Question

Show that particles hitting a plane boundary have travelled a distance 2 lambda/3 perpendicular to the plane since their last collision, on average. A diffuse cloud of neutral hydrogen atoms in space has a temperature of 50 K and number density 500 cm^-3. Estimate the mean scattering time (in years) between hydrogen atoms in the cloud. Estimate the mean free path (in astronomical units).

q 8.3

Answer 1

Lambda = [2^cap (0.5) times n times sigma]^n -1 x cos theta = integral^infinity_0 x e^-x/lambda integral vg (v) dv integral^pi/2_0 cos^2 theta sin theta dq/integral^infinity_0 e^-x/lambda integral vg(v) dv integral^pi/2_0 cos theta sin theta dq = 2lambda/3