📚 AS Physics: Radioactive Decay Key Points | AS 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 loses energy by emitting radiation. In AS Physics, understanding the nature of alpha, beta, and gamma emissions, the concept of half-life, and the exponential decay law are fundamental. This guide covers all the essential key points you need to master for your examination.
放射性衰变是一种随机且自发的核变化过程：不稳定的原子核通过发出辐射来释放能量。在 AS 物理课程中，理解 α、β 和 γ 射线的本质、半衰期的概念以及指数衰减规律是基础要求。本文梳理了所有必考的要点，帮助你系统复习。
1. What is Radioactive Decay? | 什么是放射性衰变？
Radioactive decay occurs when an unstable nucleus changes into a more stable configuration by emitting particles or electromagnetic radiation. The process is spontaneous — it cannot be influenced by temperature, pressure, or chemical bonding. The decay of any individual nucleus is entirely random, meaning we cannot predict exactly when a given nucleus will decay, only the probability of decay within a certain time interval.
当不稳定的原子核通过发射粒子或电磁辐射转变为更稳定的结构时，就发生了放射性衰变。这个过程是自发的——温度、压强或化学键均不能影响它。单个核的衰变是完全随机的，我们无法精确预测某个特定核何时衰变，只能知道它在一段时间内衰变的概率。
2. Types of Radioactive Emission: Alpha, Beta and Gamma | 放射性发射的类型：α、β 和 γ
There are three main types of radiation emitted during radioactive decay: alpha (α) particles, beta (β) particles, and gamma (γ) rays. An alpha particle consists of two protons and two neutrons — equivalent to a helium nucleus, ⁴₂He. Beta-minus (β⁻) decay occurs when a neutron converts into a proton and emits an electron and an antineutrino. Beta-plus (β⁺) decay involves a proton converting into a neutron, emitting a positron and a neutrino. Gamma radiation is high-energy electromagnetic radiation emitted when a nucleus transitions from an excited state to a lower energy state, often following alpha or beta decay.
放射性衰变中主要发射三种射线：α 粒子、β 粒子和 γ 射线。α 粒子由两个质子和两个中子构成，相当于一个氦核 ⁴₂He。β⁻ 衰变是中子转变为质子，同时放出一个电子和一个反中微子。β⁺ 衰变则是质子转变为中子，放出一个正电子和一个中微子。γ 辐射是原子核从激发态跃迁到较低能态时发出的高能电磁波，常伴随 α 或 β 衰变发生。
Alpha particles are highly ionising but have very low penetration; they can be stopped by a sheet of paper or a few centimetres of air. Beta particles are moderately ionising and can penetrate a few millimetres of aluminium. Gamma rays are weakly ionising and highly penetrating, requiring several centimetres of lead or metres of concrete to reduce their intensity significantly.
α 粒子电离能力强但穿透力很弱，一张纸或几厘米空气即可阻挡。β 粒子的电离能力中等，可穿透几毫米的铝。γ 射线的电离能力弱但穿透力极强，需要几厘米厚的铅或数米混凝土才能显著减弱其强度。
3. Decay Law and Activity | 衰变规律与活度
The activity (A) of a radioactive sample is the number of decays occurring per unit time. It is measured in becquerels (Bq), where 1 Bq = 1 decay per second. Activity is proportional to the number of undecayed nuclei (N) present: A = λN, where λ is the decay constant. As a radioactive sample decays, its activity decreases exponentially with time.
放射性样品的活度 A 是单位时间内发生的衰变次数，单位为贝克勒尔 (Bq)，1 Bq = 1 次衰变/秒。活度与现存的未衰变原子核数目 N 成正比：A = λN，其中 λ 为衰变常数。随着样品衰变，其活度随时间呈指数规律下降。
4. The Concept of Half-Life | 半衰期的概念
Half-life (T1/2) is the time taken for half the radioactive nuclei in a sample to decay, or equivalently, the time taken for the activity of the sample to halve. Each radioactive isotope has a characteristic half-life, which is constant and independent of the initial number of nuclei. For example, carbon-14 has a half-life of about 5730 years, while uranium-238 has a half-life of 4.5 × 10⁹ years.
半衰期 T1/2 是样品中放射性原子核数衰变掉一半所需的时间，也等于样品的活度减半所需的时间。每种放射性同位素都有其特定的半衰期，这一数值恒定不变，与初始核的数量无关。例如，碳-14 的半衰期约为 5730 年，而铀-238 的半衰期则为 4.5 × 10⁹ 年。
5. Exponential Decay Equation | 指数衰减方程
The number of undecayed nuclei N after time t can be expressed by the exponential decay law:
经过时间 t 后，未衰变原子核数 N 的指数衰减规律可表示为：
N = N₀ e–λt
where N₀ is the initial number of nuclei, λ is the decay constant, and t is the elapsed time. The same equation applies to activity: A = A₀ e–λt. Another useful form involves half-life:
其中 N₀ 为初始核数，λ 为衰变常数，t 为经历的时间。同样的方程也适用于活度：A = A₀ e–λt。另一种使用半衰期的常用形式为：
N = N₀ (½)t / T1/2
The decay constant λ is related to half-life by λ = ln 2 / T1/2. This linkage allows calculation of one quantity from the other.
衰变常数 λ 与半衰期的关系为 λ = ln 2 / T1/2。通过这一关系式，可以从其中一量求出另一量。
6. Decay Constant and Probability | 衰变常数与概率
The decay constant λ represents the probability that an individual nucleus will decay per unit time. It has units of s⁻¹ (or min⁻¹, year⁻¹ depending on the time unit used). A large λ corresponds to a short half-life and rapid decay; a small λ corresponds to a long half-life and slow decay. This statistical interpretation helps explain why radioactive decay is a random process governed by chance.
衰变常数 λ 代表单个原子核在单位时间内发生衰变的概率，其单位为 s⁻¹（也可用 min⁻¹、year⁻¹ 等）。λ 越大，半衰期越短，衰变越快；λ 越小，半衰期越长，衰变越慢。这种统计解释有助于理解为什么放射性衰变是一个由概率支配的随机过程。
7. Measuring Activity and Correcting for Background Radiation | 活度的测量与背景辐射修正
In the laboratory, a Geiger–Müller (GM) tube connected to a counter is often used to measure the count rate of a radioactive sample. However, even without any source, the counter will register a background count caused by cosmic rays and naturally occurring radioactive materials in the environment. To obtain the true count rate from the source, you must subtract the background count rate.
在实验室中，常用连接计数器的盖革-米勒 (GM) 计数管来测量放射性样品的计数率。不过，即使没有放射源，计数器也会因宇宙射线和环境中的天然放射性物质而记录到本底计数。要获得放射源的真实计数率，必须扣除本底计数率。
| Step | Action | 操作 |
| 1 | Measure background count rate without source. | 在无源条件下测量本底计数率。 |
| 2 | Measure total count rate with source present. | 放入源后测量总计数率。 |
| 3 | Corrected count rate = total – background. | 修正后的计数率 = 总计数率 – 本底计数率。 |
For more precise work, especially with low-activity samples, longer counting times should be used to reduce the statistical uncertainty in the readings.
对于更精确的实验，特别是低活度样品，应使用较长的计数时间来降低读数的统计不确定性。
8. Radioactive Dating | 放射性年代测定
Radioactive isotopes with long half-lives can be used to estimate the age of archaeological and geological samples. Carbon-14 dating relies on the known half-life of ¹⁴C and the ratio of ¹⁴C to ¹²C in once-living organisms. After death, no new ¹⁴C is taken in, and the existing ¹⁴C decays exponentially. By measuring the remaining ¹⁴C activity, the time since death can be calculated using the exponential decay equation.
半衰期长的放射性同位素可用于估算考古和地质样品的年龄。碳-14 测年法依赖于 ¹⁴C 的已知半衰期以及曾经存活的生物体内 ¹⁴C 与 ¹²C 的比值。生物死亡后，不再摄取新的 ¹⁴C，已有的 ¹⁴C 按指数规律衰变。测量剩余的 ¹⁴C 活度，便可根据指数衰减方程推算出死亡时间。
Other dating methods include uranium-lead dating for rocks, using the decay chain of uranium isotopes to lead. The reliability of radioactive dating depends on accurate knowledge of the initial composition and a constant half-life.
其他测年法包括用于岩石的铀-铅测年法，利用铀同位素到铅的衰变链进行测定。放射性定年的可靠性取决于对初始组成的准确了解以及半衰期的恒定性。
9. Radioactive Tracers and Medical Uses | 放射性示踪剂与医学应用
Radioisotopes emitting gamma rays (such as technetium-99m) are widely used as tracers in medical imaging. Because gamma radiation is penetrating and can be detected outside the body, a small amount of the tracer is introduced into the patient and its path through organs is monitored with a gamma camera. Short half-lives are chosen to minimise the dose to the patient while still allowing sufficient time for imaging.
发射 γ 射线的放射性同位素（例如锝-99m）广泛用作医学成像中的示踪剂。由于 γ 射线穿透力强且可在体外探测，医生将少量示踪剂引入患者体内，用 γ 相机监测其在器官中的路径。选择短半衰期的同位素可最大限度地减少对患者的辐射剂量，同时仍保证足够的成像时间。
In industry, tracers are used to detect leaks in pipelines or to study mixing and flow patterns. The principles of activity measurement and half-life are crucial in designing such applications.
在工业中，示踪剂用于检测管道泄漏或研究混合与流动模式。活度测量和半衰期的原理在设计这些应用时至关重要。
10. Hazards and Safety Precautions | 辐射的危害与安全注意事项
Ionising radiation can damage living cells and DNA, potentially leading to cancer or genetic mutations. Alpha sources are particularly dangerous if ingested or inhaled, as they cause intense local damage. Gamma sources present an external hazard due to their high penetration. Safety measures include:
电离辐射会损伤活细胞和 DNA，可能导致癌症或基因突变。α 放射源若被摄入或吸入体内尤其危险，因为会造成强烈的局部损伤。γ 源因其强穿透力而构成外部危害。安全措施包括：
- Keeping a large distance from the source (inverse-square law reduces intensity).
- Minimising exposure time.
- Using shielding appropriate to the radiation type (lead for gamma, Perspex for beta).
- Never handling sources with bare hands; use tongs or robotics.
- 与源保持较大距离（平方反比定律可降低辐射强度）。
- 尽量缩短照射时间。
- 选用与辐射类型相适应的屏蔽材料（γ 用铅、β 用有机玻璃）。
- 切勿赤手接触放射源；应使用钳子或机械手。
Strict regulations govern the use, storage, and disposal of radioactive materials to protect both people and the environment.
为保护人员和环境，放射性材料的使用、储存和处置均有严格规定。
11. Summary and Exam Tips | 考点总结与应试技巧
For AS Physics examinations, ensure you can:
在 AS 物理考试中，请确保你能做到：
- State that radioactive decay is random and spontaneous, and that activity is the rate of decay.
- Compare the properties of alpha, beta, and gamma radiation in terms of nature, ionising ability, and penetration.
- Write down and use N = N₀ e–λt and A = A₀ e–λt, and relate half-life to the decay constant.
- Interpret activity–time and number–time graphs, including the exponential fall-off and constant half-life.
- Correct count rate measurements for background radiation.
- Describe applications such as carbon dating and medical tracers, linking principles to the equations.
- Outline safety precautions for handling radioactive sources.
- 指出放射性衰变是随机的和自发的，活度是衰变速率。
- 比较 α、β 和 γ 射线在本质、电离能力和穿透力方面的性质。
- 写出并运用 N = N₀ e–λt 和 A = A₀ e–λt，关联半衰期与衰变常数。
- 解释活度-时间图和核数-时间图，包括指数下降和恒定半衰期特征。
- 对背景辐射进行计数率修正。
- 描述碳定年和医学示踪等应用，并将原理与方程联系起来。
- 概述操作放射源的安全注意事项。
Mastering these points will give you a solid foundation in the nuclear physics section of your physics course.
掌握这些要点，将为你在物理课程中的原子核物理部分打下扎实的基础。
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