Problem 73 - Chemistry: An Atoms-Focused Approach

Question

What nuclide is produced in the core of a giant star by each of the following fusion reactions? Assume there is only one product in each reaction. a. \(^{12} \mathrm{C}+^{4} \mathrm{He} \rightarrow\) b. \(^{20} \mathrm{Ne}+^{4} \mathrm{He} \rightarrow\) c. \(^{32} S+^{4}\) He \(\rightarrow\)

Step-by-Step Solution

Answer

Question: Identify the nuclide produced in each of the following fusion reactions in a star's core: a. \(^{12} \mathrm{C}+^{4} \mathrm{He}\) b. \(^{20} \mathrm{Ne}+^{4} \mathrm{He}\) c. \(^{32} S+^{4} \mathrm{He}\) Answer: a. \(^{16}\mathrm{O}\) b. \(^{24}\mathrm{Mg}\) c. \(^{36}\mathrm{Ar}\)

Step 1: Identify the atomic numbers and nucleon numbers of the elements

For each reaction, we have to identify the atomic numbers (number of protons) and nucleon numbers (total number of protons and neutrons) of the elements involved. Here they are: a. \(^{12} \mathrm{C}\) - Carbon has an atomic number (Z) of 6 (6 protons) and a nucleon number (A) of 12 (6 protons + 6 neutrons). \(^{4} \mathrm{He}\) - Helium has an atomic number (Z) of 2 (2 protons) and a nucleon number (A) of 4 (2 protons + 2 neutrons). b. \(^{20} \mathrm{Ne}\) - Neon has an atomic number (Z) of 10 (10 protons) and a nucleon number (A) of 20 (10 protons + 10 neutrons). \(^{4} \mathrm{He}\) - Same as in a. c. \(^{32} S\) - Sulfur has an atomic number (Z) of 16 (16 protons) and a nucleon number (A) of 32 (16 protons + 16 neutrons). \(^{4} \mathrm{He}\) - Same as in a and b.

Step 2: Calculate the atomic numbers and nucleon numbers of the resulting nuclei

For each reaction, we need to add the atomic numbers and nucleon numbers of the elements involved. Here are the results: a. Atomic number: 6 (C) + 2 (He) = 8 Nucleon number: 12 (C) + 4 (He) = 16 b. Atomic number: 10 (Ne) + 2 (He) = 12 Nucleon number: 20 (Ne) + 4 (He) = 24 c. Atomic number: 16 (S) + 2 (He) = 18 Nucleon number: 32 (S) + 4 (He) = 36

Step 3: Identify the resulting nuclide for each reaction

Using the atomic numbers and nucleon numbers calculated in Step 2, we can now identify the resulting nuclide for each reaction: a. The nuclide with atomic number 8 and nucleon number 16 is \(^{16} \mathrm{O}\). So the reaction is: \(^{12} \mathrm{C}+^{4} \mathrm{He} \rightarrow ^{16}\mathrm{O}\). b. The nuclide with atomic number 12 and nucleon number 24 is \(^{24} \mathrm{Mg}\). So the reaction is: \(^{20} \mathrm{Ne}+^{4} \mathrm{He} \rightarrow ^{24}\mathrm{Mg}\). c. The nuclide with atomic number 18 and nucleon number 36 is \(^{36} \mathrm{Ar}\). So the reaction is: \(^{32} S+^{4} \mathrm{He} \rightarrow ^{36}\mathrm{Ar}\). Thus, the nuclides produced in the core of a giant star for each fusion reaction are as follows: a. \(^{16}\mathrm{O}\) b. \(^{24}\mathrm{Mg}\) c. \(^{36}\mathrm{Ar}\)

Key Concepts

Fusion Reactions

Fusion reactions are a crucial process occurring in the cores of stars, including our Sun. These reactions are the heart of stellar nucleosynthesis—the creation of new elements within stars. In a fusion reaction, lighter atomic nuclei come together, or "fuse," to form a heavier nuclide. This process not only creates new elements but releases a significant amount of energy in the form of radiation and heat.

Key aspects of fusion reactions include:

• Combining atomic nuclei: For fusion to occur, the reacting atoms must overcome the repulsive electrostatic forces between their positively charged nuclei. This requires extreme environmental conditions, typically found in the cores of stars, where temperatures and pressures are incredibly high.
• Energy release: Fusion reactions release more energy than they consume, a stark contrast to other types of nucleosynthesis processes. This energy is what powers stars, allowing them to shine and provide light and heat.
• Production of heavier elements: As seen in typical reactions such as hydrogen fusing into helium in the Sun, or in heavier element creation during later stages in a star's life cycle, these reactions create increasingly heavier elements up the periodic table.

Fusion reactions are therefore fundamental for understanding the lifecycle of stars and the composition of the universe.

Nuclide Formation

Nuclide formation is a key aspect of fusion reactions. A nuclide represents a distinct kind of atomic nucleus defined by its number of protons and neutrons, and fusion in stars leads to the creation of new nuclides.

As illustrated in the exercise, here are examples of nuclide formation in fusion:

• Carbon-12 and Helium-4 fuse to form Oxygen-16 ( \(^{12}\text{C} + ^{4}\text{He} \rightarrow ^{16}\text{O} \)). This process shows how two different atomic nuclei can combine to create a heavier, stable nuclide, contributing to the variety of elements present in nature.
• In another reaction, Neon-20 and Helium-4 combine to yield Magnesium-24 ( \(^{20}\text{Ne} + ^{4}\text{He} \rightarrow ^{24}\text{Mg} \)), again demonstrating how stars synthesize heavier elements through fusion.
• Similarly, Sulfur-32 and Helium-4 react to produce Argon-36 ( \(^{32}\text{S} + ^{4}\text{He} \rightarrow ^{36}\text{Ar} \)). Each of these reactions highlights the nature of nuclide formation in stellar environments.

Through this constant fusion and nuclide creation, stars act as cosmic engines of creation, forging the elements necessary for planetary systems and life.

Nuclear Reactions in Stars

Nuclear reactions, particularly fusion, are the defining features of a star's life and evolution. These reactions occur under the intense heat and pressure in the stellar core, driving the star’s energy production and lifecycle phases. As stars age, the types of nuclear reactions they undergo evolve, influencing the elements they produce.

• In a young, main sequence star, hydrogen fuses into helium via the proton-proton chain reaction or the CNO cycle, depending on the star's size. This phase provides the star with the majority of its energy over billions of years.
• As the hydrogen fuel diminishes, stars enter a new phase where helium and heavier elements undergo fusion. This includes reactions like the ones from the exercise, where helium is fused with carbon, neon, or sulfur, producing heavier elements such as oxygen, magnesium, and argon.
• The life cycle of a star dictates which nuclear reactions will dominate. In massive stars, a series of fusion processes known as the alpha process occur, steadily building up heavier elements through successive helium capturing.

Ultimately, the nuclear reactions within stars are responsible for the diversity of elements in the universe and play a fundamental role in creating and enriching the interstellar medium with elements that form new stars, planets, and, eventually, life.