📚 Nuclear Physics Key Points for WJEC A-Level | A-Level WJEC 物理：核物理考点精讲
Nuclear physics is a fascinating topic in WJEC A-Level Physics that covers the structure of the nucleus, radioactivity, and the powerful processes of fission and fusion. Understanding these concepts not only helps in exams but also reveals the principles behind nuclear energy and medical imaging. This article breaks down the essential topics, formulas, and common exam pitfalls to boost your revision.
核物理是WJEC A-Level物理中的一个引人入胜的主题，涵盖原子核结构、放射性以及裂变和聚变等强大过程。掌握这些概念不仅有助于考试，还能揭示核能与医学成像背后的原理。本文将梳理核心知识点、关键公式和常见考试陷阱，高效备考。
1. Atomic Nucleus & Nuclide Notation | 原子核与核素符号
The atomic nucleus consists of protons and neutrons, collectively called nucleons. The number of protons Z determines the element, while the total number of nucleons A = Z + N (where N is the neutron number) gives the mass number. Nuclides are represented as ᵘzX, e.g. ²³⁸₉₂U for uranium-238. In WJEC questions, you may be given a table of particles and asked to deduce unknown species in decay equations. Remember, in nuclide notation the bottom number is proton number and the top is mass number.
原子核由质子和中子组成，统称核子。质子数Z决定元素种类，核子总数A = Z + N（N为中子数）为质量数。核素用符号 ᵘzX表示，如铀-238写作 ²³⁸₉₂U。在WJEC试题中，你可能会遇到根据表格粒子推断衰变方程中未知核素的问题。记住，核素符号中下角标是质子数，上角标是质量数。
The notation ¹₂H represents deuterium, an isotope of hydrogen with one neutron. To determine the neutron number, simply subtract Z from A: N = A – Z.
¹₂H表示氘，是氢的一种同位素，含有一个中子。要计算中子数，只需用A减去Z：N = A – Z。
2. Isotopes and Nuclear Forces | 同位素与核力
Isotopes are atoms of the same element with the same proton number but different neutron numbers. They have identical chemical properties but different nuclear stabilities. For instance, carbon-12 (¹²₆C) and carbon-14 (¹⁴₆C) are isotopes.
同位素是质子数相同但中子数不同的同种元素原子。它们化学性质相同，但核稳定性不同。如碳-12 (¹²₆C) 和碳-14 (¹⁴₆C) 互为同位素。
The strong nuclear force binds nucleons together, overcoming the electrostatic repulsion between protons. It is a short-range force, effective only up to a few femtometres, and is independent of charge. This force explains why nuclei with more than one proton can remain stable.
强核力束缚核子，克服质子间的静电斥力。它是一种短程力，仅在几飞米范围内有效，且与电荷无关。这就解释了为什么含有多个质子的原子核仍能保持稳定。
3. Mass Defect and Binding Energy | 质量亏损与结合能
When nucleons come together to form a nucleus, the total mass of the nucleus is slightly less than the sum of the masses of its individual nucleons. This difference is called the mass defect (Δm). The binding energy is the energy equivalent of this mass loss, calculated using Einstein’s equation E = Δm c². It represents the work needed to separate a nucleus into its constituent nucleons.
当核子结合形成原子核时，原子核的总质量略小于其各个核子质量之和，这一差值称为质量亏损（Δm）。结合能则相当于该质量损失的能量，通过爱因斯坦方程E = Δm c²计算。它代表了将原子核拆散成单个核子所需的能量。
Binding energy per nucleon is a measure of nuclear stability; the higher the binding energy per nucleon, the more stable the nucleus. The curve of binding energy per nucleon against mass number peaks around iron-56, explaining why energy is released in both fission of heavy elements and fusion of light ones.
每个核子的结合能（比结合能）是衡量核稳定性的一种指标；比结合能越高，原子核越稳定。比结合能随质量数变化的曲线在铁-56附近达到峰值，这就解释了为什么重核裂变和轻核聚变都能释放能量。
4. Einstein’s Mass–Energy Equivalence | 爱因斯坦质能方程
The equation E = mc² shows that mass and energy are interchangeable. In nuclear processes, a tiny amount of mass can be converted into a huge amount of energy. This principle underlies the energy release in fission and fusion.
方程E = mc²表明质量与能量可以相互转化。在核过程中，微小的质量可转化为巨大的能量。这是裂变和聚变能量释放的基础。
1 u = 1.66 × 10²⁷ kg = 931.5 MeV/c²
This conversion factor is essential for energy calculations: if the mass defect is known in atomic mass units, simply multiply by 931.5 to obtain the energy in MeV.
这一换算因子对能量计算至关重要：如果质量亏损以原子质量单位给出，只需乘以931.5即可得到以MeV为单位的能量。
5. Radioactive Decay: Types and Properties | 放射性衰变类型
Alpha decay involves the emission of a helium nucleus (⁴₂He), which reduces the mass number by 4 and the proton number by 2. Alpha particles are highly ionising but have low penetration, being stopped by paper or a few cm of air.
α衰变发射一个氦核（⁴₂He），使质量数减少4，质子数减少2。α粒子电离能力强，但穿透力弱，可被纸张或几厘米空气阻挡。
In beta-minus (β¹) decay, a neutron turns into a proton, emitting an electron (⁰₁₋e) and an anti-electron-neutrino (ν̅₁). The mass number remains unchanged, but the proton number increases by 1.
在β¹衰变中，一个中子转变成一个质子，同时发射一个电子（⁰₁₋e）和一个反电子中微子（ν̅₁）。质量数不变，但质子数增加1。
Beta-plus (β⁺) decay involves a proton converting into a neutron, emitting a positron (⁰₁&e) and an electron-neutrino (ν₁). The daughter nucleus has the same mass number but a proton number decreased by 1.
β⁺衰变涉及一个质子转变成中子，同时发射一个正电子（⁰₁&e）和一个电子中微子（ν₁）。子核的质量数不变，但质子数减少1。
Gamma (γ) decay is the emission of high-energy electromagnetic radiation, usually after alpha or beta decay, allowing the nucleus to release excess energy without changing A or Z.
γ衰变是发射高能电磁辐射，通常发生在α或β衰变之后，使原子核释放过剩能量而不改变A或Z。
6. Decay Equations and Conservation Laws | 衰变方程与守恒律
In any nuclear decay, the total mass number and total proton number are conserved. For example, uranium-238 alpha decay is written as:
在任何核衰变中，总质量数和总质子数守恒。例如铀-238 α衰变方程式为：
²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He
For beta-minus decay of carbon-14:
碳-14的β¹衰变：
¹⁴₆C → ¹⁴₇N + ⁰₁₋e + ν̅₁
Conservation of charge is also observed: the total charge before and after must be the same. Likewise, energy and momentum are conserved, which is why the neutrino was originally postulated to account for the continuous energy spectrum of beta particles.
电荷守恒也同样遵循：反应前后的总电荷必须相等。此外能量与动量也守恒，这就是当初为解释β粒子的连续能谱而提出中微子的原因。
7. Activity and the Decay Constant | 活度与衰变常数
The activity (A) of a radioactive source is the number of decays per second. It is proportional to the number of undecayed radioactive nuclei (N), given by:
放射源的活度（A）是每秒衰变次数。它与未衰变放射性核的数量（N）成正比，关系式为：
A = λ N
Activity is measured in becquerels (Bq), where 1 Bq = 1 decay per second. The decay constant λ (s¹) is the probability of a nucleus decaying per unit time. A larger λ means a more active source and a shorter half-life.
活度以贝克勒尔（Bq）为单位，1 Bq = 每秒1次衰变。衰变常数λ（单位s¹）是每个核在单位时间内衰变的概率。λ越大意味着源越活跃，半衰期越短。
8. Exponential Decay Law and Half-life | 指数衰变与半衰期
Radioactive decay follows an exponential law:
放射性衰变遵循指数规律：
N = N₀ e–λt and A = A₀ e–λt
The half-life T₁⁄₂ is the time taken for half the nuclei to decay, or for the activity to halve. It is related to the decay constant by:
半衰期T₁⁄₂是半数核衰变所需的时间，或活度减半所需时间。它与衰变常数的关系为：
T₁⁄₂ = ln 2 / λ ≈ 0.693 / λ
For example, if a sample of iodine-131 has an initial activity of 800 Bq and a half-life of 8 days, after 24 days its activity will be 800 × (½)³ = 100 Bq. In WJEC exams, you may need to read half-lives from graphs or solve for time using the exponential equation.
例如，一个碘-131样品的初始活度为800 Bq，半衰期为8天，则24天后活度为800 × (&
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