Problem 75 - Chemistry: The Central Science in SI Units, Global Edition

Question

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

Step-by-Step Solution

Answer

The nuclear equation for the fusion of two protons is: \( ^{1}_{1}\mathrm{H} + ^{1}_{1}\mathrm{H} \rightarrow ^{2}_{1}\mathrm{H} + e^{+}\).

Step 1: Identify the reactants and products

The reactants of the fusion process are two protons, and the products are \({ }^{2}\mathrm{H}\) (Deuterium) and a positron. Reactants: - Proton 1: \({ }^{1}\mathrm{H}\) (Mass Number: 1, Atomic Number: 1) - Proton 2: \({ }^{1}\mathrm{H}\) (Mass Number: 1, Atomic Number: 1) Products: - Deuterium: \({ }^{2}\mathrm{H}\) (Mass Number: 2, Atomic Number: 1) - Positron: \(e^{+}\) (Mass Number: 0, Atomic Number: +1)

Step 2: Write the nuclear equation

To write the nuclear equation for this process, we need to represent the initial reactants on the left side of the equation and the final products on the right side of the equation, making sure that both mass numbers and atomic numbers are conserved in this process. Reactants: \( ^{1}_{1}\mathrm{H} + ^{1}_{1}\mathrm{H} \) Products: \( ^{2}_{1}\mathrm{H} + e^{+} \) Nuclear Equation: \( ^{1}_{1}\mathrm{H} + ^{1}_{1}\mathrm{H} \rightarrow ^{2}_{1}\mathrm{H} + e^{+}\)

Key Concepts

Nuclear Equations

Nuclear equations are vital for representing nuclear reactions occurring in stars and other cosmic events. They display how particles change during fusion reactions and maintain the conservation of mass and charge. In a nuclear equation, we reflect the atoms involved as well as their transformations.

When writing a nuclear equation, we must ensure both sides balance. This means that the total number of protons and neutrons (mass number) is consistent across the equation, just like the total charge (atomic number).

• The left side of the equation shows the reactants, or starting particles.
• The right side shows the products, or resulting particles after the reaction.

For example, when two protons, denoted as \( ^{1}_{1}\mathrm{H} \), combine, they form a deuterium \( ^{2}_{1}\mathrm{H} \) and a positron \( e^{+} \). The nuclear equation capturing this reaction looks like: \( ^{1}_{1}\mathrm{H} + ^{1}_{1}\mathrm{H} \rightarrow ^{2}_{1}\mathrm{H} + e^{+} \). This balance exemplifies how each element transforms in the star's heart.

Proton-Proton Fusion

Proton-proton fusion is a critical process powering stars, including our sun. It refers to the reactions where hydrogen nuclei combine to form helium, releasing energy. It’s the heart of stellar energy production, converting mass into energy through nuclear fusion.

In this context, when two protons fuse, the reaction results in the creation of deuterium. This is one of the first steps in the multi-step proton-proton chain reaction that fuels stars. Here's a quick breakdown:

• Initial Protons: Two \( ^{1}_{1}\mathrm{H} \) or hydrogen nuclei begin the reaction.
• Creation of Deuterium: These fuse to form \( ^{2}_{1}\mathrm{H} \), a heavier hydrogen isotope, also known as deuterium.
• Positron Emission: This reaction also releases a positron, \( e^{+} \), a particle similar to an electron but with a positive charge.

This fusion occurs in the extreme heat and pressure found in stellar cores, where the protons have enough energy to overcome their electrostatic repulsion.

Deuterium Synthesis

Deuterium synthesis is the formation of a deuterium nucleus, a stable hydrogen isotope, consisting of one proton and one neutron. This process occurs naturally in the early stages of star formation as part of nuclear fusion.

The synthesis happens when two protons, under extreme stellar conditions, come together, overcoming repulsion due to positive charges. During this fusion:

• Neutron Formation: One of the protons in the fusion process turns into a neutron, creating the stable deuterium.
• Energy Release: The process releases energy in the form of gamma rays and other subatomic particles, crucial for the star's energy output.
• Neutrino Emission: Often, a neutrino, an elusive, neutral particle, is also released, helping maintain conservation laws.

Understanding deuterium synthesis helps astrophysicists comprehend star life cycles, including how energy is generated and how elemental creation progresses in the universe.