📚 IB Edexcel Physics: Radioactive Decay – Key Points Summary | IB Edexcel 物理：放射性衰变 考点精讲
Radioactive decay is a cornerstone of nuclear physics, describing how unstable nuclei transform spontaneously, releasing energy in the form of radiation. For IB Edexcel Physics students, a thorough grasp of decay types, the mathematical laws governing decay, half-life calculations, and practical applications is vital. This revision guide distils all the essential concepts into a clear, exam-focused resource.
放射性衰变是核物理的基石，描述了不稳定原子核如何自发转化并以辐射形式释放能量。对于 IB Edexcel 物理学生来说，深入掌握衰变类型、支配衰变的数学定律、半衰期计算以及实际应用至关重要。本复习指南将所有核心概念浓缩为一份清晰、紧扣考试的参考资料。
1. Introduction to Radioactive Decay | 放射性衰变简介
Radioactive decay is a spontaneous and random process in which an unstable atomic nucleus emits particles or electromagnetic radiation to reach a more stable configuration. External conditions such as temperature, pressure, or chemical environment have no influence on the decay rate.
放射性衰变是一种自发且随机的过程，不稳定的原子核通过发射粒子或电磁辐射达到更稳定的结构。温度、压力或化学环境等外部条件对衰变速率没有影响。
The original unstable nucleus is called the parent nuclide; the nucleus produced after decay is the daughter nuclide. If the daughter is still unstable, a decay series continues until a stable nuclide is formed.
原始的不稳定核称为母核；衰变后产生的核称为子核。如果子核仍不稳定，衰变链会持续进行，直到形成稳定核为止。
2. Types of Radiation: Alpha, Beta and Gamma | 辐射类型：α、β与γ
Three main types of radiation are emitted in radioactive decay. They differ in composition, charge, penetrating ability and ionising power.
放射性衰变中主要发射三种辐射，它们在组成、电荷、穿透能力和电离能力上各不相同。
- Alpha (α) particle: a helium nucleus (2 protons + 2 neutrons), charge +2e, low penetration (stopped by paper or a few cm of air), very high ionising power.
α粒子：氦核（2个质子+2个中子），带+2e电荷，穿透性低（被纸张或几厘米空气阻挡），电离能力非常强。 - Beta-minus (β⁻) particle: a fast electron emitted when a neutron transforms into a proton; charge –e, moderate penetration (stopped by a few mm of aluminium), medium ionising power.
β⁻粒子：中子转变为质子时发射的高速电子，带–e电荷，穿透性中等（被几毫米铝片阻挡），中等电离能力。 - Beta-plus (β⁺) particle: a positron emitted when a proton converts into a neutron; charge +e, behaves like β⁻ but annihilates with electrons producing gamma rays.
β⁺粒子：质子转变为中子时发射的正电子，带+e电荷，行为类似β⁻，但与电子湮灭产生伽马射线。 - Gamma (γ) radiation: high-energy electromagnetic photons, no charge, highly penetrating (reduced by thick lead or concrete), low ionising power.
γ射线：高能电磁光子，不带电，穿透性极强（厚铅或混凝土才能削弱），电离能力弱。
3. Nuclear Equations and Conservation Laws | 核方程与守恒定律
In writing nuclear equations, the total mass number A (nucleons) and total atomic number Z (proton number) must be conserved. Energy, momentum and charge are also conserved. The released energy appears as kinetic energy of the products and as photon energy.
书写核方程时，总质量数A（核子数）和总原子序数Z（质子数）必须守恒。能量、动量和电荷也守恒。释放的能量表现为产物的动能和光子能量。
Example of alpha decay: ²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He. The mass number drops by 4, the atomic number by 2.
α衰变示例：²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He。质量数减少4，原子序数减少2。
Example of beta-minus decay: ¹⁴₆C → ¹⁴₇N + ⁰₋₁e + ν̄ₑ. A neutron becomes a proton, emitting an electron and an antineutrino.
β⁻衰变示例：¹⁴₆C → ¹⁴₇N + ⁰₋₁e + ν̄ₑ。中子变为质子，发射一个电子和一个反中微子。
Example of beta-plus decay: ¹⁸₉F → ¹⁸₈O + ⁰₊₁e + νₑ. A proton becomes a neutron, emitting a positron and a neutrino.
β⁺衰变示例：¹⁸₉F → ¹⁸₈O + ⁰₊₁e + νₑ。质子变为中子，发射一个正电子和一个中微子。
4. The Random Nature of Decay | 衰变的随机性
Radioactive decay is inherently random at the level of individual nuclei. It is impossible to predict exactly when a particular nucleus will decay. The probability of decay per unit time is constant for a given isotope.
放射性衰变在单个原子核层面上本质上是随机的。无法准确预测某个特定原子核何时会衰变。对于给定的同位素，单位时间内的衰变概率是恒定的。
When observing a large number of nuclei, the overall behaviour follows a definite statistical pattern. The count rate measured by a detector therefore fluctuates; these fluctuations are well described by a Poisson distribution, and the standard deviation in a count N is approximately √N.
当观察大量原子核时，整体行为遵循确定的统计规律。探测器测得的计数率因此会波动；这些涨落可以用泊松分布很好地描述，计数N的标准差近似为√N。
5. Decay Constant and Activity | 衰变常数与活度
The decay constant λ (lambda) is the probability that an individual nucleus will decay per unit time. Its unit is s⁻¹. A large λ indicates a rapidly decaying isotope.
衰变常数λ是一个原子核在单位时间内发生衰变的概率，单位为s⁻¹。λ大表示同位素衰变快。
The activity A of a radioactive sample is the number of decays occurring per second, measured in becquerels (Bq), where 1 Bq = 1 decay per second. Activity is directly proportional to the number of undecayed nuclei N:
放射性样品的活度A是每秒发生的衰变次数，单位为贝克勒尔（Bq），1 Bq = 每秒1次衰变。活度与未衰变核数N成正比：
A = λN
As N decreases over time, so does the activity, following the same exponential law. The initial activity is A₀ = λN₀.
随着时间推移N减少，活度也遵循相同的指数规律下降。初始活度为A₀ = λN₀。
6. Exponential Decay Law | 指数衰减定律
The number of undecayed nuclei N in a sample decreases exponentially with time t according to the equation:
样品中未衰变的核数N随时间t呈指数衰减，遵循以下方程：
N = N0 e−λt
where N₀ is the initial number of undecayed nuclei, and e is the base of natural logarithms. The same relationship holds for activity A and for the mass of the radioisotope.
其中N₀是初始未衰变核数，e是自然对数的底。同样的关系也适用于活度A和放射性同位素的质量。
Taking natural logarithms gives a linear form: ln N = ln N₀ − λt, which is useful for determining λ from experimental data.
取自然对数得到线性形式：ln N = ln N₀ − λt，这有助于从实验数据中确定λ。
A = A0 e−λt
7. Half-Life | 半衰期
Half-life T1/2 is the time required for half of the radioactive nuclei in a sample to decay, or for the activity to reduce by half. It is related to the decay constant by:
半衰期T1/2是样品中一半放射性核发生衰变所需的时间，或活度减半所需的时间。它与衰变常数的关系为：
T1/2 = ln 2 / λ ≈ 0.693 / λ
After n half-lives, the fraction of remaining nuclei is (1/2)ⁿ. The number of undecayed nuclei can also be expressed as N = N₀ (½)t / T½. Half-life is independent of the initial amount of material and is a constant for each isotope.
经过n个半衰期后，剩余核的比例为(1/2)ⁿ。未衰变核数也可表示为N = N₀ (½)t / T½。半衰期与材料的初始量无关，是每种同位素的常数。
8. Background Radiation and Corrections | 背景辐射与修正
Background radiation originates from cosmic rays, naturally occurring radioactive materials in rocks and soil (e.g., uranium, thorium), radon gas, and also from artificial sources such as medical X-rays. In any experiment, the measured count rate includes a background contribution that must be subtracted to obtain the true count rate from the source.
背景辐射来源于宇宙射线、岩石和土壤中天然存在的放射性物质（如铀、钍）、氡气以及医疗X射线等人造源。在任何实验中，测得的计数率包含背景贡献，必须减去以得到源自放射源的真实计数率。
To correct for background, measure the count rate without the source for a suitable time, calculate the background count rate, and subtract it from the gross count rate. The uncertainty in the corrected rate depends on the statistical uncertainties of both measurements.
修正背景的方法是：在没有源的情况下测量足够长时间，计算背景计数率，然后从总计数率中减去它。修正后计数率的不确定度取决于两次测量的统计不确定度。
9. Detecting Radiation | 探测辐射
The Geiger-Müller (GM) tube is a common radiation detector. Ionising radiation entering the tube causes gas ionisation, producing an electrical pulse that is counted. It is suitable for detecting alpha, beta and gamma radiation, though a thin window is needed for alpha particles.
盖革-米勒管是一种常见的辐射探测器。电离辐射进入管内引起气体电离，产生电脉冲并被计数。它适用于探测α、β和γ辐射，但探测α粒子需要薄窗。
Scintillation counters use a material that emits flashes of light when struck by ionising radiation; a photomultiplier converts the flashes into electrical signals. Cloud chambers show visible tracks of particles, allowing identification by track thickness and curvature in magnetic fields.
闪烁计数器利用被电离辐射击中时会发出闪光的材料；光电倍增管将闪光转换为电信号。云室显示粒子的可见径迹，通过径迹粗细和磁场中的弯曲可以识别粒子类型。
10. Applications and Hazards | 应用与危害
Radioisotopes are widely used: technetium-99m in medical imaging for its short half-life and gamma emission; cobalt-60 in radiotherapy to destroy cancer cells; americium-241 in smoke detectors; carbon-14 in archaeological dating; and iridium-192 for industrial weld inspections.
放射性同位素应用广泛：锝-99m因半衰期短且发射伽马射线用于医学成像；钴-60用于放射治疗杀灭癌细胞；镅-241用于烟雾探测器；碳-14用于考古年代测定；铱-192用于工业焊缝检测。
Ionising radiation damages living tissue by breaking chemical bonds and creating free radicals. Acute exposure can cause radiation sickness; long-term exposure increases cancer risk. Safety measures include using shielding (lead for gamma, aluminium for beta), minimising exposure time, maximising distance from sources, and wearing dosimeter badges.
电离辐射通过断裂化学键和产生自由基来损伤活体组织。急性暴露可导致辐射病；长期暴露增加患癌风险。安全措施包括使用屏蔽（伽马用铅，贝塔用铝），尽可能缩短暴露时间，远离放射源，并佩戴剂量计。
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