In chemistry, reactivity


In nuclear engineering, reactivity is a parameter that indicates a nuclear reactor's “departure from criticality”. The control rods of a nuclear reactor control reactivity.

In a nuclear reactor, when nuclei of uranium-235 are struck by a slow-moving neutron, they fission, releasing fragments, radiation, and neutrons. If these neutrons are slowed down  and strike another U-235 nucleus, that nucleus will also fission, continuing the reaction. But some neutrons escape through the sides of the reactor.  For the chain reaction to be self-sustaining, each generation of fission events has to produce enough neutrons that, even after some leak away, enough are left to cause just as many fission events in the next generation. Whether this is happening is monitored by the effective multiplication factor, k, which is 

A fraction. The numerator is rate of neutron production. The denominator is rate of neutron absorption plus rate of leakage

When k = 1, the chain reaction is just self-sustaining.  On average, each generation of fission events produces enough neutrons to cause just as many (but no more!) fission events in the next generation. In this state a reactor is said to be critical. 

Reactivity is defined as 

a fraction whose numerator is k minus one and whose denominator is k

 So when k = 1, reactivity is zero. The absolute numerical value of the reactivity indicates how far the reactor is from critical. Negative values indicate the reactor is trending to a shutdown; positive values indicate a trend to supercriticality. 

A number of units have been employed in measuring reactivity. The simplest is percent: 100 times the reactivity. Others are the inhour, milli-k, nile, ppc and dollar.

The word “reactivity” is also sometimes used, even by expert authorsĀ¹, in the more general sense of k itself. This is not the sense which the units measure.

1. For example, see page 293 of
Samuel Glasstone and Alexander Sesonske.
Nuclear Reactor Engineering, 3rd edition.
New York: Van Nostrand Reinhold Company, 1981.

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