📚 IB & WJEC Physics: Nuclear Physics | IB WJEC 物理：核物理考点精讲
Nuclear physics is a cornerstone of the IB and WJEC Physics syllabuses, probing the heart of matter and the forces that shape the universe. From the stability of the nucleus to energy release in stars, this revision guide consolidates every essential topic — nuclide notation, radioactive decay, mass–energy equivalence, binding energy, fission and fusion — so you can face your exam with confidence.
核物理是IB和WJEC物理课程的核心板块，探究物质最深处与塑造宇宙的力量。原子核的稳定性、放射性衰变规律、质能等价原理、结合能以及裂变与聚变，都是高频考点。本精讲系统梳理上述主题，助你理清线索、从容应对考试。
1. Nuclear Structure and Nuclide Notation | 原子核结构与核素符号
The atomic nucleus contains protons and neutrons, collectively called nucleons. The atomic number Z is the number of protons and determines the element. The mass number A is the total number of nucleons. A nuclide is represented as ᴬX, such as ²³⁸₉₂U or ¹⁴₆C. Isotopes have the same Z but different neutron numbers N = A − Z.
原子核由质子和中子（统称核子）组成。原子序数Z等于质子数，决定了元素种类。质量数A是核子总数。核素符号写作 ᴬX，例如 ²³⁸₉₂U 或 ¹⁴₆C。同位素具有相同的质子数 Z，但中子数 N = A − Z 不同。
The strong nuclear force binds nucleons together, overcoming the electrostatic repulsion between protons. This force is very short-range (≈ 1 fm) and acts equally between all nucleons. For nuclei to be stable, the neutron-to-proton ratio must lie on the stability band; as Z increases, more neutrons are needed to dilute Coulomb repulsion.
强核力将核子束缚在一起，克服质子间的静电斥力。强核力属于短程力（约1 fm），在所有核子之间等价作用。原子核要稳定，中质比必须落在稳定带内；随着原子序数Z增大，需要更多中子来稀释库仑排斥。
2. Radioactivity and Types of Decay | 放射性与衰变类型
Unstable nuclei spontaneously emit radiation to become more stable. The three classic emissions are alpha (α) particles, beta (β⁻ and β⁺) particles, and gamma (γ) rays. α decay emits a helium-4 nucleus ⁴₂He: ²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He. β⁻ decay occurs when a neutron converts to a proton, emitting an electron and an antineutrino: ¹⁴₆C → ¹⁴₇N + ⁰₋₁e + ν̅ₑ.
不稳定原子核会自发辐射以趋向稳定。三种典型辐射是α粒子、β粒子（β⁻/β⁺）和γ射线。α衰变释放一个氦-4核 ⁴₂He：²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He。β⁻衰变由一个中子转变成质子，释放电子与反中微子：¹⁴₆C → ¹⁴₇N + ⁰₋₁e + ν̅ₑ。
β⁺ decay (positron emission) occurs when a proton changes to a neutron, emitting a positron and a neutrino: ¹⁹₁₀Ne → ¹⁹₉F + ⁰₊₁e + νₑ. Gamma decay follows other decays; an excited nucleus releases a high‑energy photon without changing Z or A. Gamma rays are electromagnetic waves of very short wavelength and are highly penetrating.
β⁺衰变（正电子发射）是质子转变成中子，放出一个正电子与中微子：¹⁹₁₀Ne → ¹⁹₉F + ⁰₊₁e + νₑ。γ衰变通常伴随其他衰变，激发态核释放高能光子，不改变Z和A。γ射线是波长极短的电磁波，穿透力极强。
3. Decay Law and Half-Life | 衰变规律与半衰期
Radioactive decay is a random process described by the exponential decay law: N = N₀ e^(-λt), where N₀ is the initial number of undecayed nuclei, λ is the decay constant, and t is time. The activity A = λN also decays exponentially. The half‑life T½ is the time taken for half the nuclei to decay, given by T½ = ln 2 / λ ≈ 0.693 / λ.
放射性衰变是随机过程，遵循指数衰减规律：N = N₀ e^(-λt)，N₀为初始未衰变核数，λ为衰变常量，t为时间。活度A = λN也呈指数衰减。半衰期T½是半数核发生衰变所需的时间，由 T½ = ln 2 / λ ≈ 0.693 / λ 给出。
N = N₀ e^(-λt) and A = A₀ e^(-λt)
In exam problems, you often use the fraction remaining after n half‑lives: remaining fraction = (½)ⁿ, where n = t / T½. This approach avoids calculus and is heavily tested in both IB Paper 1 and WJEC Unit 4.
考题中常利用半衰期个数 n = t / T½ 计算剩余比例 = (½)ⁿ，这种方法避免了微积分，却是IB试卷一和WJEC单元四的高频考查点。
4. Mass Defect and Binding Energy | 质量亏损与结合能
The mass of a nucleus is always less than the sum of the masses of its individual nucleons. This mass difference is the mass defect Δm. The binding energy Eb is the energy equivalent of Δm via Einstein’s equation: Eb = Δm c². Binding energy represents the work needed to separate a nucleus into its constituent nucleons.
原子核的质量总是小于其所有核子各自质量之和，该质量差值称为质量亏损Δm。根据爱因斯坦质能方程，结合能 Eb = Δm c²。结合能可以理解为将原子核拆散为自由核子所需的最小能量。
In nuclear calculations, atomic masses are given in unified atomic mass units (u). 1 u = 1.6605 × 10⁻²⁷ kg, and 1 u × c² = 931.5 MeV. So, Eb (MeV) = Δm (u) × 931.5. Average binding energy per nucleon = Eb / A is a measure of nuclear stability.
核计算中，原子质量通常用统一原子质量单位 u 给出。1 u = 1.6605 × 10⁻²⁷ kg，且 1 u × c² = 931.5 MeV。因此，结合能 Eb (MeV) = Δm (u) × 931.5。核子平均结合能 = Eb / A，是核稳定性的量度。
5. Nuclear Reactions and Conservation Laws | 核反应与守恒定律
All nuclear reactions obey strict conservation laws: the total electric charge, the total mass number A, and total energy‑momentum are conserved. A typical nuclear reaction can be written as a + X → Y + b. For example, the first artificial transmutation by Rutherford: ¹⁴₇N + ⁴₂He → ¹⁷₈O + ¹₁H.
所有核反应必须遵守严格的守恒定律：总电荷守恒、总质量数A守恒以及总能量‑动量守恒。典型的核反应可写作 a + X → Y + b。例如卢瑟福首次实现的人工嬗变：¹⁴₇N + ⁴₂He → ¹⁷₈O + ¹₁H。
The reaction energy (Q‑value) is the difference between the total rest masses before and after the reaction: Q = (mᵢₙᵢₜᵢₐₗ − m_fᵢₙₐₗ) c². A positive Q means the reaction releases energy; a negative Q requires an energy input. Such calculations are common in HL papers and WJEC Unit 5.
反应能（Q值）定义为反应前后总静止质量差对应的能量：Q = (m_initial − m_final) c²。Q > 0 表示放能反应，Q < 0 表示需输入能量。这类计算是IB进阶和WJEC Unit 5的必考题型。
6. Fission and Fusion | 裂变与聚变
Nuclear fission is the splitting of a heavy nucleus into two medium‑mass fragments, releasing neutrons and energy. A classic example is the neutron‑induced fission of uranium‑235: ²³⁵₉₂U + ¹₀n → ¹⁴¹₅₆Ba + ⁹²₃₆Kr + 3 ¹₀n + energy. The released neutrons can trigger a chain reaction, exploited in reactors and weapons.
核裂变是指重核分裂成两个中等质量碎片，同时释放中子与能量。典型实例是中子诱发铀‑235裂变：²³⁵₉₂U + ¹₀n → ¹⁴¹₅₆Ba + ⁹²₃₆Kr + 3 ¹₀n + energy。释放的中子能引发链式反应，用于核反应堆及核武器。
Nuclear fusion is the joining of light nuclei to form a heavier nucleus, releasing even more energy per reaction. The deuterium‑tritium reaction is a key example: ²₁H + ³₁H → ⁴₂He + ¹₀n + 17.6 MeV. Fusion powers the stars and holds promise for future clean energy, but it requires extremely high temperatures and pressures to overcome Coulomb repulsion.
核聚变是轻核结合成较重核的过程，单次反应释放能量更巨大。氘‑氚聚变是关键实例：²₁H + ³₁H → ⁴₂He + ¹₀n + 17.6 MeV。聚变是恒星的能量来源，也是未来清洁能源的希望，但需极高温度和压力以克服库仑位垒。
7. Applications of Radioisotopes | 放射性同位素的应用
Radioisotopes have widespread uses in medicine, industry, and archaeology. Technetium‑99m (half‑life 6 hours) emits gamma rays and is used as a tracer in medical imaging, while iodine‑131 is used to treat thyroid disorders. In industry, beta sources monitor paper thickness, and gamma rays inspect welds.
放射性同位素在医学、工业和考古领域有广泛应用。锝‑99m（半衰期6小时）放出γ射线，用作医学影像示踪剂；碘‑131用于治疗甲状腺疾病。工业上，β源可监测纸张厚度，γ射线用于焊缝探伤。
Radiocarbon dating uses the decay of ¹⁴₆C (half‑life 5730 years) to estimate the age of organic materials. The measured activity ratio of ¹⁴C to ¹²C is compared against known reference levels. This technique is crucial for dating archaeological artifacts up to about 50 000 years old.
放射性碳定年法利用 ¹⁴₆C 衰变（半衰期5730年）估算有机物年龄。测量样本的 ¹⁴C/¹²C 活度比，并与已知参考值比较。这一方法对测定约5万年以内的考古样品至关重要。
8. Radiation Detection and Safety | 辐射探测与安全
Common detectors include the Geiger‑Müller (GM) tube, which produces a pulse of current for each ionising particle, and scintillation counters that convert radiation flashes into electrical signals. The cloud chamber shows visible vapour trails of charged particles, aiding visualisation of alpha and beta tracks.
常用探测器包括盖革‑米勒管（GM管），每个电离粒子产生一个电流脉冲；闪烁计数器将辐射闪光转换为电信号。云室可显示带电粒子的雾径迹，帮助直观观察α和β轨迹。
Radiation dose is measured in sieverts (Sv) and accounts for biological damage. Background radiation comes from cosmic rays, rocks, and radon gas. Safety principles involve minimising exposure time, maximising distance from sources, and using shielding (e.g., lead for gamma, paper for alpha). You must be able to explain these precautions in written responses.
辐射剂量以希沃特（Sv）为单位，考虑了生物损害。背景辐射源自宇宙射线、岩石和氡气。安全原则包括缩短照射时间、增大距离和使用屏蔽（如γ射线用铅，α粒子用纸）。在简答题中需能阐述这些防护措施。
9. Energy Calculations in Nuclear Physics | 核物理中的能量计算
Whether calculating the energy released in a decay or the binding energy of a nucleus, always use E = Δm c². Convert all masses to the same unit — atomic mass unit u or kilograms — and use the conversion 1 u = 931.5 MeV. For a decay, Δm = mass(parent) − [mass(daughter) + mass(emitted particle)].
无论是计算衰变释放的能量还是原子核结合能，都须使用 E = Δm c²。将所有质量统一为 u 或 kg，并利用换算 1 u = 931.5 MeV。对于衰变，Δm = 质量(母核) − [质量(子核) + 质量(发射粒子)]。
In fission and fusion problems, tabulate the rest masses before and after the reaction. The Q‑value is Q = (Σmᵢₙᵢₜᵢₐₗ − Σm_fᵢₙₐₗ) × 931.5 MeV/u. Pay attention to significant figures and unit consistency. Numerous past paper questions require you to verify that a given reaction is energetically possible by showing Q > 0.
在裂变与聚变问题中，列出反应前后的静止质量。Q值= (Σm_initial − Σm_final) × 931.5 MeV/u。注意有效数字和单位统一。大量真题要求通过证明 Q > 0 来判断给定反应在能量上是否可行。
10. Binding Energy Curve and Stability | 结合能曲线与稳定性
Average binding energy per nucleon vs. mass number
The graph of binding energy per nucleon against mass number A peaks around iron‑56 (≈ 8.8 MeV per nucleon). Nuclei to the left can release energy by fusion, while nuclei to the right can release energy by fission. This explains why stellar fusion builds up elements to iron, and fission reactors use heavy nuclei.
核子平均结合能对质量数A的曲线在铁‑56附近达到峰值（约8.8 MeV/核子）。左边的轻核可通过聚变释放能量，右边的重核可通过裂变释放能量。这解释了恒星通过聚变一路合成到铁元素，以及核反应堆选用重核裂变的原理。
The stability of nuclei decreases for very heavy nuclei (Z > 83) which are all radioactive. The neutron‑to‑proton ratio for stable nuclei rises from 1:1 for light elements to about 1.5:1 for lead‑208. Understanding this trend allows you to predict the mode of decay: neutron‑rich nuclei undergo β⁻, while proton‑rich nuclei undergo β⁺ or electron capture.
极重核（Z > 83）都不稳定，具有放射性。稳定核的中质比从轻元素的1:1逐步升至铅‑208的约1.5:1。理解该趋势可预测衰变方式：中子过量的核发生β⁻衰变，质子过量的核则发生β⁺衰变或电子俘获。
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