📚 Radioactive Decay | IGCSE AQA 物理：放射性衰变 考点精讲
Radioactive decay is a fundamental process in nuclear physics where unstable atomic nuclei lose energy by emitting radiation. In the IGCSE AQA Physics syllabus, understanding the nature of radioactivity, the different types of radiation, half‑life, and the applications and hazards of radioactive materials is essential. This article covers all key points you need to master the topic.
放射性衰变是核物理中的基本过程，指不稳定的原子核通过发出辐射来释放能量。在 IGCSE AQA 物理课程中，理解放射性的本质、不同类型的辐射、半衰期以及放射性物质的应用与危害非常重要。本文涵盖了你需要掌握的所有关键知识点。
1. Atomic Structure and Isotopes | 原子结构与同位素
Atoms consist of a small central nucleus containing protons and neutrons, surrounded by electrons in shells. The number of protons (atomic number, Z) defines the element, while the total number of protons and neutrons gives the mass number (A). Isotopes are atoms of the same element with the same number of protons but different numbers of neutrons. Some isotopes are unstable and radioactive, meaning their nuclei will decay spontaneously.
原子由一个包含质子和中子的小原子核以及核外分层排布的电子组成。质子数（原子序数 Z）决定了元素种类，质子数与中子数之和为质量数（A）。同位素是质子数相同但中子数不同的同种元素原子。某些同位素不稳定并具有放射性，意味着它们的原子核会自发衰变。
2. What is Radioactive Decay? | 什么是放射性衰变？
Radioactive decay is the random process by which an unstable nucleus emits radiation to become more stable. The decay is spontaneous and cannot be influenced by external conditions such as temperature or pressure. The nucleus may emit an alpha particle (α), a beta particle (β), or gamma rays (γ), often transforming into a different element.
放射性衰变是不稳定原子核通过发出辐射而变得更稳定的随机过程。衰变是自发的，不受温度或压力等外部条件的影响。原子核可能发射 α 粒子、β 粒子或 γ 射线，通常会转变为另一种元素。
3. Types of Radiation | 辐射的类型
There are three main types of nuclear radiation: alpha particles, beta particles, and gamma rays. Each has different penetrating power, ionising ability, and behaviour in electric and magnetic fields.
核辐射主要有三种类型：α 粒子、β 粒子和 γ 射线。它们的穿透能力、电离能力以及在电场和磁场中的表现各不相同。
- Alpha particles (α) are helium nuclei (2 protons + 2 neutrons, charge +2e). They are heavy, highly ionising, but have low penetration – stopped by a few centimetres of air or a sheet of paper.
α 粒子 是氦核（2个质子+2个中子，带 +2e 电荷）。它们质量大、电离能力强，但穿透力弱——几厘米空气或一张纸就能阻挡。 - Beta particles (β⁻) are fast-moving electrons emitted when a neutron turns into a proton. They are moderately ionising and can penetrate a few millimetres of aluminium.
β⁻ 粒子 是快电子，在中子转变为质子时放出。电离能力中等，能穿透几毫米铝。 - Gamma rays (γ) are electromagnetic waves of very short wavelength. They are weakly ionising but highly penetrating, requiring several centimetres of lead or thick concrete to significantly reduce their intensity.
γ 射线 是波长极短的电磁波。电离能力弱，但穿透力极强，需要几厘米铅板或厚混凝土才能显著减弱其强度。
4. Properties and Penetration | 辐射的性质与穿透能力
Alpha particles have the greatest mass and charge, so they cause the most ionisation per unit length. Because of this, they quickly lose energy and are easily absorbed. Beta particles are lighter and travel faster, penetrating further. Gamma rays have no mass or charge and interact the least with matter, making them the most penetrating. A visual comparison of penetration is often illustrated with paper, aluminium, and lead absorbers.
α 粒子质量和电荷最大，因此单位长度上产生的电离最多，能量损失快，容易被吸收。β 粒子较轻、速度更快，穿透距离更远。γ 射线没有质量和电荷，与物质相互作用最少，因此穿透力最强。通常用纸、铝、铅的吸收效果来直观比较穿透能力。
| Type 类型 | Penetration 穿透力 | Ionising ability 电离能力 | Stopped by 可被阻挡 |
|---|---|---|---|
| α | Low 弱 | Very high 很强 | Paper / skin 纸张 / 皮肤 |
| β | Moderate 中等 | Moderate 中等 | 3–5 mm aluminium 3–5毫米铝板 |
| γ | Very high 很强 | Low 弱 | Thick lead / concrete 厚铅 / 混凝土 |
This table summarises the relative properties that are commonly examined. Remember that ionising ability is inversely related to penetration.
这个表格总结了常考的相对性质。记住，电离能力与穿透能力成反比。
5. Nuclear Decay Equations | 核衰变方程
When writing nuclear equations, both mass number (total nucleons) and atomic number (proton number) must balance on each side. In alpha decay, the nucleus loses 2 protons and 2 neutrons, so the atomic number decreases by 2 and the mass number by 4. For example, radium‑226 decays by alpha emission:
写核反应方程时，两边质量数（总核子数）和原子序数（质子数）必须守恒。在 α 衰变中，原子核失去2个质子和2个中子，因此原子序数减2，质量数减4。例如，镭‑226 发生 α 衰变：
²²⁶₈₈Ra → ²²²₈₆Rn + ⁴₂He
In beta‑minus decay, a neutron is converted into a proton and an electron (beta particle) is emitted. The atomic number increases by 1, while the mass number stays the same. For carbon‑14:
在 β⁻ 衰变中，一个中子转变为质子，同时放出电子（β 粒子）。原子序数增加1，质量数不变。例如碳‑14：
¹⁴₆C → ¹⁴₇N + ⁰₋₁e
Gamma emission does not change the mass number or atomic number; the nucleus simply loses energy. Gamma radiation is often emitted after an alpha or beta decay if the daughter nucleus is left in an excited state.
γ 辐射不改变质量数或原子序数，原子核仅释放能量。如果子核处于激发态，通常在 α 或 β 衰变后伴随发射 γ 射线。
6. Half‑Life | 半衰期
Half‑life (T₁/₂) is the time taken for the number of radioactive nuclei in a sample to halve, or for the activity (decays per second) to fall to half its initial value. Half‑life is constant for a given isotope and is unaffected by physical conditions. It can be determined from a decay curve by reading the time taken for the activity to drop from any value to half of that value.
半衰期（T₁/₂）是指样本中放射性原子核的数量减半，或每秒衰变次数（活度）降到初始值一半所需的时间。对特定同位素，半衰期是恒定的，不受物理条件影响。可通过衰变曲线读出活度从任意值降至该值一半所用的时间来确定。
For example, if a sample starts with 800 undecayed nuclei and has a half‑life of 2 hours, after 2 hours 400 remain, after 4 hours 200 remain, and so on. Calculations often involve finding the fraction remaining after n half‑lives: (½)ⁿ.
例如，某样品起初有800个未衰变的原子核，半衰期为2小时，则2小时后剩下400个，4小时后剩下200个，以此类推。计算中常用 n 个半衰期后剩余比例：(½)ⁿ。
7. Activity and Count Rate | 活度与计数率
The activity of a radioactive source is the number of decays per second, measured in becquerels (Bq), where 1 Bq = 1 decay per second. A Geiger‑Müller tube connected to a counter records the count rate (counts per second), which is proportional to the activity, but background radiation must be subtracted to obtain the corrected count rate.
放射源的活度是每秒衰变次数，单位为贝克勒尔（Bq），1 Bq 等于每秒1次衰变。连接计数器的盖革‑米勒管记录计数率（每秒计数），计数率与活度成正比，但必须扣除本底辐射才能得到修正后的计数率。
Background radiation comes from natural sources such as cosmic rays, rocks, and radon gas, as well as artificial sources like medical waste. The background count should be measured before an experiment and subtracted from all readings.
本底辐射来自天然来源（如宇宙射线、岩石和氡气）以及人工来源（如医疗废物）。实验前应测量本底计数，并从所有读数中减去。
8. Uses of Radioactive Isotopes | 放射性同位素的应用
Radioisotopes are widely used in medicine, industry, and archaeology. Key examples in the AQA specification include:
放射性同位素广泛应用于医学、工业和考古学。AQA 考试大纲中的关键例子包括：
- Medical tracers: Gamma‑emitting isotopes like technetium‑99m are injected into the body to diagnose organ function. Gamma rays can be detected outside the body because they are penetrating and weakly ionising, minimising tissue damage. The isotope should have a short half‑life (a few hours) so that it decays quickly after the procedure.
医学示踪剂： 将发射 γ 射线的同位素如锝‑99m 注入体内，以诊断器官功能。γ 射线穿透力强且电离作用弱，能在体外被探测且组织损伤小。所用同位素应具有短半衰期（几小时），以便检查后快速衰变消失。 - Radiotherapy: Gamma rays from cobalt‑60 are focused on cancerous tumours to destroy malignant cells.
放射治疗： 钴‑60 发出的 γ 射线聚焦于癌变肿瘤，杀死恶性细胞。 - Industrial thickness monitoring: Beta sources are used to measure the thickness of paper or plastic in production. A detector measures the amount of radiation passing through; a change indicates a change in thickness.
工业厚度监测： 使用 β 源测量生产过程中纸张或塑料的厚度。探测器测量穿透的辐射量，变化表明厚度改变。 - Carbon dating: The ratio of carbon‑14 to carbon‑12 in dead organic material decreases predictably (half‑life 5730 years), allowing archaeologists to estimate the age of samples up to ~50 000 years.
碳定年法： 死亡有机物中碳‑14 与碳‑12 的比例按可预测的规律下降（半衰期5730年），考古学家可据此估算样品年龄（可达约5万年）。 - Smoke alarms: A weak alpha source ionises air between two electrodes; smoke particles absorb the alphas, reducing the current and triggering the alarm.
烟雾报警器： 一个弱 α 源将两电极间的空气电离；烟雾颗粒吸收 α 粒子，减小电流从而触发警报。
9. Hazards of Radiation | 辐射的危害
Ionising radiation can damage living cells by altering DNA. Alpha particles are extremely hazardous if ingested or inhaled because they cause intense localised ionisation. Beta and gamma radiation can penetrate the skin and damage internal organs. High doses cause radiation sickness, cancer, or genetic mutations. Safety precautions include using tongs, storing sources in lead‑lined containers, and minimising exposure time.
电离辐射可以通过改变 DNA 损伤活细胞。α 粒子一旦被摄入或吸入体内危害极大，因为它们会造成强烈的局部电离。β 和 γ 辐射可穿透皮肤损伤内部器官。高剂量会引起辐射病、癌症或遗传突变。安全措施包括使用镊子操作、将放射源存放在衬铅容器内，并尽可能减少接触时间。
10. Background Radiation and Its Sources | 本底辐射及其来源
Background radiation is the low‑level ionising radiation that is always present in the environment. Natural sources include cosmic rays from space, radon gas released from rocks, and radioactive isotopes in food and building materials. Artificial sources include medical X‑rays, nuclear power, and fallout from weapons testing. The average annual dose in the UK is about 2.5 millisieverts (mSv).
本底辐射是环境中始终存在的低水平电离辐射。天然来源包括宇宙射线、岩石释放的氡气以及食物和建筑材料中的放射性同位素。人工来源包括医用 X 射线、核能以及武器试验的沉降物。在英国，平均年辐射剂量约为2.5毫希沃特（mSv）。
11. Detecting Radiation | 辐射的探测
The Geiger‑Müller (GM) tube is the most common detector. It contains a low‑pressure gas that becomes momentarily conductive when ionised by radiation, producing an electrical pulse. These pulses are counted and give a reading in counts per second. To distinguish between alpha, beta, and gamma, absorbers are placed between the source and the GM tube: alpha is stopped by paper, beta by aluminium, and gamma penetrates all but is reduced by lead. A cloud chamber can also show tracks of ionising radiation visually.
盖革‑米勒（GM）管是最常用的探测器。管内充有低压气体，当被辐射电离时短暂导电，产生电脉冲。这些脉冲被计数，得出每秒计数读数。为区分 α、β 和 γ，可在源与 GM 管之间放置吸收材料：α 被纸挡住，β 被铝挡住，γ 能穿透所有材料但铅可减弱其强度。云室也可以直观显示电离辐射的径迹。
12. Random Nature of Decay | 衰变的随机性
Radioactive decay is a random process. It is impossible to predict which individual nucleus will decay next, or when a particular nucleus will decay. However, with a large number of nuclei, the overall decay rate follows a predictable statistical pattern described by the half‑life. This random nature is an important concept that underpins the analysis of experimental data, where variations in count rate are expected.
放射性衰变是一个随机过程。无法预测哪个原子核会下一个衰变，或者某个特定原子核何时会衰变。然而，对于大量原子核，整体衰变率遵循由半衰期描述的可预测统计规律。这种随机性是支撑实验数据分析的重要概念，实验中计数率的变化是意料之中的。
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