Question

Write the nuclear reaction that produces \({ }^{233} \mathrm{U}\) from \({ }^{232}\) Th following the absorption of a neutron.

Short answer

^{232} ext{Th} + ^{1} ext{n} ightarrow ^{233} ext{U} (via ext{beta decays}).

Step-by-step solution

Identify Initial Nucleus

We start with thorium-232 ( ^{232} ext{Th} ext{) as the initial nucleus which undergoes a nuclear reaction after absorbing a neutron.

Neutron Absorption

Thorium-232 absorbs a neutron ( ^{1} ext{n} ext{), which indicates the addition of an extra nucleon to the thorium nucleus. The equation for this process can start as: ^{232} ext{Th} + ^{1} ext{n} ightarrow ... .

Identify Intermediate Nucleus

When ^{232} ext{Th} absorbs a neutron, it becomes ^{233} ext{Th} (thorium-233). The reaction is now: ^{232} ext{Th} + ^{1} ext{n} ightarrow ^{233} ext{Th} .

Beta Decay Process

^{233} ext{Th} is radioactive and undergoes beta decay. During beta decay, a neutron is converted into a proton, and a beta particle (an electron) and an antineutrino are emitted. This transforms thorium-233 into protactinium-233: ^{233} ext{Th} ightarrow ^{233} ext{Pa} + eta^{-} + ar{ u} .

Further Decay to Uranium

Protactinium-233 is also unstable and undergoes beta decay itself. In this decay, another neutron in ^{233} ext{Pa} is converted into a proton, producing uranium-233: ^{233} ext{Pa} ightarrow ^{233} ext{U} + eta^{-} + ar{ u} .

Complete Reaction Identity

Finally, the complete nuclear reaction from start to finish showing the production of ^{233} ext{U} is: ^{232} ext{Th} + ^{1} ext{n} ightarrow ^{233} ext{Th} ightarrow ^{233} ext{Pa} ightarrow ^{233} ext{U} .

Key concepts

Neutron Absorption

Neutron absorption is a crucial process in nuclear reactions. Specifically, it occurs when an atomic nucleus captures a neutron, integrating it into its own structure. When a neutron is absorbed, it becomes part of the nucleus and thus changes both the mass number and the energy state of the atom.
For example, in our exercise, thorium-232, which is denoted as \( ^{232}\text{Th} \), absorbs a neutron \( ^{1}\text{n} \). This process can be represented by the equation:
\[ ^{232}\text{Th} + ^{1}\text{n} \rightarrow ^{233}\text{Th} \]

• The increase in the mass number results in a new isotope, which is thorium-233 in this case.
• Neutron absorption does not directly change the charge of the nucleus because neutrons are neutral particles.

This process can often make the atom more unstable, leading to subsequent radioactive decay.

Beta Decay

Beta decay is a type of radioactive decay where a neutron in the nucleus is transformed into a proton. Accompanying this transformation is the emission of a beta particle (which is essentially an electron) and an antineutrino.
During beta decay, the atomic number of the element increases by one, while the mass number remains constant. This is because a neutron changes to a proton.
For example, in our sequence of reactions:

• Thorium-233 \( ^{233}\text{Th} \) undergoes beta decay to form protactinium-233 \( ^{233}\text{Pa} \).
• The reaction for this decay is \( ^{233}\text{Th} \rightarrow ^{233}\text{Pa} + \beta^- + \bar{u} \).
• Protactinium-233 \( ^{233}\text{Pa} \) undergoes another round of beta decay resulting in uranium-233 \( ^{233}\text{U} \).

Beta decay is a transformation process that allows the element to change its identity while stabilizing its nuclear configuration.

Uranium-233 Production

Producing uranium-233 \(^{233}\text{U} \) is the end goal of the neutron absorption and beta decay processes described in this exercise. Uranium-233 is a significant isotope and is notable for its use in nuclear reactors, particularly in thorium fuel cycles. It is produced from thorium-232 through a series of nuclear reactions.
The entire process involves:

• Initially, thorium-232 \(^{232}\text{Th} \) absorbs a neutron to become thorium-233 \(^{233}\text{Th} \).
• Thorium-233 is unstable and undergoes beta decay to become protactinium-233 \(^{233}\text{Pa} \).
• Finally, protactinium-233 experiences further beta decay to form uranium-233 \(^{233}\text{U} \).

Each of these transformations helps illustrate the powerful chain reaction that can culminate in the production of a fuel source capable of supporting nuclear energy requirements. Understanding how uranium-233 is produced not only unravels the nucleus interactions but also highlights the potential of thorium as a nuclear fuel.