B. Rouben
McMaster University
4D03/6D03 Nuclear Reactor Analysis
2015 Sept.-Dec.
Assignment 3
Assigned 2015/09/23
Due by 2015/09/30 11:00 am
5 Problems, but only 4 will be marked
Note: Problems 1 and 2 are worth 10 marks each. Jason will mark only one of these, at
random. Since you do not know which one he will mark, you should do all the problems.
Total: 28 marks
1. [10 marks]
Suppose that you have an isotropic point source which emits N neutrons/s in a
homogeneous moderating material.
1. Calculate the number of neutrons which pass outward per second through
the surface of a sphere of radius r with its centre at the source
2. Calculate the number of neutrons absorbed per second within that sphere
3. Verify the neutron-balance equation for the sphere as a whole.
2. [10 marks]
Suppose you have an infinite plane source of neutrons in the plane at x = 0, of
strength S0 per cm2. The medium is characterized by properties a and D, and extends
on either side of the plane source to x =  a. Solve for the flux within the medium.
You will need to apply a boundary condition with an extrapolation distance, say equal
to d, beyond the boundary at x =  a.
3. [8 marks]
An infinite lattice has a=0.00813 cm-1. The value of  is known to be 2.38.
(a) If the reactivity of this infinite lattice is +97.5 mk, what is the value of f?
(b) Maintaning this value of the fission cross section, if we could magically “tune”
the value of , to what value should it be tuned to make the infinite lattice
subcritical by 50 mk?
(c) Boron (B) is a neutron absorber. If we mix 1 part per million (ppm) B uniformly
in the infinite lattice, it adds a “a2 = 0.72*10-4 cm-1 to a2. How much boronpoison addition (im ppm B, to 3 decimal places) would make the infinite lattice
(with the original a and, and the f as in (a)) critical?
(d) By how many mk does 1 ppm B increase from (c) the reactivity?
4. [5 marks]
A uniform cylindrical reactor with properties a = 0.00752 cm-1, f = 0.00760 cm-1,
and D = 1.02 cm is operating at a steady-state power of 550 MW. If the reactor has a
diameter of 8.70 m, what is its axial length? [Neglect the extrapolation distance.]
5. [5 marks]
A uniform spherical reactor is to be made with fuel of properties:
a = 0.00803 cm-1, f = 0.00830 cm-1, D = 1.12 cm,
to which can be mixed a poison, of which 1 unit adds a a2 = 0.15*10-4 cm-1 to a2.
The maximum amount of poison that can be added is 8 units.
What are the smallest and largest diameters for which the reactor can be run in steady
state?