Task #1 — the point source in the infinite spherical geometry. We consider a point source of intensity q power [neutrons per second] in infinite, non-multiplying, homogeneous medium. It is obvious that the flux depends only on the distance from localized source, we denoted it as r. It is necessary to find the Φ(r) function. The diffusion equation contains the term of external source described by the Delta function. We can rewrite the equation for all values of coordinates except of the point of source location like depicted there. The presence of localized source we are taking into account in boundary conditions. The general solution contains two unknown constants, the first can be found from the condiotion of boundedness of the neutrn flux at infinity because we have the infinite medium. Thus the constant C2 equals zero. The second constant can be found from the conditions of localized source. We should count the number of neutrons crossing through the sphere of infinitesimal radium per one second and this number equals the source power. The number of neutron crossing the unit area on the surface of sphere is the neutron current. This function can be found from Fick’s law as follows. For the total number of neutrons crossing the whole surface of sphere we have to integrate over the surface, but we have the isotropic source and homogeneous medium thus instead of integration we can simply multiply by the area of the sphere surface. In the end we can get the expression for the last unknown constant. So the flux equals q divided to 4ΦD, multiplied by the exponential function and divided by r. This function is depicted there. Please take into account what value the function takes at the point zero. The function tends tends to infinity and it is absolutely incorrect compared to the reality. However, the source represents the heterogeneity of the medium where the diffusion approximation doesn’t work. Therefore our solution is incorrect at the distance less than 2 or three transport mean free paths. However, for larger distances the solution is absolutely correct. Using the last formula we can discover the Physical meaning of the diffusion length square. Let's calculate the average square of length shift of a neutron from birth point to the absorption point. By definition of the averaged value we use this integral formula, where the probability density is the absorption rate. In the end we can get the diffusion length squared, it is one sixth of the average shift length squared (on a straight line) of a neutron from the birth point to the absorption point.