• For an infinite H₂O reactor, if K_∞ = 1.001, T_P = 0.2 s.
• This implies that in 2 s, the power will increase by e¹⁰, or 22000 times! It will be impossible to control such reactors.
• Interestingly, reactors exist and are being controlled. The key for this is the presence of delayed neutrons.
• Some of the fission products like Br⁸⁷, I¹³⁷ undergo the following radioactive decay chain

• It may be observed that Br and I after some time delay decay to Kr and Xe respectively. These emit neutrons instantly. Hence Br and I shall be called precursors. Thus the neutrons emitted are delayed in time and hence called delayed neutrons.
• There are several precursors and for simplicity, they can be lumped on to one group with a decay constant of 0.08 s^-1.
• The fraction of delayed neutrons are typically 0.0065 and these play a crucial role in controlling the reaction.
• Since we know that the mean life of the radioactive specie is given by 1/λ, we can say that the neutron comes with a delay of  1/0.08 = 12.5 s.
• From a simplistic view point we can define the effective life of neutron to be

2 x 10^-4 x (1-0.0065) + 12.5 x 0.0065 = 0.08 s

• The Reactor period T_P for the same example of K_∞ =  1.001 and water reactor works out to be 80 s, making the reactor amply controllable.
• The above treatment is fairly crude, but illustrative.
• We shall now refine this analysis a bit further to appreciate what are called point kinetics equations.
• There are two point Kinetics equations, one for the neutron population and the other for the precursor concentrations.
• We shall now derive them and appreciate their solutions.