Which of the following statements about the uranium used in nuclear reactors is or are true? (i) Natural uranium has too little \(^{235} U\) to be used as a fuel. (ii) \(^{238} U\) cannot be used as a fuel because it forms a supercritical mass too easily. (iii) To be used as fuel, uranium must be enriched so that it is more than 50\(\%^{235} \mathrm{U}\) in composition. (iv) The neutron-induced fission of \(^{235} \mathrm{U}\) releases more neutrons per nucleus than fission of \(^{238} \mathrm{U}\).

Nuclear fission is a process where the nucleus of an atom splits into two or more smaller nuclei, along with the release of energy. In the context of a nuclear reactor, this energy is used to generate electricity. The most common isotope used in nuclear fission is uranium-235 (²³⁵U). When a neutron hits the nucleus of a ²³⁵U atom, it can cause the nucleus to become unstable and split, releasing a significant amount of energy in the form of heat. This heat is then used to produce steam which drives turbines to generate electricity.

One of the hallmarks of fission is the release of additional neutrons during the process. These neutrons can then go on to initiate fission in other ²³⁵U atoms, potentially leading to a chain reaction. The ability to control the chain reaction is critical in a nuclear reactor to ensure it proceeds at a safe and steady pace. The use of control rods, which absorb excess neutrons, and moderating materials to slow down neutron speeds, helps to regulate the fission process in a reactor.

Uranium enrichment is the process of increasing the concentration of uranium-235 (²³⁵U) in natural uranium. Natural uranium contains about 0.7% ²³⁵U, which is not enough to sustain a nuclear chain reaction efficiently. To be used as a fuel in most types of nuclear reactors, the uranium must be enriched to increase its ²³⁵U content. This is usually achieved through methods such as gas centrifugation or gaseous diffusion.

The optimal level of enrichment for the fuel depends on the reactor design but is typically between 3% and 5% ²³⁵U for commercial light-water reactors. Some research and naval reactors may use highly enriched uranium (HEU), which has a much higher content of ²³⁵U, but this is less common for civilian energy production due to proliferation concerns. The enrichment process ensures that there are enough fissile atoms to maintain a steady and controlled nuclear chain reaction.

Fissile materials are a subset of nuclides that can sustain a nuclear chain reaction with neutrons of nearly any energy – high or low. The primary fissile materials used in nuclear reactors are uranium-235 (²³⁵U) and plutonium-239 (²³⁹Pu). These materials can capture slow-moving neutrons and undergo fission readily. In contrast, uranium-238 (²³⁸U), which makes up the majority of natural uranium, is considered fertile but not fissile; it can capture fast neutrons and convert into a fissile material such as ²³⁹Pu through a series of nuclear reactions.

Fissile materials are critical in nuclear technology, not only for power generation but also for medical isotopes and in naval propulsion systems. The selection of fissile material is crucial for the design and function of a nuclear reactor, as it defines the reactor's fuel cycle and how the reactor is controlled and moderated.

Neutron-induced fission is the type of fission that occurs when a nucleus captures a neutron and splits. For uranium-235 (²³⁵U), this form of fission is particularly important because it is easily triggered by neutrons that have been slowed down, or 'thermalized.' When ²³⁵U undergoes neutron-induced fission, it not only splits, releasing energy, but also releases more neutrons which can further sustain the chain reaction.

Different isotopes of uranium and other elements can behave differently upon neutron absorption. For instance, uranium-238 (²³⁸U) is less likely to undergo fission when hit by a neutron and instead can absorb the neutron to become plutonium-239 (²³⁹Pu), a process used in breeding reactors to generate more fissile material. It's important to understand that the efficiency of neutron-induced fission in producing a sustained chain reaction is what makes a material suitable as nuclear fuel, and this is why enriched ²³⁵U, with a higher likelihood of fission upon neutron capture, is preferred.