1 NUEN 301 EXAM 1, October 1, 2009 No Calculators!!! No electronics of any kind!! [points] 1. In a certain thermal reactor, for every 100 neutrons emitted from fission, 10 get absorbed in fuel while still “fast” and 40 get absorbed in fuel after becoming “thermal.” The other 50 either leak or get absorbed in non-fuel materials. ηT is 2.0 and ηF is 1.5. [5] a) Calculate the multiplication factor (k) if sufficient information is given. [5] b) Calculate the resonance-escape probability if sufficient information is given. [5] c) Given that 20 of the 100 neutrons are absorbed in non-fuel materials after becoming thermal, calculate the thermal utilization (f) if you have enough information. 2. What is the physical meaning of: [10] a) the energy-dependent scalar flux integrated over all energies and integrated over a surface of area A? [10] b) the mean free path of a 1-MeV neutron in water? 3. A mono-energetic, mono-directional neutron beam of intensity I0 = 2×106 n/cm2-s is incident upon a homogeneous cubical target. The target, which has width w = 10 cm, is NOT “thin.” [This means you cannot ignore attenuation of the beam.] The incident beam is perpendicular to one face of the cube and it completely covers this face. The neutrons in the beam are traveling in the +ex direction, which is toward the right in the figure below. The material in the cube does not scatter neutrons and does not fission – its only interaction with neutrons is radiative capture. Σt = Σcapture = 0.5 cm−1. [10] a) At what rate (n/s) are neutrons exiting from the cube? Give a number or an expression that could be punched into a calculator. [10] b) At what rate (n/s) are neutrons being absorbed in the cube? Give a number or an expression that could be punched into a calculator.2 4. A homogeneous spherical reactor of radius 60 cm is critical and operating in steady state. There are 5×1015 fissions/s taking place in the reactor. Cross section data, properly averaged over nucleus velocities and over all neutron energies, are: Σt = 2 cm–1, Σa = 1.0 cm–1, Σf = 0.5 cm–1, ν = 2.4 n/fission. [10] a) What is the average scalar flux in the reactor? Include units, and give a number or an expression that can be punched into a calculator. [10] b) What is the absorption rate (n/s) in the reactor? Give a number or an expression that can be punched into a calculator. [10] c) What is the net leakage rate (n/s) out of the reactor? Give a number or an expression that can be punched into a calculator. [10] 5. In the middle of a large homogeneous reactor, the energy-dependent scalar flux is roughly independent of position. Suppose that in such a reactor the energy-dependent scalar flux is approximately: φ(E) = [4×109 n/cm2-s] / E , for 10 eV < E < 1 MeV, and the differential scattering cross section is . What is the rate density (scatters per cm3 per s) at which neutrons scatter directly from energies between 100 keV and 200 keV to energies below 5 keV? Your answer should be a number or an arrangement of numbers that I can punch into a calculator. [5] 6. Microscopic cross sections depend fundamentally on a certain speed. What speed? Extra-credit problem on next page ...3 Extra Credit Two mono-energetic, mono-directional neutron beams are incident upon a homogeneous slab that is infinite in the y and z directions. The beams completely cover the portion of the target that we are interested in. See Figure. Given the energy of the incident neutrons, the material cross sections are: [5] What is the scalar flux as a function of x in this