(a) Draw a diagram describing the neutron cycle in a thermal critical reactor,highlighting how each part of the diagram corresponds to one of the six factors in the expression for the neutron multiplication factor keffff = η f p PTNL PFNL.Defifine each of these six factors. 
(b) Describe how each of the four components of spent nuclear fuel contribute to the evolution of its radiotoxicity. 
(c) The isotope Gd-157 has a radiative capture cross section of 253 kb and is incorporated into advanced fuel assemblies. What is its purpose? How many neutrons are captured in 1 g of Gd-157 in a typical thermal neutron flflux for a power reactor? 
(d) Why was a fifission chain reaction possible in the Oklo natural nuclear reactor 1.7 billion years ago but not today? 
The fifigure below shows a typical Am-Be thermal neutron laboratory source.7.88 µg of the α-emitter Am-241 is surrounded by a spherical shell of beryllium. Fast neutrons are produced via the 9Be(α, n) 12C reaction and are then thermalised in a moderator.
(a) Show that the americium source has an α-activity of 27.0 µCi. 
(b) By fifirst calculating the α-particle flflux incident on the beryllium, determine the number of fast neutrons produced by this source per second. The inner and outer radii of the beryllium spherical shell are 0.5 and 0.6 cm, respectively. 
(c) The highest neutron kinetic energy from the 9Be(α, n) 12C reaction is 11 MeV. Determine the mean free path for scattering and the thickness of moderator required to thermalise these neutrons if the moderator is graphite. 
(d) A common piece of apparatus used in the oil industry consists of an AmBe source (without the moderator) and a thermal neutron detector. With the aid of a diagram explain how this apparatus when lowered into a borehole can be used to fifind underground oil fifields. 
(a) Show that the macroscopic fast neutron scattering cross section for light water is 0.0547 cm−1 and that the fast removal cross section is 3.22×10−4 cm−1. 
(b) Calculate the diffffusion length for fast neutrons in light water. What is the physical interpretation of this quantity? 
(c) Assuming that the fuel contribution to diffffusion is negligible, what is the neutron flflux at a distance of 15 cm outside the core boundary of a light water moderated critical reactor? Explain your answer. 
(d) A cubic light water moderated critical reactor with a side-length of 150 cm outputs 1 MW. It is fuelled such that the fifission cross section is Σf = 0.01 cm−1.
(i) the average neutron flflux;
(ii) the maximum neutron flflux;
(iii) the neutron flflux at the reactor core boundary.