Of the neutrons emitted in each fission event in a light-water reactor, an average of 0.6 neutron is absorbed by \(^{238} \mathrm{U}\), leading to the formation of \(^{239} \mathrm{Pu}\). (a) Assuming 200 MeV per fission, how much \(^{239} \mathrm{Pu}\) forms each year in a \(30 \%\) -efficient nuclear plant whose electric power output is \(1.0 \mathrm{GW} ?\) (b) With careful design, a fission explosive can be made from \(5 \mathrm{kg}\) of \(^{239} \mathrm{Pu}\). How many potential bombs are produced each year in the power plant of part (a)?

The process of neutron absorption is integral to understanding how nuclear fission reactions contribute to the production of new elements and, subsequently, energy. In the context of a nuclear reactor, like the light-water reactor considered in our exercise, uranium-238 (²³⁸U) plays a pivotal role by capturing one of the neutrons released during the fission of a fissile material such as uranium-235.

Neutron absorption occurs when a free neutron enters the nucleus of an atom, in this case, uranium-238. This addition of a neutron effectively turns the uranium-238 nucleus into an unstable uranium-239 (²³⁹U) nucleus which quickly decays. Over a period involving two beta-minus decays, where a neutron in the nucleus transforms into a proton while emitting an electron (beta particle) and an anti-neutrino, the uranium-239 becomes neptunium-239 (²³⁹Np) and then finally transforms into plutonium-239 (²³⁹Pu) which can be used as a fuel or in the production of nuclear weapons.

In our exercise, the rate of neutron absorption is a key factor in estimating the amount of plutonium-239 produced. By calculating the fraction of neutrons absorbed by uranium-238, we can deduce the number of plutonium atoms formed over a year and, as given by the exercise, this process has repercussions in terms of potential nuclear proliferation.

The formation of plutonium-239 (²³⁹Pu) from uranium-238 (²³⁸U) is a sequence of events that has both peaceful and military implications. It starts with neutron absorption, but understanding the conversion is crucial for grasping the exercise's main problem.

After ²³⁸U captures a neutron, it becomes ²³⁹U. This isotope then goes through two beta decays. A beta decay is a form of radioactive decay where an unstable nucleus transforms by emitting a beta particle (electron or positron) and changing one of its neutrons to a proton (or vice versa), effectively resulting in a different element. This process is why we eventually get plutonium-239 from initially capturing a neutron by uranium-238.

The exercise centers on quantifying just how much plutonium-239 can be produced in a year through this neutron capture and subsequent decay process. Understanding this process and its steps is fundamental in deriving the correct amount of plutonium-239, which can be utilized for energy production or, as noted in the exercise, weaponization.

Energy production in a nuclear plant involves converting the nuclear energy released during fission into electrical energy. In the exercise, we calculate the amount of plutonium-239 that forms as a byproduct of energy production in a light-water reactor nuclear plant.

The conversion efficiency of the plant is a critical piece of information for solving the exercise. With a 30% efficiency rate, the plant effectively converts only 30% of the thermal energy from fission reactions into electricity, while the rest is lost as heat. To find out how much electricity a plant generates, we would need to know the total energy produced from fission events and the plant's efficiency.

In the scenario provided by the exercise, knowing that the plant outputs 1.0 GW of electrical power, we can backtrack to find out the total energy generated from fission over a given period. This information also allows us to assess the number of potential nuclear devices that could be created from the plutonium-239 byproduct, thus connecting the process of energy production and the broader implications of managing and utilizing nuclear materials.