Problem 50 - Chemistry The Molecular Science

Question

Elements are formed by nuclear fusion reactions including so-called "carbon burning", the fusion of two carbon-12 nuclei to produce sodium- 23 and a proton. Write a balanced nuclear equation to represent this process.

Step-by-Step Solution

Answer

\( ^{12}_{6}\text{C} + ^{12}_{6}\text{C} \rightarrow ^{23}_{11}\text{Na} + ^{1}_{1}\text{H} \)

Step 1: Understand the Components

To write the nuclear equation, we need to understand that the reaction involves the fusion of two carbon-12 nuclei to form sodium-23 and a proton. The initial and final products must be written accurately.

Step 2: Identify the Reactants

The reactants in the reaction are two carbon-12 nuclei, which can be written as \( ^{12}_{6}\text{C} \) for each.

Step 3: Identify the Products

The products of the reaction are sodium-23 and a proton. Sodium-23 is written as \( ^{23}_{11}\text{Na} \), and a proton is written as \( ^{1}_{1}\text{H} \).

Step 4: Write the Nuclear Equation

Combine the reactants and products into a nuclear equation: \[ ^{12}_{6}\text{C} + ^{12}_{6}\text{C} \rightarrow ^{23}_{11}\text{Na} + ^{1}_{1}\text{H} \].

Step 5: Check for Balance

Ensure that the sum of mass numbers (top numbers) and atomic numbers (bottom numbers) are equal on both sides of the equation. Both sides have a total mass number of 24 and a total atomic number of 12.

Key Concepts

Carbon Burning

Carbon burning is a term used in astrophysics to describe a nuclear fusion reaction where two carbon-12 nuclei collide and fuse together. This reaction is one of the vital stages of a star's lifecycle, typically occurring in massive stars where temperatures and pressures are extremely high.
In essence, carbon burning is a process of energy production and element synthesis in stars, advancing the stellar evolution process.

• Occurs in the core of massive stars.
• Precedes the neon burning phase in stellar nucleosynthesis.
• Results in the formation of heavier elements, such as sodium and neon.

Understanding carbon burning is crucial in comprehending how elements heavier than helium are formed in the universe, contributing to the overall elemental makeup of celestial bodies.

Nuclear Equation

A nuclear equation is a way of representing a nuclear reaction, similar to how chemical equations represent chemical reactions. In a nuclear equation, the atomic number and mass number must be balanced on both sides of the equation, ensuring the law of conservation of mass and charge is adhered to.
When writing a nuclear equation for a reaction, such as carbon burning, it is important to accurately represent all the reactants and products.

• Identifies the nuclei involved in the reaction.
• Ensures the total mass numbers and atomic numbers are equal on both sides of the equation.
• Provides a clear visual representation of the nuclear process.

This balancing of nuclear equations is fundamental to understanding how different elements form through stellar processes.

Proton Fusion

Proton fusion refers to nuclear reactions where protons are either added or produced. Processes such as these occur frequently in stars where temperatures are extremely high, providing energy in the form of radiation.
In the case of carbon burning, a proton is a by-product of the fusion of two carbon-12 nuclei. This proton plays a significant role in subsequent nuclear reactions, contributing to various nuclear synthesis processes within a star.

• Central to several types of nuclear fusion.
• Protons can be used to form new nuclei or particles.
• Proton emission in reactions indicates changes in nuclear structure.

Protons are fundamental components of atomic nuclei, and their fusion or emission often results in the production of new elements or isotopes.

Carbon-12 Nuclei

Carbon-12 is an isotope of carbon consisting of 6 protons and 6 neutrons, making its atomic mass 12. It is one of the most abundant forms of carbon found on Earth, playing a significant role in both earthly and cosmic processes.
In nuclear fusion contexts, carbon-12 nuclei act as building blocks for heavier elements. During carbon burning, two carbon-12 nuclei combine to create sodium-23 and a proton, demonstrating their role in creating new elements in stars.

• Stable and most abundant form of carbon.
• Serves as a primary reactant in stellar fusion reactions.
• Essential to understanding nucleosynthesis in stars.

The fusion of carbon-12 nuclei is a pivotal step in the chain of stellar processes that lead to the synthesis of elements, making them critical to star life cycles and cosmic evolution.