📚 Nuclear Physics: Mass Defect and Binding Energy (A = 195) | 核物理：质量亏损与结合能（A = 195）
In Edexcel A-Level Physics, mass defect and nuclear binding energy explain why the mass of a nucleus is always smaller than the total mass of its individual protons and neutrons. This missing mass is converted into energy that holds the nucleus together. The topic is central to understanding nuclear stability, radioactivity, fission and fusion, and it often appears in calculation questions involving Einstein’s mass-energy relation.
在 Edexcel A-Level 物理中，质量亏损与核结合能解释了为什么原子核的质量总是小于其所有质子和中子单独质量之和。这部分“缺失的质量”转化为维持原子核稳定的能量。该主题是理解核稳定性、放射性、裂变和聚变的核心，也经常出现在涉及爱因斯坦质能关系的计算题中。
1. Nucleons and Nuclide Notation | 核子与核素符号
A nuclide is written as ᴬZX, where A is the mass number (total number of protons and neutrons), Z is the atomic number (number of protons), and X is the chemical symbol. For example, platinum-195 is written as ¹⁹⁵Pt. It has Z = 78 protons and N = A − Z = 117 neutrons.
核素写作 ᴬZX，其中 A 是质量数（质子数与中子数之和），Z 是原子序数（质子数），X 是元素符号。例如，铂-195 写作 ¹⁹⁵Pt。它有 Z = 78 个质子和 N = A − Z = 117 个中子。
In nuclear calculations you must be able to identify proton number and neutron number from the nuclide symbol. A common mistake is to treat A as the number of neutrons; A is always the total number of nucleons.
在核计算中，你必须能够从核素符号中识别质子数和中子数。一个常见错误是把 A 当作中子数；A 始终是核子总数。
2. Atomic Mass Unit | 原子质量单位
Nuclear masses are very small, so physicists use the unified atomic mass unit, written as u. It is defined as one twelfth of the mass of a neutral carbon-12 atom. In SI units, 1 u = 1.661 × 10⁻²⁷ kg.
原子核的质量非常小，因此物理学家使用统一的原子质量单位，写作 u。它定义为中性碳-12 原子质量的十二分之一。在国际单位制中，1 u = 1.661 × 10⁻²⁷ kg。
In nuclear energy calculations, it is usually more convenient to express 1 u in energy units: 1 u = 931.5 MeV. This conversion comes directly from E = mc² and is given in the Edexcel data booklet.
在核能计算中，通常用能量单位表示 1 u 更为方便：1 u = 931.5 MeV。这一换算直接来源于 E = mc²，并已在 Edexcel 数据手册中给出。
| Particle | Mass / u |
|---|---|
| Proton | 1.00728 |
| Neutron | 1.00867 |
| Electron | 0.00055 |
3. Mass Defect | 质量亏损
Mass defect, Δm, is the difference between the total mass of the separated nucleons and the actual mass of the nucleus. When protons and neutrons come together to form a nucleus, some mass is converted into energy and released. Therefore, the nucleus is lighter than the sum of its parts.
质量亏损 Δm 是分离核子的总质量与原子核实际质量之差。当质子和中子结合形成原子核时，部分质量转化为能量并被释放。因此，原子核比其组成部分的总和更轻。
Δm = (Z mp + N mn) − Mnucleus
For ¹⁹⁵Pt, using Z = 78 and N = 117, the separated nucleon mass is larger than the actual nuclear mass by about 1.617 u. This small mass difference is responsible for a very large energy release because c² is extremely large.
对于 ¹⁹⁵Pt，取 Z = 78 和 N = 117，分离核子的质量比原子核实际质量大约多出 1.617 u。这一微小质量差之所以对应巨大的能量释放，是因为 c² 非常大。
4. Einstein’s Mass–Energy Relation | 爱因斯坦质能关系
Einstein’s mass-energy relation states that mass and energy are interchangeable. The energy equivalent of a mass m at rest is given by the most famous equation in physics.
爱因斯坦质能关系指出质量和能量可以相互转化。质量为 m 的静止物体对应的能量由物理学最著名的方程给出。
E = mc²
For a mass defect Δm, the binding energy released or required is E = Δm c². Because 1 u of mass is equivalent to 931.5 MeV, a mass defect of about 1.617 u corresponds to roughly 1506 MeV for ¹⁹⁵Pt.
对于质量亏损 Δm，释放或所需的结合能为 E = Δm c²。由于 1 u 质量相当于 931.5 MeV，大约 1.617 u 的质量亏损对应 ¹⁹⁵Pt 约 1506 MeV 的能量。
5. Binding Energy | 结合能
Binding energy is the minimum energy needed to separate a nucleus completely into its individual protons and neutrons. Equivalently, it is the energy released when a nucleus is assembled from free nucleons. A nucleus is stable because energy must be supplied to pull it apart.
结合能是将原子核完全分离为单个质子和中子所需的最小能量。等价地，它是自由核子组装成原子核时释放的能量。原子核之所以稳定，是因为要将它拆开必须提供能量。
For ¹⁹⁵Pt, the total binding energy is approximately 1506 MeV. This is a very large amount of energy on the atomic scale, but it is spread across 195 nucleons. The total binding energy alone does not tell us how stable the nucleus is compared with others.
对于 ¹⁹⁵Pt，总结合能约为 1506 MeV。这在原子尺度上是一个非常大的能量，但它分布在 195 个核子上。仅凭总结合能并不能说明该原子核相对于其他核素的稳定程度。
6. Binding Energy per Nucleon | 平均结合能
Binding energy per nucleon is found by dividing the total binding energy by the mass number A. It is a much more useful measure of nuclear stability than total binding energy because it allows fair comparison between different nuclides.
平均结合能（每个核子结合能）由总结合能除以质量数 A 得到。它比总结合能更能有效衡量核稳定性，因为它可以对不同核素进行公平比较。
Binding energy per nucleon = total binding energy ÷ A
For ¹⁹⁵Pt, the binding energy per nucleon is about 1506 ÷ 195 ≈ 7.72 MeV. Iron-56, one of the most stable nuclides, has a binding energy per nucleon of about 8.8 MeV, so platinum is less stable than iron but still relatively
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