Question

When two protons fuse in a star, the product is \(^{2} \mathrm{H}\) plus a positron. Write the nuclear equation for this process.

Short answer

The balanced nuclear equation for the fusion of two protons in a star is: \( ^{1}\mathrm{H} + ^{1}\mathrm{H} \rightarrow ^{2}\mathrm{H} + ^{0}\mathrm{e} \)

Step-by-step solution

Identify the particles involved in the reaction

Before writing the nuclear equation, we need to identify the particles involved: 1. Protons: A proton is a hydrogen nucleus with a mass number (A) of 1 and an atomic number (Z) of 1. Its nuclear notation is \(^{1}\mathrm{H}\). 2. Deuterium: Deuterium is an isotope of hydrogen with a mass number (A) of 2 and an atomic number (Z) of 1. Its nuclear notation is \(^{2}\mathrm{H}\). 3. Positron: A positron is an anti-particle of the electron with a mass number (A) of 0 and a positive atomic number (Z) of 1. Its nuclear notation is \(^{0}\mathrm{e}\).

Write the initial (unbalanced) nuclear equation

Now that we know the particles involved, we can write the unbalanced nuclear equation: $$ ^{1}\mathrm{H} + ^{1}\mathrm{H} \rightarrow ^{2}\mathrm{H} + ^{0}\mathrm{e} $$

Check if the nuclear equation is balanced

To check if a nuclear equation is balanced, we need to make sure the mass numbers (A) and atomic numbers (Z) are conserved on both sides of the equation: Left side: - Total mass number (A) = 1 + 1 = 2 - Total atomic number (Z) = 1 + 1 = 2 Right side: - Total mass number (A) = 2 + 0 = 2 - Total atomic number (Z) = 1 + 1 = 2 Since both mass numbers and atomic numbers are conserved, the nuclear equation is balanced.

Write the final balanced nuclear equation

The balanced nuclear equation for the fusion of two protons in a star is: $$ ^{1}\mathrm{H} + ^{1}\mathrm{H} \rightarrow ^{2}\mathrm{H} + ^{0}\mathrm{e} $$

Key concepts

Nuclear Chemistry

Nuclear chemistry revolves around the study of atomic nuclei and the changes they undergo.
One of the most fundamental processes in nuclear chemistry is nuclear fusion, which is a reaction where two or more nuclei come together to form a heavier nucleus.

This is what fuels the stars, including our Sun, and is responsible for the creation of elements heavier than hydrogen. The process releases a significant amount of energy, which is why fusion reactions are being investigated as a potential source of clean and almost limitless power here on Earth.

The Basics of Nuclear Reactions

In a nuclear reaction, the total number of protons and neutrons (mass number) and the total charge (atomic number) must be conserved.
This ensures that energy and matter are not lost, in accordance with the law of conservation of mass-energy.

Balancing Nuclear Equations

Balancing nuclear equations is similar to balancing chemical equations, but it focuses on the protons and neutrons in an atom's nucleus.

To balance a nuclear equation, you must ensure that the sum of atomic numbers and the sum of mass numbers are equal on both sides of the equation.

Conservation Laws in Nuclear Equations

The conservation of mass and charge is crucial when balancing nuclear equations.
In the example of two protons fusing into deuterium and producing a positron, the total mass and charge before and after the reaction must remain the same. By following these rules and checking the sum of the mass and atomic numbers, you can verify if a nuclear equation is accurately balanced.

Isotopes

Isotopes are atoms of the same element that have the same number of protons but a different number of neutrons.

This causes them to have different mass numbers but the same atomic number. Isotopes can be stable or unstable. Unstable isotopes undergo radioactive decay over time, leading to changes in their nuclear composition.

Significance of Isotopes in Nuclear Reactions

Understanding isotopes is essential in nuclear chemistry. Each isotope has its own set of properties that can significantly influence nuclear reactions, like the fusion process mentioned in the exercise. Deuterium, for example, is a stable isotope of hydrogen that plays a key role in nuclear fusion reactions in stars and potential energy sources on Earth.