This question concerns a problem in Arfken and Weber (from the infinite series chapter, after the power series section). I went to the homework section, and the titles beneath each section specifically imply that a question from a graduate book is inappropriate for that section. I thus post it here. I apologize if this is the wrong place. The problem reads,"Neutrons are created by a nuclear reaction inside a hollow sphere of radius R. The newly created neutrons are uniformly distributed over the spherical volume. Assuming that all directions are equally probable, what is the average distance a neutron will travel before striking the surface of the sphere? Assume straight line motion, no collisions." It then goes on to give steps on the way of the answer, one stating that the result is that mean distance = 3/2 R integral( 0 to 1) integral (0 to pi) square root [(1-K*K sin(theta)*sin(theta)] K*K* dk sin(theta) d(theta) No, I have no idea what K is physically, except by the nature of of what looks like the differential element at the end (but I am confused as to how one might get a distance variable inside a square root times sine of the angle). Although help in working toward this answer would be appreciated, my request is more meager. I don't understand why the answer isn't simply R/2. If particles are spontaneously forming uniformly in a sphere, and there is total isotropy in direction, and no collisions, I would think that the mean distance traveled by a particle until colliding with the surface would be simply R/2. Why isn't it that simple?