How much energy is released (in kJ) in the fusion reaction of 2H to yield 1 mol of 3He? The atomic mass of 2H is 2.0141, and the atomic mass of 3He is 3.0160.

Verified step by step guidance

1. Identify the fusion reaction: \( ^2\text{H} + ^2\text{H} \rightarrow ^3\text{He} + \text{n} \).
2. Calculate the mass defect: Subtract the total mass of the products from the total mass of the reactants.
3. Convert the mass defect from atomic mass units (amu) to kilograms (kg) using the conversion factor: 1 amu = 1.66053906660 \times 10^{-27} \text{ kg}.
4. Use Einstein's equation \( E = mc^2 \) to calculate the energy released, where \( m \) is the mass defect in kg and \( c \) is the speed of light (\( 3.00 \times 10^8 \text{ m/s} \)).
5. Convert the energy from joules to kilojoules (1 kJ = 1000 J) to find the energy released in kJ.

Key Concepts

Nuclear Fusion

Nuclear fusion is a process where two light atomic nuclei combine to form a heavier nucleus, releasing energy in the process. This reaction is the source of energy for stars, including the sun, and occurs under extreme temperature and pressure conditions. In the context of the question, the fusion of deuterium (2H) to form helium-3 (3He) is a specific example of this phenomenon.

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 nuclear reactions, the mass of the products is often less than the mass of the reactants, and this 'missing' mass is converted into energy. Understanding this concept is crucial for calculating the energy released in the fusion reaction described in the question.

Atomic Mass and Energy Calculation

Atomic mass is the mass of an atom, typically measured in atomic mass units (amu), and is essential for calculating the energy released in nuclear reactions. To find the energy released during fusion, one must determine the mass defect (the difference in mass between reactants and products) and convert this mass defect into energy using the mass-energy equivalence principle. This calculation is key to answering the question accurately.