📚 Nuclear Energy: Mass Defect, Binding Energy, Fission and Fusion | 核能：质量亏损、结合能、裂变与聚变
Nuclear energy is released when the structure of atomic nuclei changes. The key ideas are mass-energy equivalence, mass defect, binding energy, and the processes of nuclear fission and fusion. In this article, we review the AQA International A-level physics content on nuclear energy, including reactor components and energy calculations.
当原子核结构发生变化时，就会释放核能。核心概念包括质能等价、质量亏损、结合能以及核裂变与核聚变过程。本文将复习 AQA International A-level 物理中关于核能的内容，包括反应堆组成部分和能量计算。
1. Mass-Energy Equivalence | 质能等价
Einstein's special theory of relativity shows that mass and energy are equivalent. If a system loses mass Δm, it releases energy E given by the equation:
爱因斯坦的狭义相对论表明，质量和能量是等价的。如果系统损失质量 Δm，就会释放能量 E，公式为：
E = mc²
ge, so a tiny mass loss corresponds to a very large energy release. This is why nuclear reactions release millions of times more energy per kilogram than chemical reactions.
由于 c = 3.00 × 10⁸ m s⁻¹，c² 非常大，因此极小的质量损失对应极大的能量释放。这就是为什么核反应每千克释放的能量比化学反应高数百万倍。
2. Atomic Mass Unit and Mass Defect | 原子质量单位与质量亏损
The atomic mass unit u is defined as exactly 1/12 of the mass of a carbon-12 atom. In SI units:
原子质量单位 u 的定义是碳-12 原子质量的 1/12。用 SI 单位表示：
1 u = 1.661 × 10⁻²⁷ kg
The mass defect Δm of a nucleus is the difference between the total mass of its separate protons and neutrons and the actual mass of the bound nucleus. For a nucleus with Z protons and N neutrons:
原子核的质量亏损 Δm 是单独质子和中子的总质量与实际结合后原子核质量之差。对于有 Z 个质子、N 个中子的原子核：
Δm = Z mₚ + N mₙ − M_nucleus
This 'lost' mass has not disappeared; it has been converted into binding energy when the nucleus formed.
这部分 '消失' 的质量并没有消失；它在核形成时转化为了结合能。
3. Binding Energy and Binding Energy per Nucleon | 结合能与比结合能
The binding energy BE of a nucleus is the work that must be done to separate it completely into individual protons and neutrons. It is calculated from the mass defect:
原子核的结合能 BE 是将它完全拆分为独立质子和中子所需做的功。它由质量亏损计算：
BE = Δm × c²
More useful for comparing nuclei is binding energy per nucleon, BE/A. A higher value means each nucleon is held more tightly, so the nucleus is more stable.
比较原子核时更有用的量是比结合能 BE/A。数值越高，说明每个核子被束缚得越紧，原子核就越稳定。
For example, iron-56 has a very high binding energy per nucleon of about 8.8 MeV, making it one of the most stable nuclei.
例如，铁-56 的比结合能非常高，约为 8.8 MeV，是最稳定的原子核之一。
4. The Binding Energy Curve and Nuclear Stability | 结合能曲线与核稳定性
lei, reaches a broad maximum near A ≈ 56 (iron), and then falls slowly for heavier nuclei.
比结合能对质量数 A 的曲线在轻核区迅速上升，在 A ≈ 56（铁）附近达到宽峰，然后对于更重的核缓慢下降。
This shape explains two main energy-releasing processes. Fusion of very light nuclei moves them to the right and increases BE/A, releasing energy. Fission of very heavy nuclei splits them into lighter fragments with higher BE/A, also releasing energy.
这一形状解释了两类主要的释能过程。很轻的核发生聚变向右移动，比结合能增大，释放能量；很重的核发生裂变，分裂成比结合能更高的较轻碎片，同样释放能量。
Nuclei near iron are the most tightly bound and will not release energy by either fission or fusion.
铁附近的核结合得最紧，无论是裂变还是聚变都不会释放能量。
5. Induced Nuclear Fission of Uranium-235 | 铀-235 的诱发核裂变
Fission occurs when a heavy nucleus absorbs a slow (thermal) neutron and splits into two smaller daughter nuclei, releasing energy and further neutrons. A common example is uranium-235:
当一个重核吸收一个慢（热）中子并分裂成两个较小的子核时，就发生裂变，同时释放能量和更多中子。一个常见例子是铀-235：
²³⁵₉₂U + ¹₀n → ¹⁴¹₅₆Ba + ⁹²₃₆Kr + 3 ¹₀n + energy
The daughter nuclei and the neutrons have kinetic energy. Most of the energy appears as kinetic energy of the fission fragments, which is transferred to the coolant as heat.
子核和中子具有动能。大部分能量以裂变碎片的动能形式出现，这些能量以热量形式传递给冷却剂。
Fission fragments are generally radioactive because they are neutron-rich and decay by beta emission.
裂变碎片通常具有放射性，因为它们中子过多，会通过 β 衰变释放电子。
6. Chain Reactions and Critical Mass | 链式反应与临界质量
Each fission releases several neutrons. If at least one of these neutrons goes on to induce another fission, a self-sustaining chain reaction is possible.
每次裂变都会释放多个中子。如果其中至少有一个中子继续引发另一次裂变，就可能形成自持的链式反应。
1 the reaction dies out; if k = 1 it is steady and controlled; if k > 1 it grows rapidly.
增殖系数 k 是引发下一次裂变的平均中子数。若 k < 1，反应逐渐停止；若 k = 1，反应稳定可控；若 k > 1，反应急剧增长。
Critical mass is the minimum mass of fissile material needed for a self-sustaining chain reaction. Below this mass, too many neutrons escape without causing fission.
临界质量是维持自持链式反应所需裂变材料的最小质量。低于这一质量，太多中子会逃逸而不能引发裂变。
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