The neutron flux in a bare spherical reactor, of radius R = 50 cm, is given by:%3D \phi(r)=\frac{A}{r} \sin \left(\frac{\pi r}{R}\right) where A is a constant andr is the radial

distance measured from the centre ofthe reactor. The uranium fuel has a number density of 1.20×1021 cm-3anda microscopic transport cross section of 12.0 b. The graphite moderator has anumber density of 2.30x1022 cm-3and a microscopic transport cross section of20.0 b. Derive an expression for the neutron current density as a function of r in thereactor. 1.2x1012How many neutrons escape from the reactor per second for A =neutrons cm-s? What would be the neutron multiplication factor, k, if A%3Dwas subsequently doubled? Find the magnitude of the maximum flux and the value of r at which this occurs.