📚 Radioactive Decay & Half-Life | 放射性衰变与半衰期
Radioactive decay is a spontaneous process in which an unstable atomic nucleus loses energy by emitting radiation. This fundamental concept is central to the Edexcel IGCSE Science syllabus, linking physics with real‑world applications in medicine, industry and dating ancient materials. Understanding half‑life – the time taken for the activity of a radioactive source to halve – allows you to predict how quickly a sample decays and to perform essential calculations for your exams.
放射性衰变是一种自发过程，不稳定的原子核通过放出辐射来失去能量。这一基本概念是 Edexcel IGCSE 科学课程大纲的核心，将物理与医学、工业和古代材料测年等现实应用联系起来。理解半衰期——放射性源的活度减少一半所需的时间——能让你预测样品的衰变速度，并在考试中完成必要的计算。
1. What is Radioactive Decay? | 什么是放射性衰变？
Radioactive decay occurs in the nuclei of unstable isotopes (radioisotopes). These nuclei contain an imbalance of protons and neutrons, causing them to emit particles or electromagnetic waves in order to become more stable. The original nucleus is called the parent nuclide, and the resulting nucleus after decay is the daughter nuclide.
放射性衰变发生在不稳定同位素（放射性同位素）的原子核中。这些原子核含有不平衡的质子和中子，导致它们发射粒子或电磁波，从而变得更加稳定。原来的核称为母核，衰变后产生的核称为子核。
It is important to remember that radioactive decay is not affected by external conditions such as temperature, pressure or chemical bonding. The process is entirely random and cannot be sped up or slowed down.
重要的是要记住，放射性衰变不受温度、压力或化学键等外部条件的影响。这个过程完全是随机的，不能加快或减慢。
2. Types of Radiation: Alpha, Beta, Gamma | 辐射类型：α、β、γ
During radioactive decay, three main types of radiation can be emitted: alpha (α) particles, beta (β) particles and gamma (γ) rays. Each type has different properties in terms of charge, mass and penetrating power, which you must know for the exam.
在放射性衰变过程中，可以发射出三种主要辐射：α 粒子、β 粒子和 γ 射线。每种辐射在电荷、质量和穿透能力方面有不同的性质，这些是考试中必须掌握的。
| Radiation | Nature | Charge | Penetration |
|---|---|---|---|
| Alpha (α) | Helium nucleus (2p + 2n) | +2 | Stopped by paper or skin |
| Beta (β) | Fast‑moving electron | -1 | Stopped by thin aluminium |
| Gamma (γ) | Electromagnetic wave | 0 | Reduced by thick lead |
Alpha particles are the most ionising but the least penetrating, whereas gamma rays are the least ionising but the most penetrating. This difference in properties determines how each type of radiation is used.
α 粒子电离能力最强，但穿透力最弱；γ 射线电离能力最弱，但穿透力最强。这些性质的差异决定了每种辐射的用途。
3. The Random Nature of Decay | 衰变的随机性
Radioactive decay is a truly random process. That means you cannot predict exactly when a particular nucleus will decay, nor can you influence it. This random behaviour can be modelled by throwing large numbers of dice or by using a cloud chamber to observe individual decay tracks.
放射性衰变是一个真正的随机过程。这意味着你无法精确预测某个特定原子核何时衰变，也无法影响它。这种随机行为可以通过抛掷大量骰子来模拟，或者使用云雾室观察单个衰变径迹。
Because each nucleus in a sample has the same probability of decaying in a given time interval, the overall activity of a large sample decreases in a predictable way. This is where half‑life becomes so useful: even though individual decays are random, the average behaviour of billions of nuclei follows a clear mathematical pattern.
由于样品中每个原子核在给定时间间隔内具有相同的衰变概率，因此大量样品的总体活度以可预测的方式下降。这就是半衰期如此有用的原因：尽管单个衰变是随机的，但数十亿原子核的平均行为遵循清晰的数学模式。
4. Defining Half-Life | 半衰期的定义
The half‑life of a radioactive isotope is defined as the time taken for the number of undecayed nuclei in a sample to halve. Equally, it is the time taken for the count rate or activity of the sample to drop to one half of its initial value.
放射性同位素的半衰期定义为样品中未衰变原子核的数量减半所需的时间。同样，它也是样品的计数率或活度降至其初始值一半所需的时间。
For example, if a sample starts with 1000 undecayed nuclei and has a half‑life of 2 hours, after 2 hours there will be about 500 undecayed nuclei, after 4 hours about 250, and after 6 hours about 125.
例如，如果一个样品开始时含有 1000 个未衰变原子核，半衰期为 2 小时，那么 2 小时后将剩下大约 500 个未衰变原子核，4 小时后约 250 个，6 小时后约 125 个。
5. Calculating Half-Life from Graphs | 从图形计算半衰期
In the exam, you will often be given a decay curve – a graph of count rate (or activity) against time. To find the half‑life from such a graph, choose a count rate value at the beginning of the curve, note the time, and then find the time at which the count rate falls to half of that value. The difference in time is the half‑life.
在考试中，你经常会得到一条衰变曲线——计数率（或活度）随时间变化的图。要从这样的图中求出半衰期，选择曲线开始处的一个计数率值，记录时间，然后找到计数率降至该值一半时的时间。时间差就是半衰期。
It is good practice to repeat this procedure at several different points on the graph. Because the decay is exponential, the half‑life should be roughly constant. If the graph covers multiple half‑lives, you can even divide the total time by the number of half‑lives.
最好在图上多取几个点重复这一过程。因为衰变是指数型的，半衰期应当大致恒定。如果图形覆盖了多个半衰期，你甚至可以用总时间除以半衰期的个数来得到答案。
6. Half-Life Equation and Calculations | 半衰期方程与计算
Although the syllabus mainly requires graphical determination of half‑life, it is helpful to understand the underlying exponential relationship. The fraction of nuclei remaining after n half‑lives is (1/2)n. From this, we can write:
虽然考纲主要要求学生通过图形确定半衰期，但了解底层的指数关系是有帮助的。经过 n 个半衰期后剩余的原子核比例为 (1/2)n。由此我们可以写出：
N = N₀ × (½)t / t½
Where N₀ is the initial number of undecayed nuclei, N is the number remaining after time t, and t½ is the half‑life. The same formula applies to count rate or activity.
式中 N₀ 是初始未衰变原子核的数量，N 是经过时间 t 后剩余的数量，t½ 是半衰期。同样的公式也适用于计数率或活度。
For example, if a sample has a half‑life of 5 days and begins with an activity of 800 Bq, after 15 days the activity will be:
例如，如果一个样品的半衰期为 5 天，起始活度为 800 Bq，则 15 天后的活度为：
Activity = 800 × (½)15/5 = 800 × (½)³ = 800 × 1/8 = 100 Bq
7. Worked Example: Half‑Life Graph | 例题：半衰期图
rate of 640 counts per minute (cpm). The background count rate is 20 cpm. To find the half‑ und count rate to obtain the corrected count rate. The initial corrected count rate is 640 – 20 = 620 cpm.
一道经典的考试题给出一种放射性同位素的衰变图，起始计数率为每分钟 640 次（cpm），本底计数率为 20 cpm。要求半衰期，首先减去本底计数率得到修正计数率。初始修正计数率为 640 – 20 = 620 cpm。
Now find the time when the corrected count rate falls to half of 620, i.e. 310 cpm. Looking at the graph, this occurs at around 3.5 days. To check consistency, find when it falls to 155 cpm (half of 310); this occurs at about 7 days, confirming that the half‑life is 3.5 days.
现在找到修正计数率降至 620 的一半，即 310 cpm 时的时间。观察图形，这大约发生在 3.5 天。为检验一致性，再找出它降至 155 cpm（310 的一半）的时间；这大约发生在 7 天，证实半衰期为 3.5 天。
Always remember to subtract background radiation when dealing with real experimental data; otherwise your half‑life value will be inaccurate.
处理真实实验数据时一定要记得减去本底辐射；否则你求出的半衰期值将不准确。
8. Uses of Radioisotopes and Half-Life | 放射性同位素与半衰期的应用
The half‑life of a radioisotope determines its suitability for different applications. Isotopes with short half‑lives are used in medical tracers (e.g. technetium‑99m, half‑life 6 hours) because they decay quickly, minimising the patient’s exposure to radiation. The tracer must remain active long enough to be detected, but not linger unnecessarily in the body.
放射性同位素的半衰期决定了它是否适合不同的应用。短半衰期的同位素用于医学示踪剂（如锝-99m，半衰期 6 小时），因为它们衰变快，最大限度地减少患者受到的辐射。示踪剂必须保持足够长时间的活度以被检测到，但又不能在体内不必要地滞留。
For industrial thickness gauging, a source with a very long half‑life is normally chosen so that the equipment can run for years without replacing the source. Americium‑241 (half‑life 432 years) is used in smoke detectors for the same reason.
对于工业厚度测量，通常选择半衰期很长的放射源，这样设备可以运行多年而不必更换放射源。镅-241（半衰期 432 年）因同样原因被用于烟雾探测器。
Carbon‑14 dating relies on the constant ratio of carbon‑14 to carbon‑12 in living organisms. Once the organism dies, carbon‑14 decays with a half‑life of 5730 years. By measuring the remaining carbon‑14, scientists can estimate the age of archaeological specimens up to about 50 000 years old.
碳-14 测年依赖于活生物体中碳-14 与碳-12 的恒定比例。生物体一旦死亡，碳-14 就以 5730 年的半衰期衰变。通过测量剩余的碳-14，科学家可以估算出考古标本的年龄，最远可达约 5 万年。
9. Safety Precautions and Background Radiation | 安全措施与本底辐射
All ionising radiation can damage living cells, so strict safety measures are required when handling radioactive sources. Key precautions include using forceps or remote handling tools to increase distance, storing sources in lead‑lined containers, keeping exposure time to a minimum and never pointing a source directly at anyone.
所有电离辐射都会损伤活细胞，因此在操作放射源时需要严格的安全措施。关键预防措施包括：使用镊子或遥控工具以增大距离，将放射源存放在铅衬容器中，尽量缩短暴露时间，并且绝不对准任何人。
Background radiation is the low‑level radiation that surrounds us all the time. It comes from cosmic rays, rocks (particularly granite), radon gas, and even certain foods. When performing half‑life experiments, background count rate must be measured and subtracted from all readings to obtain the true activity of the sample.
本底辐射是时刻围绕我们的低强度辐射。它来自宇宙射线、岩石（特别是花岗岩）、氡气，甚至某些食物。在进行半衰期实验时，必须先测量本底计数率，并从所有读数中减去，以获得样品的真实活度。
10. Summary and Exam Tips | 总结与备考建议
Radioactive decay is spontaneous and random, characterised by a constant half‑life for a given isotope. You should be confident in extracting half‑life from a decay graph, correcting for background radiation, and explaining the practical uses of radioisotopes based on their half‑life and radiation type.
放射性衰变是自发且随机的，给定同位素具有恒定的半衰期。你应该能熟练地从衰变图中求出半衰期、校正本底辐射，并根据同位素的半衰期和辐射类型解释其实际用途。
- Always subtract background count rate before reading half‑life from a graph.
- 从图中读取半衰期之前一定要减去本底计数率。
- Use the 'half it again' method to verify your answer: the time between two consecutive halvings should be the same.
- 使用“再减半”方法验证答案：连续两次减半之间的时间应该相同。
- Link the choice of isotope to its application: short half‑life for medical tracers, long half‑life for smoke alarms.
- 将同位素的选择与其应用联系起来：医学示踪剂用短半衰期，烟雾报警器用长半衰期。
- Revise the properties of alpha, beta and gamma radiation – their charge, mass and penetration are common multiple‑choice targets.
- 复习 α、β 和 γ 辐射的性质——电荷、质量和穿透力是常见的选择题考点。
With a solid grasp of these concepts, you will be well prepared to tackle any radioactivity question in the Edexcel IGCSE Science exam.
扎实掌握这些概念后，你将能从容应对 Edexcel IGCSE 科学考试中任何有关放射性的问题。
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