📚 Radioactive Decay – CIE IGCSE Physics Exam Focus | 放射性衰变：CIE IGCSE物理考点精讲
Radioactivity appears regularly in CIE IGCSE Physics, combining basic nuclear ideas with practical applications. Understanding the properties of alpha, beta and gamma radiation, how to write decay equations and what half-life really means will earn you marks in both the core and extended papers. This revision guide walks through every essential point.
放射性是CIE IGCSE物理的常考专题，它将基础的核概念与实际应用结合在一起。掌握α、β、γ三种辐射的性质、会书写衰变方程并理解半衰期的真正含义，能帮你稳稳拿分。这份考点精讲带你逐一攻克所有必备知识。
1. Atomic Structure and Isotopes | 原子结构与同位素
All atoms have a central nucleus containing protons and neutrons, surrounded by electrons in energy levels. The number of protons (atomic number Z) defines the element, while the total number of protons and neutrons gives the mass number A. A nuclide is written as AZX, for example ¹²₆C for carbon-12.
所有原子都有一个由质子和中子组成的原子核，核外电子分层排布。质子数（原子序数Z）决定元素种类，质子数与中子数之和为质量数A。核素记作AZX，例如碳‑12写作¹²₆C。
Isotopes are atoms of the same element (same Z) but with different numbers of neutrons (different A). They have identical chemical properties but different physical stability; some isotopes are unstable and will decay radioactively.
同位素指质子数相同而中子数不同的同种原子，化学性质几乎完全相同，但核稳定性不同。不稳定的同位素会自发发生放射性衰变。
The strong nuclear force holds the nucleus together against the electrostatic repulsion between protons. When the neutron-to-proton ratio is unbalanced, the nucleus becomes unstable.
强核力克服质子间的静电斥力将核子束缚在一起。当中子–质子比例失衡时，原子核就会变得不稳定。
2. What is Radioactivity? | 什么是放射性？
Radioactivity is the spontaneous and random emission of radiation from an unstable nucleus. The process is not affected by temperature, pressure or chemical bonding because it originates inside the nucleus. The nucleus changes into a more stable form, often a different element.
放射性是不稳定原子核自发、随机地放出辐射的过程。由于变化源于核内，温度、压强或化学键都不会影响衰变速率。衰变后原子核变为更稳定的形态，通常会变成另一种元素。
The decay is random – you cannot predict exactly when a particular nucleus will decay, but you can describe the probability and the average behaviour of a large number of nuclei. This leads to the concept of half-life.
衰变是随机事件——你无法精确预言某个具体的核何时衰变，但可以描述大量原子核的衰变概率和平均行为，由此引出半衰期的概念。
Some isotopes, like uranium-238, are naturally radioactive, while others are produced artificially in nuclear reactors. All radioactive decays are accompanied by energy release.
有些同位素（如铀‑238）天然具有放射性，另一些则通过核反应堆人工制得。所有的放射性衰变都伴随能量释放。
3. Types of Radiation: Alpha, Beta and Gamma | 辐射类型：α、β、γ
Alpha (α) particles are helium nuclei, consisting of two protons and two neutrons. They carry a double positive charge and are relatively large and heavy. They are emitted by very heavy nuclei such as radium-226.
α粒子是氦原子核，由两个质子和两个中子组成，带两个正电荷，质量较大。重核如镭‑226 常常放射α粒子。
Beta (β) particles are high-speed electrons ejected from the nucleus when a neutron transforms into a proton. They carry a single negative charge. A beta particle is represented as ⁰₋₁e. An antineutrino is also emitted but is not required at IGCSE.
β粒子是核内中子转变为质子时释放出的高速电子，带一个负电荷，记作⁰₋₁e。同时放出的反中微子在IGCSE阶段不作要求。
Gamma (γ) radiation is an electromagnetic wave of very high frequency and energy, with no mass and no charge. It often accompanies alpha or beta decay as the nucleus loses excess energy.
γ辐射是频率极高、能量极大的电磁波，无质量、不带电。它通常在α或β衰变后原子核释放剩余能量时产生。
4. Penetration and Ionisation Properties | 穿透力与电离能力
Alpha particles are the most ionising because of their large mass and double charge, but they are the least penetrating – stopped by a few centimetres of air or a sheet of paper.
α粒子质量大、带电荷多，因此电离能力最强，但穿透力最弱，几厘米空气或一张纸就能将其挡住。
Beta particles are moderately ionising and can penetrate through paper but are stopped by a few millimetres of aluminium.
β粒子电离能力中等，可穿透纸张，但几毫米厚的铝片即可阻挡。
Gamma rays are the most penetrating, requiring thick lead or several metres of concrete to reduce their intensity significantly. They are the least ionising of the three.
γ射线穿透力最强，需要厚铅板或数米混凝土才能显著削弱，电离能力在三种辐射中最弱。
The table below summarises the nature, charge, penetrating power and ionising ability of each type.
下表总结了各类辐射的本质、带电量、穿透力和电离能力。
| Radiation | Nature | Charge | Penetration stopped by | Ionising ability |
|---|---|---|---|---|
| Alpha (α) | Helium nucleus ⁴₂He | +2 | Paper / few cm of air | Very high |
| Beta (β) | Fast electron ⁰₋₁e | -1 | ~3 mm aluminium | Medium |
| Gamma (γ) | Electromagnetic wave | 0 | Thick lead / concrete | Low |
辐射类型 | 本质 | 电荷 | 阻挡材料 | 电离能力
α 粒子 | 氦核 ⁴₂He | +2 | 纸张/几厘米空气 | 非常强
β 粒子 | 高速电子 ⁰₋₁e | -1 | 约3 mm铝 | 中等
γ 射线 | 电磁波 | 0 | 厚铅板/混凝土 | 弱
5. Behaviour in Electric and Magnetic Fields | 电场与磁场中的行为
Alpha and beta particles are deflected by electric fields because they carry charge. Alpha, being positive, is attracted to the negative plate; beta, being negative, is attracted to the positive plate. The deflection of alpha is smaller than that of beta for the same field strength because alpha particles have much greater mass.
α和β粒子因带电会在电场中偏转。带正电的α粒子偏向负极板，带负电的β粒子偏向正极板。由于α粒子质量远大于β粒子，相同电场强度下α的偏转幅度更小。
Gamma rays pass straight through an electric field without deflection, confirming they have no charge.
γ射线在电场中径直穿过、不发生偏转，证实其不带电。
In a magnetic field, the direction of deflection is given by Fleming’s left-hand rule (for conventional current). Alpha and beta are deflected in opposite directions, while gamma is undeflected. The radius of curvature is larger for alpha due to its larger momentum.
在磁场中，可借助弗莱明左手定则判断偏转方向。α和β粒子向相反方向弯曲，γ依然直行。由于动量较大，α粒子的偏转半径更大。
6. Radioactive Decay Equations | 放射性衰变方程
When writing decay equations, the total mass number (top) and total atomic number (bottom) must balance on both sides.
书写衰变方程时，方程两边的总质量数（左上标）和总原子序数（左下标）必须分别相等。
In alpha decay, the mass number decreases by 4 and the atomic number decreases by 2. Example: radium-226 to radon-222.
²²⁶₈₈Ra → ²²²₈₆Rn + ⁴₂He
α衰变：质量数减4，原子序数减2。例如镭‑226 衰变为氡‑222。
²²⁶₈₈Ra → ²²²₈₆Rn + ⁴₂He
In beta decay, a neutron turns into a proton, so the mass number stays the same while the atomic number increases by 1. Example: carbon-14 to nitrogen-14.
¹⁴₆C → ¹⁴₇N + ⁰₋₁e
β衰变：中子变为质子，质量数不变，原子序数增1。例如碳‑14 变为氮‑14。
¹⁴₆C → ¹⁴₇N + ⁰₋₁e
Gamma emission does not change the mass number or atomic number. A nucleus with excess energy simply releases a gamma photon, often shown as:
²⁴¹¹Na → ²⁴₁₁Na + γ
γ辐射不改变核的组成，质量数和原子序数均不变。激发态核放出γ光子，例如钠‑24放出γ射线。
²⁴₁₁Na → ²⁴₁₁Na + γ
7. Half-Life | 半衰期
Half-life is the time taken for half the radioactive nuclei in a sample to decay, or equivalently the time for the count rate to drop to half its initial value. It is a constant for a given isotope and is not affected by external conditions.
半衰期是指样品中一半的放射性原子核发生衰变所需的时间，也等价于计数率降至初始值一半所用的时间。对某一给定同位素，半衰期是常数，不受外界条件影响。
Because decay is random, the half-life describes the average behaviour of a large number of nuclei. If you start with N₀ undecayed nuclei, after one half-life N₀/2 remain, after two half-lives N₀/4 remain, and so on.
由于衰变是随机的，半衰期描述的是大量核的平均行为。若初始时刻有N₀个未衰变核，经过一个半衰期剩余N₀/2，两个半衰期后剩余N₀/4，以此类推。
You may be asked to calculate the remaining mass or count rate. For example, a radioactive sample has an initial count rate of 800 counts/min and a half-life of 6 hours. After 18 hours (3 half-lives), the expected count rate is:
800 × (½)³ = 800 × ⅛ = 100 counts/min
题目可能要求计算剩余质量或计数率。例如，某放射性样品初始计数率为800次/分，半衰期为6小时。18小时后（3个半衰期），预期计数率为：
800 × (½)³ = 800 × ⅛ = 100 次/分
A graph of count rate against time shows the characteristic exponential decay curve. You can read the half-life from the graph by finding the time interval over which the count rate halves.
计数率–时间曲线呈典型的指数衰减形状。从图上可找到计数率减半所对应的时间间隔，从而读出半衰期。
8. Detecting Radiation | 辐射探测
A Geiger-Müller (GM) tube connected to a counter is the most common detector. When radiation enters the tube, it ionises the gas inside and produces an electrical pulse that is counted.
盖革‑穆勒计数管（GM管）连接计数器是最常用的探测器。辐射进入管内使气体电离，产生电脉冲并被计数。
Photographic film can also detect radiation; it darkens when exposed to ionising radiation and is used in film badges worn by workers to monitor exposure.
照相胶片也能探测辐射，受电离辐射照射后会变黑，常制成胶片徽章供工作人员佩戴以监测受照剂量。
A cloud chamber makes the path of radiation visible: ions left along the track act as condensation centres for vapour, producing fine droplets. Alpha tracks appear thick and straight, beta tracks are thin and twisted, while gamma shows faint, scattered tracks.
云室使辐射径迹可见：辐射沿途产生的离子作为蒸气凝结中心，形成细小液滴。α径迹粗而直，β径迹细且扭曲，γ则表现为模糊散乱的径迹。
9. Background Radiation | 背景辐射
Background radiation is always present. It comes from natural sources such as cosmic rays, rocks (e.g., granite), radon gas, and also from human activities like medical X-rays and nuclear power. When measuring the count rate of a radioactive sample, you must subtract the background count rate to find the corrected count rate.
背景辐射无处不在。它来自宇宙射线、岩石（如花岗岩）、氡气等天然源，也来自医用X光、核能等人为活动。测量放射性样品时，须从实测计数率中扣除背景计数率，得到校正计数率。
10. Uses of Radioisotopes | 放射性同位素的应用
Medical tracers: a small amount of a gamma-emitting isotope with a short half-life (e.g., technetium-99m) is injected into the body and its path is tracked by a gamma camera. Gamma is chosen because it can be detected outside the body and causes minimal damage to tissues.
医用示踪剂：将少量半衰期短、放出γ射线的同位素（如锝‑99m）注入体内，用γ相机追踪其路径。选用γ射线是因为它能穿出体外被探测，同时对组织损伤小。
Radiotherapy: high-energy gamma rays from cobalt-60 are focused on cancerous tumours to destroy cells. Careful shielding of surrounding healthy tissue is essential.
放射治疗：钴‑60放射的高能γ射线聚焦于癌变肿瘤以杀死癌细胞，同时须仔细屏蔽周围健康组织。
Industrial thickness monitoring: beta or gamma sources are used to measure the thickness of paper or metal sheets. A detector measures the radiation passing through; if the thickness changes, the count rate changes, and the rollers are automatically adjusted.
工业测厚：利用β源或γ源测量纸张、金属板的厚度。探测器测量透过的辐射强度，厚度变化会导致计数率改变，从而自动调整轧辊。
Carbon-14 dating: living organisms maintain a constant ratio of radioactive ¹⁴C to stable ¹²C. After death, the ¹⁴C decays with a half-life of about 5730 years. By measuring the remaining ¹⁴C, the age of organic artefacts can be estimated.
碳‑14定年：生物存活时体内放射性的¹⁴C与稳定的¹²C比例恒定。生物死亡后，¹⁴C以约5730年的半衰期衰变。测量剩余¹⁴C含量可估算有机物品的年代。
11. Safety Precautions | 安全防护
The three principles of radiation safety are time, distance and shielding. Limit the time you are exposed, keep as far away as possible (intensity decreases with the square of distance), and use appropriate shielding: thick lead for gamma, aluminium for beta, and even paper for alpha.
辐射安全三原则：时间、距离和屏蔽。尽量缩短接触时间，保持足够距离（强度随距离平方衰减），并使用适当屏蔽：γ用厚铅，β用铝板，α甚至一张纸即可。
Sources must be handled with tweezers or remote tools, never with bare hands. They are stored in lead-lined containers and clearly labelled. Workers wear film badges to monitor cumulative dose.
必须用镊子或远程工具操作放射源，严禁裸手接触。放射源应存放在铅封容器内并清晰标识。工作人员佩戴胶片徽章监测累积剂量。
12. Key Facts and Common Mistakes | 核心要点与常见错误
Radioactivity originates from the nucleus – not from electron transitions. An ‘alpha particle’ is a helium nucleus, not a helium atom. Beta particles are electrons from the nucleus, not from the electron shells.
放射性来源于原子核，而不是电子跃迁。“α粒子”是氦核，而非氦原子。β粒子是核内产生的电子，不是核外电子。
Half-life is a property of the isotope, not of the sample size. Even a tiny sample has the same half-life as a large one. Decay is random, but the half-life describes the average behaviour and is fixed.
半衰期是同位素本身的特性，与样品总量无关，微小样品与大块样品半衰期相同。衰变本身是随机的，但半衰期是统计平均值且恒定。
In decay equations, always check that the total mass numbers and total atomic numbers balance. A common slip is forgetting to add the atomic number of the beta particle (₋₁) on the right.
写衰变方程时务必核对质量数和原子序数两边相等。常见失误是忘记在方程右侧加上β粒子的原子序数₋₁。
When measuring half-life from a graph, always subtract background radiation first if you are using a count rate that includes background. Look for the time interval in which the corrected count rate halves.
从图像读取半衰期时，若计数率未扣除背景，须先减去背景计数率，再寻找校正计数率减半的时间间隔。
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