Calculate the energy released in the fusion reaction: ${}_2^{3}He{+}_1^{2}H{\to }_2^{4}He{+}_1^{1}H$

Verified step by step guidance

1. Step 1: Understand the fusion reaction. Fusion is a process where two lighter nuclei combine to form a heavier nucleus, releasing energy. Identify the specific nuclei involved in the reaction (e.g., hydrogen isotopes like deuterium and tritium).
2. Step 2: Write the nuclear reaction equation. For example, in the fusion of deuterium (²H) and tritium (³H), the reaction is: $H_2+H_3\to {\mathrm{He}}_4+n$. This produces helium-4 and a neutron.
3. Step 3: Calculate the mass defect. Determine the mass of the reactants (deuterium and tritium) and the products (helium-4 and neutron). Use the equation: $\mathrm{∆m}=m$_reactants-m_products, where $\mathrm{∆m}$ is the mass defect.
4. Step 4: Convert the mass defect to energy using Einstein's equation: $E=\mathrm{mc}^2$. Here, $m$ is the mass defect and $c$ is the speed of light ($3.00\times 10^8\mathrm{m/s}$).
5. Step 5: Interpret the result. The energy calculated represents the energy released during the fusion reaction. This energy is typically expressed in joules or electron volts (eV).

Key Concepts

Nuclear Fusion

Nuclear fusion is the process where two light atomic nuclei combine to form a heavier nucleus, releasing a significant amount of energy. This reaction powers stars, including our sun, and occurs under extreme temperature and pressure conditions. Understanding fusion is crucial for calculating the energy released in such reactions.

Binding Energy

Binding energy is the energy required to separate a nucleus into its constituent protons and neutrons. It is also the energy released when a nucleus is formed from these particles. The difference in binding energy before and after a fusion reaction determines the energy released, making it a key concept in energy calculations.

Mass-Energy Equivalence

Mass-energy equivalence, expressed by Einstein's equation E=mc², states that mass can be converted into energy and vice versa. In fusion reactions, a small amount of mass is lost and converted into energy, which is released during the process. This principle is fundamental for understanding how energy is calculated in nuclear reactions.