Nuclear Physics for IB Edexcel Physics | 核物理考点精讲

📚 Nuclear Physics for IB Edexcel Physics | 核物理考点精讲

Nuclear physics is a core topic in both IB and Edexcel Physics, bridging the smallest scales of matter with powerful energy applications. This revision guide breaks down the essential ideas—from nuclear structure and binding energy to radioactive decay laws and nuclear reactions. Whether you are tackling IB HL Paper 2 or Edexcel Unit 5, mastering these concepts will sharpen your problem-solving skills and deepen your understanding of how the universe works at the nuclear level.

核物理是 IB 和 Edexcel 物理课程的核心主题，它将物质的最小尺度与强大的能源应用联系起来。本考点精讲将梳理原子核结构、结合能、放射性衰变定律以及核反应等关键知识。无论你面对的是 IB 高等级试卷二还是 Edexcel 单元五，掌握这些概念都将提升你的解题技巧，加深你对核层面宇宙运行规律的理解。

1. Nuclear Structure and Isotopes | 原子核结构与同位素

The nucleus consists of protons and neutrons (collectively called nucleons). The atomic number Z is the number of protons, defining the element. The mass number A is the total number of nucleons. Isotopes are atoms of the same element (same Z) that have different numbers of neutrons (different A). They share chemical properties but differ in nuclear stability.

原子核由质子和中子（统称核子）组成。原子序数 Z 表示质子数，决定元素种类。质量数 A 是核子总数。同位素指质子数相同而中子数不同（A 不同）的原子，它们化学性质相同，但核稳定性不同。

Nuclear sizes are measured in femtometres (fm), with the radius R given approximately by R = R₀A^(1/3), where R₀ ≈ 1.2 fm. This implies that the nuclear density is roughly constant for all nuclei, around 2×10¹⁷ kg m⁻³.

原子核大小以飞米（fm）为单位，半径 R 近似满足 R = R₀A^(1/3)，其中 R₀ 约等于 1.2 fm。这意味着所有原子核的密度大致恒定，约为 2×10¹⁷ kg m⁻³。

2. Strong Nuclear Force and Stability | 强核力与稳定度

The strong nuclear force binds nucleons together. It is a short-range attractive force, acting up to about 3–4 fm, overcoming the electrostatic repulsion between protons. At very short distances (below about 0.5 fm), it becomes repulsive, preventing the nucleus from collapsing.

强核力将核子束缚在一起。它是一种短程吸引力，作用范围约 3–4 fm，足以克服质子间的静电排斥。在极短距离（小于约 0.5 fm）下，强核力变为排斥力，防止原子核坍缩。

The neutron-to-proton ratio is crucial for stability. Light stable nuclei have N ≈ Z, whereas heavier stable nuclei require more neutrons than protons to reduce repulsion. The line of stability on an N-Z graph shows this trend. Nuclei far from this line are radioactive and undergo decay to achieve stability.

中子与质子的比值对于稳定性至关重要。轻的稳定核有 N ≈ Z，而较重的稳定核需要比质子更多的中子来减弱排斥。N-Z 图上的稳定线体现了这一趋势。远离稳定线的核具有放射性，会通过衰变趋于稳定。

3. 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 protons and neutrons. This difference is called the mass defect, Δm. The energy equivalent of the mass defect is the binding energy: E = (Δm)c². Binding energy represents the work required to disassemble a nucleus into its constituent nucleons.

原子核的质量总是小于其各个质子和中子质量之和。这个差值称为质量亏损 Δm。质量亏损对应的能量即为结合能：E = (Δm)c²。结合能表示将原子核分解为自由核子所需做的功。

Binding energy = (Δm)c²

Binding energy per nucleon is a measure of nuclear stability. It is obtained by dividing the total binding energy by A. The graph of binding energy per nucleon against mass number peaks at iron‑56 (around 8.8 MeV per nucleon), indicating maximum stability.

平均每个核子的结合能是衡量核稳定性的尺度。总结合能除以 A 得到比结合能。比结合能随质量数变化的曲线在铁-56 附近达到峰值（约 8.8 MeV 每核子），表明该处最稳定。

4. Einstein’s Mass-Energy Equivalence | 爱因斯坦质能方程

Einstein’s equation, E = mc², is the foundation of nuclear energy. It states that mass and energy are interchangeable. In nuclear reactions, a small loss in mass is accompanied by a large release of energy because c² is so large. Energy units in nuclear physics are often electronvolts (eV) or megaelectronvolts (MeV).

爱因斯坦方程 E = mc² 是核能的基础。它指出质量与能量可以相互转化。在核反应中，微小的质量损失会伴随巨大的能量释放，因为 c² 数值极大。核物理中的能量单位常用电子伏特（eV）或兆电子伏特（MeV）。

When using E = mc², one must be consistent with units. For example, 1 u (unified atomic mass unit) is equivalent to 931.5 MeV. Thus, a mass defect of 0.1 u releases about 93.15 MeV of energy.

使用 E = mc² 时必须保持单位一致。例如，1 u（原子质量单位）相当于 931.5 MeV。因此，0.1 u 的质量亏损约释放 93.15 MeV 的能量。

5. Radioactive Decay: Alpha, Beta, Gamma | 放射性衰变：α、β、γ

Radioactive decay occurs when an unstable nucleus emits particles or radiation. The three principal types are alpha (α), beta (β), and gamma (γ) emissions.

放射性衰变发生于不稳定原子核发射粒子或辐射时。三种主要类型是 α 衰变、β 衰变和 γ 衰变。

Alpha decay: An alpha particle, ⁴₂He, is ejected. The parent nucleus loses 2 protons and 2 neutrons, so Z decreases by 2 and A decreases by 4. Example: ²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He.

α 衰变：发射一个 α 粒子 ⁴₂He。母核失去 2 个质子和 2 个中子，因此 Z 减 2，A 减 4。例：²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He。

Beta-minus decay: A neutron transforms into a proton, emitting an electron (β⁻) and an antineutrino. Z increases by 1, A unchanged. Example: ¹⁴₆C → ¹⁴₇N + ⁰₋₁e + ν̅.

β⁻ 衰变：一个中子转化为质子，放出一个电子（β⁻）和一个反中微子。Z 增加 1，A 不变。例：¹⁴₆C → ¹⁴₇N + ⁰₋₁e + ν̅。

Beta-plus decay: A proton converts into a neutron, emitting a positron (β⁺) and a neutrino. Z decreases by 1. Gamma decay follows alpha or beta emissions to release excess energy; a photon is emitted with no change in Z or A.

β⁺ 衰变：一个质子转变为中子，放出一个正电子（β⁺）和一个中微子。Z 减 1。γ 衰变常跟随 α 或 β 发射，以释放多余能量；放出一个光子，Z 和 A 不变。

6. Decay Law and Half-Life | 衰变定律与半衰期

Radioactive decay is a random process; for a large number of nuclei, the activity A (decays per second) is proportional to the number of undecayed nuclei N: A = λN, where λ is the decay constant. The exponential decay law is N = N₀e^(-λt).

放射性衰变是一种随机过程；对于大量原子核，活度 A（每秒衰变数）与未衰变核数 N 成正比：A = λN，其中 λ 是衰变常数。指数衰变规律为 N = N₀e^(-λt)。

The half-life T₁/₂ is the time taken for half of the radioactive nuclei to decay. It is related to λ by T₁/₂ = ln 2 / λ. After n half-lives, the fraction remaining is (1/2)^n.

半衰期 T₁/₂ 是半数放射性核发生衰变所需的时间。它与 λ 的关系为 T₁/₂ = ln 2 / λ。经过 n 个半衰期后，剩余分数为 (1/2)^n。

T₁/₂ = ln 2 / λ ≈ 0.693 / λ

7. Measuring Half-Life | 半衰期的测量

Half-life can be determined from a graph of activity against time. For a source emitting a single type of radiation, the activity is measured at regular intervals, corrected for background radiation. The exponential curve gives T₁/₂ from the time interval for activity to halve. A log-linear plot (ln A versus t) yields a straight line with slope –λ.

半衰期可以从活度-时间图测定。对于发射单一辐射的源，定期测量活度并扣减本底辐射。从指数曲线读出活度减半的时间间隔即为 T₁/₂。对数-线性图（ln A 对 t）给出斜率为 –λ 的直线。

Simulation or using multichannel analysers in schools can also illustrate decay statistics. In exams, students are often given data to calculate T₁/₂ or λ using the decay equation.

模拟实验或使用多道分析仪也可展示衰变统计特性。考试中常给出一组数据，要求学生利用衰变方程计算 T₁/₂ 或 λ。

8. Nuclear Reactions and Q-value | 核反应与 Q 值

Nuclear reactions involve the rearrangement of nucleons, such as ¹⁴N + ⁴He → ¹⁷O + ¹H. The Q-value of a reaction is the net energy released (exothermic, Q > 0) or absorbed (endothermic, Q < 0). It is calculated from the mass difference between reactants and products: Q = (m_reactants – m_products)c².

核反应涉及核子的重新排布，例如 ¹⁴N + ⁴He → ¹⁷O + ¹H。反应的 Q 值指净释放（放热，Q > 0）或吸收（吸热，Q < 0）的能量。它由反应物与生成物的质量差计算：Q = (m_reactants – m_products)c²。

Conservation laws apply: charge, nucleon number, and energy/momentum are conserved. Balancing equations ensures that total Z and total A are the same on both sides.

守恒定律适用：电荷数、核子数和能量/动量均守恒。配平方程式时须确保两侧总 Z 和总 A 相等。

9. Fission and Chain Reactions | 核裂变与链式反应

Nuclear fission is the splitting of a heavy nucleus into two lighter nuclei, accompanied by the release of neutrons and a large amount of energy. Uranium-235 fission induced by slow neutrons is a classic example: ²³⁵U + n → ⁹²Kr + ¹⁴¹Ba + 3n + energy.

核裂变是一个重核分裂为两个较轻的核，同时释放出中子和大量能量。慢中子引发的铀-235 裂变是经典例子：²³⁵U + n → ⁹²Kr + ¹⁴¹Ba + 3n + 能量。

The released neutrons can trigger further fissions, creating a chain reaction. In a nuclear reactor, control rods absorb excess neutrons to maintain a steady rate. The binding energy per nucleon curve explains the energy release: products lie closer to the iron peak than the parent nucleus.

释放的中子可引发进一步裂变，形成链式反应。在核反应堆中，控制棒吸收过量中子以维持恒定速率。比结合能曲线解释了能量释放：产物比母核更靠近铁峰。

10. Nuclear Fusion | 核聚变

Nuclear fusion combines light nuclei to form a heavier nucleus, also releasing energy because the product has a higher binding energy per nucleon. Example: deuterium-tritium fusion: ²H + ³H → ⁴He + n + 17.6 MeV.

核聚变将轻核结合成较重核，同样释放能量，因为生成物具有更高的比结合能。例如氘-氚聚变：²H + ³H → ⁴He + n + 17.6 MeV。

Fusion requires extremely high temperatures (~10⁸ K) to overcome Coulomb repulsion between nuclei. This is the energy source of stars. On Earth, magnetic confinement (tokamaks) and inertial confinement are being explored for controlled fusion power.

聚变需要极高温度（约 10⁸ K）来克服核间的库仑排斥。这是恒星的能源。在地球上，磁约束（托卡马克）和惯性约束正被研究用于受控聚变能源。

11. Applications and Safety | 应用与安全

Nuclear physics has wide-ranging applications: medical imaging (PET scans using β⁺ emitters), radiotherapy (gamma rays from cobalt-60), radioactive dating (carbon-14), and smoke detectors (americium-241 alpha source). Radioisotopes are chosen based on half-life and radiation type suitable for the task.

核物理有广泛应用：医学成像（利用 β⁺ 发射体的 PET 扫描）、放射治疗（钴-60 的伽马射线）、放射性测年（碳-14）和烟雾探测器（镅-241 α 源）。放射性同位素的选择取决于半衰期和适合该项任务的辐射类型。

Safety measures include using shielding (lead for gamma, thick paper for alpha), keeping distance, limiting exposure time, and monitoring with film badges or Geiger counters. Storage of radioactive waste demands long-term isolation to protect the environment.

安全措施包括使用屏蔽（铅屏蔽 γ，厚纸屏蔽 α）、保持距离、限制照射时间，并使用胶片徽章或盖革计数器监测。放射性废物的储存需要长期隔离以保护环境。

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Nuclear Physics for IB Edexcel Physics | 核物理考点精讲