Fission occurs when the nucleus of an atom captures a subatomic particle called a neutron and splits into two lighter nuclei. This causes energy to be released. At the same time, other neutrons are emitted, two or three on the average. If at least one of these is captured by another fissionable nucleus, then a chain reaction is possible.

(a) Consider a reaction in which three neutrons are emitted initially. Let c denote that a given neutron is captured by another nucleus; let n denote that the neutron is not captured by another nucleus. Construct a tree denoting the possible behavior for these three neutrons.

(b) List the sample points generated by the tree.

(c) List the sample points that constitute each of these events: AI: a chain reaction is possible A,: all three neutrons are captured A3: a chain reaction is not possible

(d) Are AI and A, mutually exclusive? Are A and A3 mutually exclusive? Are A, and A3 mutually exclusive? Are AI, A2, A3 mutually exclusive?

(e) The probability that a neutron will be captured depends on its neutron energy and is not the same for each neutron. Under these circumstances, is it correct to say that the probability that all three neutrons will be captured is 1/8 because this can occur in only one way and there are eight paths through the tree of part (a)? Explain.