Question

For a nuclear reactor to run in critical condition the reproduction factor K should be
A. = 1
B. > 1
C. < 1
D. >> 1

Answer 1

K is the neutron reproduction factor in the nuclear fission of Uranium. If one neutron is incident on a uranium nucleus, it gives K neutrons as the products in the fission reaction

Complete step-by-step answer:
When a slow neutron called thermal neutron with energy in the order of eV hits a Uranium
(235) nucleus, it results in fission of the uranium into smaller nuclei like krypton and Barium along with the production of about three neutrons and massive amounts of energy ( about 177 MeV). This can be written as:
$^{235}_{92} U + n \rightarrow ^{144}_{56} Ba + ^{89}_{36} Kr + 3n + 177 eV$.
If we take some mass of Uranium and one neutron enters this uranium, it will create 3 neutrons as products which will then again hit three different uranium nuclei and so on. Therefore, all the uranium nuclei in the sample will react quickly releasing a massive amount of energy in the form of a blast. But for us, this energy is not useful as it cannot be harnessed for the purpose of energy production. Therefore in nuclear reactors we use a concept of controlled fission reaction. If one uranium reaction will produce one neutron then the reaction will proceed at a favorable pace for energy production.
The reproduction factor give the net change in the number of thermal neutrons from one
generation (reaction) to the next, on the average, each thermal neutron produces K new
thermal neutrons. The critical condition for nuclear reaction of Uranium to sustain for a given
sample is that K = 1

So, the correct answer is “Option A”.

Note: If the reaction produces fast neutrons then the reproduction factor can quickly drop below 1. This means that reproduction factor is a measure of how many thermal neutrons we obtain and not just the number of neutrons. Fast neutrons are not useful for fission.