Equation 21.28 is the nuclear reaction responsible for much of the helium-4 production in our Sun. How much energy is released in this reaction?

Verified step by step guidance

1. Step 1: Identify the nuclear reaction responsible for helium-4 production in the Sun. This is typically the fusion of hydrogen nuclei (protons) into helium-4 through a series of reactions known as the proton-proton chain.
2. Step 2: Write down the balanced nuclear equation for the proton-proton chain reaction. The overall reaction can be summarized as: 4 \(^1_1\text{H} \rightarrow \ ^4_2\text{He} + 2\beta^+ + 2\nu_e\), where \(^1_1\text{H}\) is a proton, \(^4_2\text{He}\) is a helium-4 nucleus, \(\beta^+\) is a positron, and \(\nu_e\) is a neutrino.
3. Step 3: Calculate the mass defect, which is the difference between the mass of the reactants and the mass of the products. Use the atomic masses of the hydrogen and helium nuclei to find this difference.
4. Step 4: Use Einstein's mass-energy equivalence principle, \(E=mc^2\), to calculate the energy released. Here, \(m\) is the mass defect and \(c\) is the speed of light in a vacuum (approximately \(3.00 \times 10^8\) m/s).
5. Step 5: Convert the energy from joules to a more convenient unit, such as mega-electronvolts (MeV), using the conversion factor \(1 \text{ J} = 6.242 \times 10^{12} \text{ MeV}\).

Key Concepts

Nuclear Reactions

Nuclear reactions involve changes in an atom's nucleus and can result in the transformation of elements. In the context of the Sun, these reactions primarily include fusion processes where lighter nuclei combine to form heavier nuclei, releasing energy. Understanding the types of nuclear reactions, such as fusion and fission, is essential for analyzing energy production in stars.

Energy Release in Fusion

The energy released during nuclear fusion is a result of the mass-energy equivalence principle, described by Einstein's equation E=mc². When lighter nuclei fuse, the mass of the resulting nucleus is less than the sum of the original masses, and this 'missing' mass is converted into energy. This principle is crucial for calculating the energy output of fusion reactions in the Sun.

Helium-4 Production

Helium-4 is a product of the fusion of hydrogen nuclei in the Sun, primarily through the proton-proton chain reaction. This process not only produces helium but also releases significant amounts of energy in the form of gamma rays and kinetic energy of particles. Understanding the specific pathways of helium production helps in quantifying the energy released in solar nuclear reactions.