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The first self-sustaining nuclear chain reaction was initiated by a team led by Enrico Fermi below the bleachers of Stagg Field at the University of Chicago on December 2, 1942 during the Manhattan Project.

Suppose that on average a neutrons from a nuclear fission reaction cause another fission reaction. Then we can distinguish the following cases:

• a<1 (sub-critical mass): starting with one fission, we have on average a total of 1/(1-a) fissions.
• a=1 (critical mass): starting with one fission, we have on average one fission per unit time; this unit of time is the time it takes for the neutron to hit another nucleus; the distance is something like the diameter of a critical mass; e.g. the speed may be 10 km/s and the distance 10 cm, then the time is 10 ns.
• a>1 (super-critical mass): starting with one fission, we have on average in every generation of the chain reaction, say again once every 10 ns, a multiplication of the number of fissions by a factor a. This cannot continue, of course: a decreases when the amount of fission material that is left decreases, or when the remaining fission material is torn apart. In a nuclear weapon this may e.g. happen after 80 generations of 10 ns, is 800 ns, when there have been fissions.

When a is close to 1, this calculation somewhat over-estimates the 'doubling rate'. When a uranium nucleus absorbs a neutron it enters a metastable excited state which then decays by several possible routes. Typically it decays into two fragments, fission products, typically isotopes of Iodine and Caesium, with expulsion of a number of neutrons. The fission products are themselves unstable, with a wide range of lifetimes, but typically several seconds, and decay producing further neutrons.

It is usual to split the population of neutrons which are emitted into two sorts - 'prompt neutrons' and 'delayed neutrons' Typically, the 'delayed neutron fraction' is less than 1 percent of the whole. In a nuclear reactor the variable a is typically around 1 to have a steady process. When a value of a is achieved when _all_ neutrons produced are considered the reaction is said to be 'critical'. This is the situation achieved in a nuclear reactor. The power changes are then slow, and controllable e.g. with control rods. When a =1 is achieved counting only the 'prompt' neutrons, the reaction is said to be 'prompt critical' - much shorter doubling rates can then occur, depending on the excess criticality (a-1). The change in reactivity needed to go from critical to prompt critical (ie the delayed neutron fraction) is defined as a dollar.

See also

• nuclear physicsNuclear physics is that branch of physics concerned with the nucleus of the atom. Topics include: Strong interaction Radioactivity Models of the nucleus liquid drop model shell model interacting boson model Fission Fusion Nuclear reactions Applications Nu
• nuclear reactionIn nuclear physics, a nuclear reaction is a process in which two nuclei or nuclear particles collide, to produce products different to the initial products. In principle a reaction can involve more than two particles colliding, but such an event is except
• nuclear weapon designNuclear weapon designs are often divided into two classes, based on the dominant source of the nuclear weapon's energy. Fission bombs derive their power from nuclear fission, where heavy nuclei ( uranium or plutonium) split into lighter elements when bomb
• chain reactionA chain reaction is a sequence of reactions: A causes B, which causes C, etc. In particular, one of the agents necessary to the reaction may itself be produced by the reaction, thus causing additional reactions. Examples: The neutron- fission chain reacti