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.

검증된 단계별 안내

Identify the fusion reaction: \( ^2\text{H} + ^2\text{H} \rightarrow ^3\text{He} + \text{n} \).

Calculate the mass defect: Subtract the total mass of the products from the total mass of the reactants.

Convert the mass defect from atomic mass units (amu) to kilograms (kg) using the conversion factor: 1 amu = 1.66053906660 \(\times\) 10^{-27} \(\text{ kg}\).

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 (\( 3.00 \times 10^8 \text{ m/s} \)).

Convert the energy from joules to kilojoules (1 kJ = 1000 J) to find the energy released in kJ.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

10m

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.