he photons that make up the cosmic microwave background were emitted about 380,000 years after the Big Bang. Today, 13.8billion years after the Big Bang, the wavelengths of these photons have been stretched by a factor of about 1100 since they were emitted because lengths in the expanding universe have increased by that same factor of about 1100. Consider a cubical region of empty space in today’s universe 1.00 m on a side, with a volume of 1.00 m3. What was the length s0 of each side and the volume V0 of this same cubical region 380,000 years after the Big Bang? s0 = ? m V0 = ? m^3 Today the average density of ordinary matter in the universe is about 2.4×10−27 kg/m3. What was the average density ?(rho)0 of ordinary matter at the time that the photons in the cosmic microwave background radiation were emitted? (rho)0 = ? kg/m^3

The radio galaxy Cygnus A possesses a lobe of plasma that is detected by both radio and X-ray observatories. The temperature of the X-ray-emitting plasma is 4 keV and the number density of the particles in the plasma is 4x103 m-3. Assume that the plasma is composed solely of completely ionized hydrogen, so the number densities of protons and electrons per cubic meter are identical. * the given number density of particles corresponds to the number density of hydrogen nuclei, so you can safely assume that the number density of electrons is equivalent to this number density a) Compute the collision frequency in Hertz between electrons and ions in the plasma. b) Compute the Debye wavelength in meters of the plasma. c) Compute the plasma parameter of the plasma.

Name: Hubble Distances Redshift z parameter The relativistic redshift is parametrized by z and given by Δ In terms of the scale factor, 2= X do - de de 1+z= ao a (2) Problem 01. Find the redshift z for a Hydrogen spectral line originally at 656 nm which has been observed at a wavelength of 1.64 μm. Astro 001 Fall 2022 Problem 02. How much smaller was the universe when this light was emitted? U₁ = DHO Using the redshift to measure the velocity, we find D~ (1) 0.1 Hubble's Law Hubble's Law states that the recession velocity of a redshifted galaxy is given by the product of the distance and the Hubble constant. (3) ZC Ho where c = 3 x 108 m/s and Ho = 2.3 x 10-18 s in standard units. The standard measurement of the Hubble constant is Ho = 71 (km/s)/Mpc. Problem 03. What is the distance in Mpc and ly to the galaxy measured in problem 01? 1 pc = 3.26 ly.

In the deep space between galaxies, the number density of atoms is as low as 106 atoms/m3, and the temperature is a frigid 2.7 K. part (a)  What is the pressure, in pascals, in the region between galaxies?  part (b)  What volume, in cubic meters, is occupied by 3.5 mol of gas? Part (c)  If this volume is a cube, what is the length of one of its edges, in kilometers?

In a parallel universe, the quantity t has the value 3.14049... Express a in that universe to (a) four significant figures: (b) five significant figures:

The Planck time is the unique interval of time that can be built out of G, c, and h.  Some physicists think that time intervals shorter than the Planck time have no meaning.  Using G = 6.7 x 10-11 kg-1 m3 s-2, c = 3 x 108 m s-1, and h = 6.6 x 10-34 kg m2 s-1, calculate the Planck time, in units of 10-43 s.

The visible section of the Universe is a sphere centered on the bridge of your nose, with radius 13.7 billion light-years. (a) Explain why the visible Universe is getting larger, with its radius increasing by one light-year in every year. (b) Find the rate at which the volume of the visible section of the Universe is increasing.

The radio galaxy Cygnus A possesses a lobe of plasma that is detected by both radio and X-ray observatories. The temperature of the X-ray-emitting plasma is 4 keV and the number density of the particles in the plasma is 4x103 m-3. Assume that the plasma is composed solely of completely ionized hydrogen, so the number densities of protons and electrons per cubic meter are identical. * the given number density of particles corresponds to the number density of hydrogen nuclei, so you can safely assume that the number density of electrons is equivalent to this number density a) Compute the temperature of the plasma in Kelvin. b) Using the calculated temperature for the plasma, compute the mean velocity in meters per second of an electron within the plasma. c) Compute the Coulomb cross section in square meters for a collision between an electron and a proton in the plasma.

The peak intensity of the CMBR occurs at a wavelength of 1.1 mm. (a) What is the energy in eV of a 1.1-mm photon? (b) There are approximately 109 photons for each massive particle in deep space. Calculate the energy of 109 such photons. (c) If the average massive particle in space has a mass half that of a proton, what energy would be created byconverting its mass to energy? (d) Does this imply that space is “matter dominated”? Explain briefly.