Consider a gas mixture containing n e electrons and n i oxygen ions per unit volume, all
Question:
Consider a gas mixture containing ne electrons and ni oxygen ions per unit volume, all in thermal equilibrium at a temperature T and having no drift velocity.
(a) Resolve the motion of the particle species into the motion in space of the center of mass plus the relative motion of one species with respect to the other, but using the reduced mass. Calculate the Jacobian J of this velocity transformation and show that |J| = 1.
(b) Show that the center of mass velocities have a Maxwellian distribution and that the relative velocities also have a Maxwellian distribution, but
with the reduced mass.
(c) What must be the magnitude of T such that 1/5 of the electrons have a relative kinetic energy greater than 2 e V? The following integral will be useful:
where erfc (α1/2 x0) denotes the complementary error function.
Step by Step Answer:
To solve this problem we will first resolve the motion of the particle species into the motion of the center of mass and the relative motion using the reduced mass Then well calculate the Jacobian and ...View the full answer
