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

Given: The X-ray emitting plasma is 4 keV. The number density of particles is 4×103 m-3. Introduction: Plasma is the fourth state of matter. To put it very simply, a plasma is an ionized gas, a gas into which sufficient energy is provided to free electrons from atoms or molecules and to allow both species, ions, and electrons, to coexist. Plasmas are the most common state of matter in the universe.Calculation: Write the expression relating the energy and temperature of the plasma. E=32kBT Here, kB is the Boltzmann constant. Substitute 4 keV for E, 8.615×10-5 eVK-1 for kB in the above expression. 4×103 eV=8.615×10-5 eVK-1TT=4×103 eV8.615×10-5 eVK-1T=0.4643×108 KT=4.643×107 K Thus, the temperature of the plasma is 4.643×107 K.(b) Calculation: Write the expression of average velocity per particle. v=kBTme Here, me is the mass of the electron. v=1.38×10-23 JK-14.643×107 K9.1×10-31 kgv=2.65×107 ms-1 Thus, the value of the mean velocity is 2.65×107 ms-1.

Answered: The radio galaxy Cygnus A possesses a…