A breeder nuclear reactor is a reactor in which nonfissionable (nonfissile) \(\mathrm{U}-238\) is converted into fissionable (fissile) \(\mathrm{Pu}-239 .\) The process involves bombardment of U- 238 by neutrons to form \(U-239,\) which then undergoes two sequential beta decays. Write nuclear equations for this process.

Nuclear equations are a way of representing nuclear reactions using atomic symbols. They detail the transformation of an atom's nucleus due to processes such as neutron bombardment, beta decay, and nuclear fission or fusion. The initial and final state of each reaction component is written, with the understanding that the total atomic mass and the total atomic number must be the same on both sides of the equation to satisfy the laws of conservation.

Let's look at an example: When a nucleus of uranium-238 captures a neutron, it transforms into uranium-239. This is depicted in the nuclear equation \[ {}^{238}_{92}U + {}^{1}_{0}n \rightarrow {}^{239}_{92}U \.\] Each component, whether it's an isotope like \( {}^{238}_{92}U \) or a subatomic particle like a neutron \( {}^{1}_{0}n \) is shown, along with changes resulting from the reaction.

Beta decay is a type of radioactive decay in which a beta particle, which is an electron (\(e^{-1}\)) or positron, is emitted from an atomic nucleus. This process changes the atom from one element to another and occurs when an atom has either too many protons or neutrons to be stable.

In the context of a breeder nuclear reactor, uranium-239 undergoes beta decay, converting into neptunium-239 with the emission of a beta particle as shown: \[ {}^{239}_{92}U \rightarrow {}^{239}_{93}Np + {}^{0}_{-1}e \.\] This process not only changes the element but also increases the atomic number by one, while the atomic mass remains unchanged. The neptunium-239 then undergoes a second beta decay, resulting in plutonium-239: \[ {}^{239}_{93}Np \rightarrow {}^{239}_{94}Pu + {}^{0}_{-1}e \.\] These steps highlight the crucial role of beta decay in the production of fissile materials in breeder reactors.

Neutron bombardment is an essential process in nuclear reactors where neutrons are used to initiate and sustain nuclear reactions. Neutrons can be absorbed by atomic nuclei, causing changes that may lead to a nuclear reaction.

When a uranium-238 nucleus absorbs a neutron, it becomes uranium-239, as represented by the equation: \[ {}^{238}_{92}U + {}^{1}_{0}n \rightarrow {}^{239}_{92}U \.\] This interaction is crucial for a breeder reactor, which converts nonfissionable elements to fissionable ones through neutron bombardment. It's a key step in creating materials that can undergo fission to release energy or be used in nuclear weapons.

The distinction between fissile and nonfissile materials is fundamental to understanding nuclear reactions and reactor design. Fissile materials, such as uranium-235 and plutonium-239, are capable of sustaining a nuclear fission chain reaction. When struck by a slow-moving ('thermal') neutron, a fissile nucleus may split into smaller nuclei, releasing a massive amount of energy and more neutrons that can continue the reaction.

In contrast, nonfissile materials, like uranium-238, do not typically undergo fission when they absorb a neutron. However, these materials can be transformed into fissile ones through neutron bombardment, as seen in breeder reactors where \( {}^{238}_{92}U \) is converted to \( {}^{239}_{94}Pu \), a fissile material. This process not only helps to generate more fuel than consumed but also contributes to the efficient use of uranium resources by creating more energy-yielding substances.