📚 A-Level CIE Physics: Radioactive Decay - Key Revision Points | A-Level CIE 物理：放射性衰变 考点精讲
Radioactive decay is a random and spontaneous process in which an unstable atomic nucleus releases energy and particles to become more stable. Understanding the different types of radiation, the mathematical laws governing decay, and the practical applications are essential parts of the CIE A‑Level Physics syllabus. This revision guide breaks down every key point, from the nature of alpha, beta, and gamma radiation to the exponential decay law, half‑life, activity, background radiation, and radio‑carbon dating, equipping you with clear explanations and exam‑ready facts.
放射性衰变是一种随机且自发的过程，不稳定的原子核通过释放能量和粒子变得更加稳定。理解不同类型的辐射、支配衰变的数学定律以及实际应用，是CIE A‑Level物理考纲的核心内容。本精讲指南逐一拆解每一个关键考点，从α、β、γ辐射的特性，到指数衰变定律、半衰期、活度、背景辐射以及放射性碳定年，为你提供清晰的解释和应考必备的知识。
1. Nuclear Composition and the Need for Stability | 原子核的组成与稳定性的需求
The nucleus contains protons and neutrons, collectively called nucleons. The number of protons Z determines the element, while the mass number A is the total number of nucleons. A nuclide is written as AZX, for example 146C.
原子核由质子和中子组成，统称为核子。质子数Z决定了元素的种类，质量数A是核子的总数。核素记作AZX，例如146C。
For light nuclei (Z ≤ 20), stability occurs when the neutron‑to‑ counteract the electrostatic repulsion between protons. If a nucleus lies outside the band of stability on an N‑Z graph, it will undergo radioactive decay to move toward stability.
对于轻核（Z ≤ 20），当中子数与质子数之比接近1时，原子核是稳定的。对于重核，这一比例会增大到约1.5，因为额外的中子可以提供更强的强核力来平衡质子之间的静电排斥。如果原子核在N‑Z图上位于稳定带之外，它就会发生放射性衰变，趋向稳定。
The strong nuclear force is a very short‑ tractive force that acts between all nucleons, whereas the electrostatic force is a longer‑range repulsive force acting only between protons.
强核力是一种极短程（约10⁻¹⁵米）的吸引力，作用于所有核子之间；而静电力是较长程的排斥力，仅作用于质子之间。
2. Types of Radioactive Decay – Alpha, Beta, Gamma | 放射性衰变的类型 – α、β、γ衰变
There are three main types of radiation emitted during radioactive decay: alpha (α) particles, beta (β⁻) particles, and gamma (γ) rays. Each has distinct properties in terms of ionising ability, penetrating power, and behaviour in electric and magnetic fields.
放射性衰变过程中主要发射三种辐射：α粒子、β⁻粒子和γ射线。它们在电离能力、贯穿本领以及在电场和磁场中的行为方面各有特点。
- Alpha (α) particle: A helium nucleus 42He, consisting of 2 protons and 2 neutrons. It has a charge of +2e and is heavily ionising but has low penetrating power (stopped by a few cm of air or a sheet of paper). In a magnetic field it is deflected according to Fleming's left‑hand rule.
- α粒子：氦核42He，由2个质子和2个中子组成。带+2e电荷，电离能力强，但贯穿本领低（几厘米空气或一张纸即可阻挡）。在磁场中会按左手定则偏转。
- Beta (β⁻) particle: A high‑speed electron emitted when a neutron in the nucleus changes into a proton (n → p + e⁻ + ν̄e). It has a charge of -e, is moderately ionising, and has moderate penetrating power (stopped by a few mm of aluminium). It is more easily deflected than alpha particles in a magnetic field because of its much smaller mass.
- β⁻粒子：一个高速电子，原子核内一个中子转变为质子时放出（n → p + e⁻ + ν̄e）。带‑e电荷，电离能力中等，贯穿本领中等（几毫米铝片可阻挡）。由于其质量远小于α粒子，在磁场中更易偏转。
- Gamma (γ) ray: Electromagnetic radiation of very short wavelength (high frequency), emitted when a nucleus loses excess energy. It has no charge and no mass, is weakly ionising, but has very high penetrating power (reduced significantly by several cm of lead or metres of concrete). Gamma rays are not deflected by electric or magnetic fields.
- γ射线：极短波长（高频）的电磁辐射，原子核释放多余能量时发出。不带电荷，没有质量，电离能力弱，但穿透本领极强（数厘米铅或数米混凝土才能显著衰减）。γ射线在电场或磁场中不发生偏转。
3. Decay Equations and Conservation Laws | 衰变方程与守恒定律
In alpha decay, the mass number decreases by 4 and the atomic number decreases by 2. In beta (β⁻) decay, the mass number remains unchanged while the atomic number increases by 1. A gamma emission does not change A or Z, and usually accompanies alpha or beta decay.
在α衰变中，质量数减少4，原子序数减少2。在β⁻衰变中，质量数不变，原子序数增加1。γ辐射不会改变A或Z，通常伴随α或β衰变出现。
Examples of balanced nuclear equations:
平衡核方程示例：
Alpha decay: 23892U → 23490Th + 42He
Beta decay: 146C → 147N + 0-1e + ν̄e
In all nuclear processes, mass‑ leon number are conserved. The mass defect manifests as the binding energy of the nucleus.
在所有核过程中，质能（E = mc²）、电荷以及核子数均守恒。质量亏损体现为原子核的结合能。
4. The Exponential Law of Radioactive Decay | 放射性衰变的指数定律
The decay of a radioactive sample is a random process, but the behaviour of a large number of nuclei can be described by an exponential relationship. The number of undecayed nuclei N at time t is given by:
单个放射性原子核的衰变是随机的，但大量原子核的行为可以用指数关系描述。在时间t时尚未衰变的原子核数目N满足：
N = N₀ e-λt
nit: s⁻¹, min⁻¹, or yr⁻¹). The decay constant λ is the probability per unit time that a given nucleus will decay.
其中N₀为t = 0时的初始原子核数，λ为衰变常量（单位：s⁻¹、min⁻¹或yr⁻¹）。衰变常量λ是单位时间内某一个原子核发生衰变的概率。
5. Activity and Its Units | 活度及其单位
oportional to the number of undecayed nuclei: A = λN. It can also be expressed as A = A₀ e-λt.
活度A是单位时间内发生衰变的次数，与尚未衰变的原子核数目成正比：A = λN。同样可以表示为A = A₀ e-λt。
⁰ Bq). In the exam you must use Bq unless the question specifically asks for a conversion.
活度的国际单位是贝克勒尔（Bq），1 Bq = 每秒1次衰变。旧单位居里（Ci）有时仍被使用（1 Ci = 3.7 × 10¹⁰ Bq）。考试中必须使用Bq，除非题目特别要求转换。
taining 10²⁰ undecayed nuclei with a decay constant of 0.1 s⁻¹. Using A = λN, A = 10¹⁹ Bq.
典型的考题可能会要求你计算含有10²⁰个尚未衰变原子核、衰变常量为0.1 s⁻¹样品的活度。由A = λN可得A = 10¹⁹ Bq。
6. Half‑Life – Definition and Graphical Interpretation | 半衰期 – 定义与图像解读
Half‑life T½ is the time taken for the number of undecayed nuclei (or the activity) of a radioactive sample to fall to half its original value. It is related to the decay constant by:
半衰期T½是指放射性样品中尚未衰变的原子核数目（或活度）减少到初始值一半所需的时间。它与衰变常量的关系为：
T½ = ln 2 / λ ≈ 0.693 / λ
After n half‑lives, the fraction remaining is (½)n. This simple idea is often easier to use than the exponential equation in many exam contexts.
经过n个半衰期后，剩余比例为 (½)n。在许多考题中，这个简单的概念往往比指数方程更简便。
On an N–t or A–t graph, the half‑life can be read directly by finding the time interval over which the quantity halves. In a log‑linear graph of ln(N) against t, the gradient is -λ, which provides an accurate method for determining the decay constant.
在N–t或A–t图上，可以通过找到数值减半的时间间隔直接读出半衰期。在ln(N)对t的半对数图中，斜率为-λ，为确保精确测定衰变常量提供了方法。
7. Background Radiation and Corrected Count Rate | 背景辐射与修正计数率
Background radiation comes from natural sources such as cosmic rays, rocks, and radon gas, as well as artificial sources like medical waste. When measuring the count rate from a radioactive source using a Geiger‑Müller (GM) tube, the measured count rate includes background radiation.
背景辐射来自宇宙射线、岩石、氡气等自然源，以及医疗废物等人造源。使用盖革‑米勒（GM）管测量放射源计数率时，测得的计数率包含了背景辐射。
The corrected count rate is obtained by subtracting the background count rate (measured when no source is present or with the source removed) from the measured count rate. This step is crucial for obtaining accurate values in half‑life experiments.
修正计数率通过从实测计数率中减去背景计数率（无源或移开源时测得）来得到。这一步对于在半衰期实验中获得准确数值至关重要。
8. Radio‑Carbon Dating and Other Applications | 放射性碳定年及其他应用
Radio‑carbon dating uses the decay of 14C (half‑life ≈ 5730 years) to estimate the age of once‑ erials. While alive, organisms exchange carbon with the atmosphere, maintaining a constant 14C to 12C ratio. After death, the 14C decays exponentially without replenishment. By measuring the current activity or the ratio of 14C to 12C, the time elapsed since death can be calculated.
放射性碳定年利用14C的衰变（半衰期约5730年）来估算曾经存活物质的年龄。生物存活时，与大气进行碳交换，维持恒定的14C与12C比值。死亡后，14C不再补充，按指数规律衰变。通过测量当前的活度或14C与12C之比，可计算出死亡至今的时间。
Other applications of radioactive isotopes include medical imaging (technetium‑99m), radiotherapy (cobalt‑60), thickness control in industry (beta attenuation), and smoke detectors (americium‑241).
放射性同位素的其他应用包括：医学成像（锝‑99m）、放射治疗（钴‑60）、工业厚度控制（β射线衰减）和烟雾探测器（镅‑241）。
9. Safety Precautions When Handling Radioactive Sources | 处理放射源的安全措施
Because ionising radiation can damage living cells and cause mutations or cancer, stringent safety measures are required. These include using sources of the lowest activity that is still effective, minimising exposure time, maximising distance from the source (inverse square law), and using appropriate shielding (lead for gamma, aluminium for beta). Sources must never be touched directly; handling tongs and a lead container for storage are standard.
由于电离辐射会损伤活细胞并可能导致突变或癌症，必须采取严格的安全措施。这些包括：使用尽可能低活度但仍能有效工作的放射源、尽量缩短暴露时间、尽量远离放射源（平方反比定律），以及使用适当的屏蔽（γ射线用铅，β粒子用铝）。绝对不可直接触碰放射源；标准做法是使用操作钳和铅制储存容器。
In a school laboratory, sealed sources should always be used, a risk assessment must be carried out, and wash hands thoroughly after the practical. The GM tube window must be handled carefully (it is thin and fragile).
在学校实验室，只能使用密封源，必须进行风险评估，实验后须彻底洗手。GM管的窗口必须小心操作（它很薄且易碎）。
10. Experimental Determination of Half‑Life | 半衰期的实验测定
A common CIE practical involves measuring the half‑life of a protactinium‑234 generator (23491Pa, beta emitter, T½ ≈ 70 s). A GM tube connected to a scaler or data‑ kground subtraction, a graph of corrected count rate against time is plotted, and the half‑ mined by finding the time taken for the count rate to halve from any chosen initial value.
CIE常见的实验是测量镤‑234发生器（23491Pa，β放射源，T½ ≈ 70秒）的半衰期。GM管连接计数器或数据记录器，以固定时间间隔记录计数率。扣除背景后，绘制修正计数率对时间的图像，通过找出计数率从任意选定的初始值减半所需的时间，即可测定半衰期。
For sources with much longer half‑lives, the direct count‑rate graph may appear almost linear; in such cases the log‑linear method is necessary. Plotting ln(corrected count rate) against time yields a straight line whose gradient gives -λ, from which T½ = ln2 / λ can be calculated.
对于半衰期长得多的放射源，直接绘制的计数率图可能几乎呈线性；此时必须采用对数线性法。绘制ln(修正计数率)对时间的关系图，得到一条直线，其斜率即为-λ，进而可由T½ = ln2 / λ计算出半衰期。
Always state that the process is random, therefore repeated measurements and averaging will improve reliability. Specify that the volume/position of the liquid source must be kept constant and the GM tube must not be moved during the experiment.
务必说明衰变过程是随机的，因此重复测量并取平均值会提高可靠性。要明确液体源的体积/位置必须保持不变，GM管在实验过程中不可移动。
11. Decay Series and Nuclear Stability Revisited | 衰变系列与核稳定性回顾
Heavy nuclei, such as uranium‑238, decay through a series of alpha and beta emissions into stable lead‑206. Each step is called a daughter product, and the whole chain is a decay series. In such a series, the equation at each stage must satisfy conservation of nucleon number and charge.
重核如铀‑238，经过一系列α和β衰变最终变成稳定的铅‑206。每一步的产物称为子体，整个链条就是衰变系列。在这个系列中，每一阶段的方程都必须满足核子数和电荷守恒。
An N‑Z plot shows how each decay moves the nucleus: alpha decay reduces both N and Z by 2, moving the point diagonally down‑left; beta decay converts a neutron into a proton, moving the point up‑left (Z increases, N decreases). The position of the nuclide after each decay should approach the line of stability.
N‑Z图展示了每次衰变如何移动原子核的位置：α衰变使N和Z各减2，点向左下方对角移动；β衰变将中子转化为质子，点向左上方移动（Z增加，N减少）。每次衰变后核素的位置应趋于稳定线。
12. Exam Tips for Radioactive Decay Questions | 放射性衰变考题应试技巧
When solving numerical problems, first convert all units to SI (e.g., time in seconds, λ in s⁻¹) unless the question uses different consistent units. Always write the equation you intend to use before substituting numbers, and show the steps for logarithmic rearrangements clearly.
在解答数值题时，除非题目使用了其他自洽的单位，否则先将所有单位转换为国际单位（如时间用秒，λ用s⁻¹）。务必先写出打算使用的方程再代入数值，对对数形式的推导步骤要展示清楚。
For descriptive questions, refer to key terms like "random", "spontaneous", "exponential", and "background radiation". When comparing alpha, beta, and gamma, use a table to list charge, relative mass, ionising power, penetrating power, and deflection in a magnetic field. This structured approach wins marks efficiently.
面对描述性问题，要运用“随机”、“自发”、“指数式”和“背景辐射”等关键词。比较α、β、γ时，可使用表格列出电荷、相对质量、电离本领、贯穿本领和磁场偏转。这种结构化的作答方式能高效得分。
| Property | Alpha (α) | Beta (β⁻) | Gamma (γ) |
|---|---|---|---|
| Charge | +2e | -e | 0 |
| Mass (u) | 4 | 1/1840 | 0 |
| Ionising power | High | Medium | Very low |
| Penetrating power | Stopped by paper or few cm of air | Stopped by ≈3 mm aluminium | Reduced by several cm Pb or m concrete |
| Deflection in mag field | Slight, opposite to beta | Large, opposite to alpha | None |
Finally, always check that your answer to a half‑life problem is sensible: if the fraction remaining is 1/8, you should get 3 half‑lives, etc. Use the fraction‑remaining method as a quick check of exponential calculation results.
最后，始终检查半衰期问题的答案是否合理：如果剩余比例为1/8，应得出3个半衰期等等。可用剩余比例法快速检验指数计算的结果。
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