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 time in seconds between collisions between electrons and ions in the plasma. b) Compute the ratio of the time in seconds between collisions to the age of the Universe (13.7 billion years, where 1 year = 3.15x107 s). Therefore, how many collisions has a typical elec- tron experienced with a proton in this plasma during the lifetime of the Universe? c) Compute the mean free path in meters traveled by the electron between collisions.

In 1999, scientists discovered a new class of black holes with masses 100 to 10,000 times the mass of our sun that occupy less space than our moon. Suppose that one of these black holes has a mass of 1x10^3 suns and a radius equal to one-half the radius of our moon. What is the density of the black hole in g/cm^3? The radius of our sun is 7.0x10^5 km, and it has an average density of 1.4x10^3 kg/m^3. The diameter of the moon is 2.16x10^3 miles.

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.