Question

In a nuclear fission reactor, each fission of a uranium nucleus is accompanied by the emission of one or more highspeed neutrons, which travel through the surrounding material. If one of these neutrons is captured in another uranium nucleus, it can trigger fission, which produces more fast neutrons, which could make possible a chain reaction. However, fast neutrons have low probability of capture and usually scatter off uranium nuclei without triggering fission. In order to sustain a chain reaction, the fast neutrons must be slowed down in some material, called a “moderator.” For reasons having to do with the details of nuclear physics, slow neutrons have a high probability of being captured by uranium nuclei.

A slow neutron induces fission of U-235, with the emission of additional (fast) neutrons. The moderator is some material that slows down the fast neutrons, enabling a chain reaction.

In the following analyses, remember that neutrons have almost no interaction with electrons. Neutrons do, however, interact strongly with nuclei, either by scattering or by being captured and made part of the nucleus. Therefore you should think about neutrons interacting with nuclei (through the strong force), not with entire atoms.

1. Based on what you now know about collisions, explain why fast neutrons moving through a block of uranium experience little change in speed.

2. Explain why carbon should be a much better moderator of fast neutrons than uranium.

3. Should water be a better or worse moderator of fast neutrons than carbon? Explain briefly.

Answer 1

1) Relative mass of Uranium nuclei is approximately 235 times the mass of neutron. So neutron collision can be considered as colliding with heavy mass so after collision neutron will retain almost all of its speed as this collision will be analogous to reflection from a fixed immovable wall.

2) Carbon is approximately 12 times the mass of neutron. So colliding masses are comparable. So neutron will loose substantial amount of its speed on collision with carbon nuclei.

3) In water there are two hydrogen atom per molecule and mass of nuclei of hydrogen is same as neutron mass. So for head on collision of neutron with hydrogen nuclei, neutron will stop and transfer all of it's velocity to hydrogen nuclei. So water has relatively high neutron absorption rate than carbon, removing neutrons from the fission process. But heavy water avoids this huge loss as neutron collision happens with Deuteron nuclei and not hydrogen nuclei. So during head on collision neutron doesn't stop as Deuteron nuclei is twice the mass of neutron and can be used as moderator. But using heavy water is costly so in this respect carbon is a better moderator.

We have used the following facts:

i) Mass colliding with very heavy mass retains its speed after collision

ii) Two equal masses colliding head-on with one at rest interchanges their velocity after collision.

iii) One moving mass colliding with other mass at rest and their masses are comparable then the moving mass looses its speed and its new speed is greater than zero and less than its initial speed.