is a maximum and, to make the units consistent, convert this wavelength from nanometers to meters. m lb} Following up on part (a), calculate the energy {in J} of a typical photon. Assume forthis approximate calculation that each photon has the wavelength calculated in part (a). The energy ofa photon is given by E: be A , where h is Planck's constant and is equal to 6.626 x 103\"1 J x s, c is the speed of light in m/s, and A is the wavelength in m. J (C) Continuing the thinking in parts (a) and (b), calculate the energy in a cubic meter of space, multiply the energy per photon calculated in part [b] by the number of photons per cubic meter given above (Enter your answer in J/m3]. J/m3 (d1 Continuing the thinking in the last three exercises, convert this energy to an equivalent in mass, use Einstein's equation E: mc2. Hint: Divide the energy per m3 calculated in part (c) by the speed of light squared. Check your units; you should have an answer in kg/m3. kg/m3 Now compare this answer with the critical density. Your answer should be several powers of 10 smaller than the critical density. In other words, you have found for yourself that the contribution of the CMB photons to the overall density of the universe is much, much smaller than the contribution made by stars and galaxies. The mass denisity is about 100 times smaller than the critical density.The mass denisity is about 10,000 times smaller than the critical density. The mass denisity is about 1,000,000 times smaller than the critical density.The mass denisity is about 100,000,000 times smaller than the critical density