Question

The most abundant isotope of uranium, \({ }^{238} \mathrm{U}\), does not undergo fission. In a breeder reactor, however, \(\mathrm{a}^{238} \mathrm{U}\) atom captures a neutron and emits two \(\beta\) particles to make a fissionable isotope of plutonium, which can then be used as fuel in a nuclear reactor. Write a balanced nuclear equation.

Short answer

\( ^{238}_{92} \text{U} + ^1_0 \text{n} \rightarrow ^{239}_{94} \text{Pu} + 2 \beta^- \)

Step-by-step solution

Identify the Neutron Capture

The uranium-238 isotope, represented as \( ^{238}_{92} \text{U} \), captures a neutron, symbolized as \( ^1_0 \text{n} \). This process increases the mass number by 1 while maintaining the same atomic number.

Form the Intermediate Neptunium Isotope

After capturing a neutron, \( ^{238}_{92} \text{U} \) becomes \( ^{239}_{92} \text{U} \), which is an unstable isotope. This isotope quickly undergoes beta decay to transform into neptunium, \( ^{239}_{93} \text{Np} \).

Beta Decay to Plutonium

The neptunium \( ^{239}_{93} \text{Np} \) undergoes a second beta decay, where a neutron becomes a proton, releasing a beta particle \( \beta^- \) (electron). This results in the formation of \( ^{239}_{94} \text{Pu} \), which is the fissionable plutonium isotope.

Write the Balanced Equation

The complete nuclear reaction can be summarized and balanced as follows:\[ ^{238}_{92} \text{U} + ^1_0 \text{n} \rightarrow ^{239}_{94} \text{Pu} + 2 \beta^- \] This equation correctly represents the capture of a neutron, transformation through two beta decays, and the formation of plutonium-239, with beta particles as byproducts.

Key concepts

Nuclear Reactions

Nuclear reactions involve the transformation of one element into another. These transformations occur in the nucleus of an atom, in contrast to chemical reactions that involve the electrons surrounding the nucleus. During a nuclear reaction, there can be a change in the identity or number of protons and neutrons inside the nucleus. This results in the formation of a different element.

In the exercise example, we observe a specific nuclear reaction where uranium-238 undergoes changes to form plutonium-239, a usable nuclear fuel type. This process involves capturing a neutron followed by a series of beta decays. The equation summarizing these processes is known as a nuclear equation. It must be balanced to appropriately demonstrate the conservation of mass and charge.

Key components to look for in a nuclear reaction include:

• The initial isotope or element.
• The particle that initiates the reaction (e.g., a neutron).
• The final products, including any new isotopes or emitted particles.

It is essential to ensure that both the total atomic number and mass number remain the same on both sides of the nuclear equation.

Isotopes

Isotopes are variants of a specific element that have the same number of protons but differ in the number of neutrons. This results in atoms that have the same atomic number but different mass numbers. For example, uranium-238 and uranium-239 are isotopes of uranium; they both contain 92 protons, but uranium-238 has 146 neutrons whereas uranium-239 has 147.

Isotopes can be stable or unstable. Unstable isotopes, also known as radioisotopes, tend to undergo radioactive decay, where they emit particles to reach a stable state. In nuclear chemistry, isotopes are crucial because they can display vastly different properties. Some isotopes are more suitable for certain reactions, like how uranium-238 can be transformed into a fissionable form in a breeder reactor.

When working with isotopes, remember:

• The atomic number (bottom number) remains the same for isotopes of a given element.
• The mass number (top number) varies due to different neutron counts.
• Radioactive isotopes often perform nuclear reactions as they seek stability.

Beta Decay

Beta decay is a type of radioactive decay where a neutron in an unstable nucleus transforms into a proton, releasing an electron (beta particle) in the process. This type of decay increases the atomic number of the element by one while keeping the mass number the same. It is a common way for unstable isotopes to stabilize themselves.

This is seen in the exercise example, where after uranium-239 is formed, it undergoes beta decay to become neptunium-239. This decay emits a beta particle and transforms a neutron into a proton, increasing the atomic number from 92 to 93. Subsequently, neptunium-239 undergoes another beta decay to form plutonium-239, raising the atomic number to 94.

Important characteristics of beta decay include:

• The transformation of a neutron into a proton.
• The emission of a beta particle, which is an electron or positron.
• An increase in the atomic number of the resulting isotope.

Beta decay is a crucial process in nuclear reactions, particularly for neutron-rich isotopes moving towards stability.