Consider an infinite planar neutron source of strength \(100 \mathrm{n} / \mathrm{cm}^{2} / \mathrm{s}\), emitting neutrons in an infinite medium with \(\Sigma_{a}\) and \(D\) as \(2.56 \mathrm{~cm}^{-1}\) and \(0.5252 \mathrm{~cm}\), respectively.

a) What is the rms distance traveled by a neutron from birth to absorption?

b) Sketch the neutron flux profile as a function of distance.

c) How does the nature of flux profile changes if the medium is finite?