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 \(1 \text{ J} = 6.242 \times 10^{12} \text{ MeV}\).