📚 Radioactivity | 放射性
Radioactivity is the spontaneous decay of unstable atomic nuclei through the emission of ionising radiation. In A-Level CIE Physics, you need to understand the nature of α, β and γ radiations, how to write balanced nuclear equations, the mathematical treatment of activity and decay, as well as the practical uses and hazards of radioactive sources. This article revisits every key concept with bilingual explanations to support your revision.
放射性是不稳定原子核通过发射电离辐射而自发衰变的过程。在A-Level CIE物理中，你需要理解α、β和γ射线的本质，会书写平衡的核方程，掌握活度与衰变的数学处理，同时熟悉放射源的实际应用与危害。本文以中英双语回顾每一个关键概念，助力你的复习。
1. The Atomic Nucleus and Isotopes | 原子核与同位素
Every atom consists of a small, dense nucleus surrounded by electrons. The nucleus contains protons and neutrons, collectively called nucleons. The number of protons Z defines the element, while the total number of nucleons A is the mass number. Isotopes are atoms of the same element (same Z) that have different numbers of neutrons, hence different A. For example, carbon-12 (126C) and carbon-14 (146C) are isotopes.
每个原子都有一个微小而致密的原子核，周围环绕着电子。原子核由质子和中子组成，统称为核子。质子数Z决定了元素种类，而核子总数A为质量数。同位素是指质子数相同（Z相同）而中子数不同，因而A不同的原子。例如碳-12 (126C) 和碳-14 (146C) 互为同位素。
Stable nuclei have a balance between the number of protons and neutrons. If this balance is disrupted, the nucleus becomes unstable and will undergo radioactive decay to move towards a more stable configuration. The strong nuclear force holds nucleons together, counteracting the electrostatic repulsion between protons.
稳定核的质子和中子数之间存在平衡。一旦这种平衡被打破，原子核就不稳定，便会发生放射性衰变，向更稳定的状态转变。强核力将核子束缚在一起，同时抵消质子间的静电排斥。
2. Types of Radioactive Emission | 放射性发射类型
Three main types of radiation are emitted during radioactive decay: alpha (α) particles, beta (β) particles and gamma (γ) rays. Alpha particles are helium nuclei (42He), consisting of two protons and two neutrons. Beta-minus (β⁻) decay occurs when a neutron converts into a proton, emitting an electron and an antineutrino. Beta-plus (β⁺) decay involves a proton converting into a neutron, releasing a positron and a neutrino. Gamma radiation is high-energy electromagnetic radiation emitted when a nucleus de‑excites from a higher energy state.
放射性衰变中主要发射三种辐射：α粒子、β粒子和γ射线。α粒子是氦核 (42He)，由两个质子和两个中子组成。β⁻衰变发生于中子转变为质子时，放出一个电子和一个反中微子。β⁺衰变则是一个质子转变为中子，放出正电子和一个中微子。γ辐射是原子核从高能态退激时发射的高能电磁辐射。
In some heavy nuclei, spontaneous fission can occur, but syllabus emphasis is on α, β and γ. Electron capture, where a proton captures an inner-shell electron to become a neutron, is another mode of β decay often mentioned alongside β⁺.
在某些重核中可发生自发裂变，但考纲重点在α、β和γ。电子俘获，即质子俘获内层电子变为中子，是β衰变的另一种模式，常与β⁺一同提及。
3. Properties of Alpha, Beta and Gamma Radiations | α、β和γ射线的性质
| Property | Alpha (α) | Beta (β⁻/β⁺) | Gamma (γ) |
|---|---|---|---|
| Nature | Helium nucleus, 2p+2n | Electron or positron | Electromagnetic wave |
| Charge | +2e | −1e (β⁻) or +1e (β⁺) | 0 |
| Ionising ability | Strong (highly ionising) | Medium | Weak |
| Penetrating power | Low (stopped by paper or few cm air) | Medium (stopped by ~3 mm aluminium) | High (reduced by thick lead or concrete) |
| Deflection in electric/magnetic field | Slight, towards negative plate | Large, towards positive plate (β⁻) or negative (β⁺) | None |
Alpha particles are the most ionising because of their large mass and double charge. They lose energy quickly in matter and are therefore the least penetrating. Beta particles are less ionising and more penetrating. Gamma rays, being uncharged photons, cause the least direct ionisation but can travel through several centimetres of lead.
α粒子因质量大并带有双电荷，电离能力最强。它们在物质中迅速损失能量，因此穿透力最弱。β粒子电离能力较弱，穿透力较强。γ射线是不带电的光子，直接电离最少，但能穿透数厘米厚的铅。
In a magnetic field, alpha and beta particles experience a magnetic force perpendicular to their velocity, following curved paths in opposite directions because of opposite charges. Gamma radiation is undeflected. The radius of curvature depends on charge, mass and speed.
在磁场中，α和β粒子受洛伦兹力作用，因电荷相反沿相反方向弯曲。γ辐射不受偏转。曲率半径取决于电荷、质量和速度。
4. Decay Equations and Neutrinos | 衰变方程与中微子
Nuclear equations must balance both mass number A and proton number Z. For α decay: AZX → A−4Z−2Y + 42He. An example is 23892U → 23490Th + 42He. In β⁻ decay: AZX → AZ+1Y + 0−1e + ν̅e, where ν̅e is the antineutrino. An example is 146C → 147N + 0−1e + ν̅e.
核方程必须同时平衡质量数A和质子数Z。α衰变：AZX → A−4Z−2Y + 42He。例如 23892U → 23490Th + 42He。β⁻衰变：AZX → AZ+1Y + 0−1e + ν̅e，其中ν̅e是反中微子。例如 146C → 147N + 0−1e + ν̅e。
For β⁺ decay: AZX → AZ−1Y + 0+1e + νe. An example is 116C → 115B + 0+1e + νe. Gamma decay involves no change in A or Z; the nucleus simply emits a photon: AZX* → AZX + γ. The asterisk denotes an excited nuclear state.
β⁺衰变：AZX → AZ−1Y + 0+1e + νe。例如 116C → 115B + 0+1e + νe。γ衰变中，A和Z均不变；原子核仅放出光子：AZX* → AZX + γ。星号表示核激发态。
The existence of the neutrino was postulated to account for the continuous energy spectrum of beta particles, which would otherwise violate conservation of energy and momentum. Neutrinos have negligible mass, no charge, and interact very weakly with matter.
中微子的提出是为了解释β粒子的连续能谱，否则能量和动量守恒将不成立。中微子几乎无质量、不带电，与物质的相互作用极弱。
5. Activity and the Decay Constant | 活度与衰变常数
ond. Activity is proportional to the number of undecayed nuclei N present at that instant:
放射性样品的活度A是单位时间内发生的衰变数，单位为贝克勒尔 (Bq)，1 Bq等于每秒1次衰变。活度与该时刻未衰变核的数目N成正比：
A = λN
where λ is the decay constant, characteristic of the particular isotope, with units s⁻¹. The decay constant is the probability per unit time that a given nucleus will decay. A large λ means the isotope decays rapidly.
其中λ为衰变常数，是特定同位素的特征参数，单位为s⁻¹。衰变常数是单位时间内某个核发生衰变的概率。λ大表示该同位素衰变快。
Since the activity A is also the rate of decrease of N, we have A = –dN/dt. Combining with A = λN gives the differential equation dN/dt = –λN. The solution to this equation is the exponential decay law.
由于活度A也是N的减少率，即A = –dN/dt。结合A = λN，得到微分方程 dN/dt = –λN。该方程的解即指数衰变定律。
6. Exponential Decay Law | 指数衰变定律
The number of undecayed nuclei decreases exponentially over time:
未衰变的核数随时间按指数规律减少：
N = N₀ e−λt
where N₀ is the initial number of nuclei at t = 0. Correspondingly, the activity follows:
其中N₀为t=0时的初始核数。相应地，活度满足：
A = A₀ e−λt
. This exponential behaviour implies that equal time intervals reduce the quantity by the same fraction, not by the same absolute amount.
其中A₀ = λN₀为初始活度。这种指数行为意味着相同的时间间隔使数量按相同比例减少，而非相同的绝对数值。
On a graph of N against t, the curve is a decreasing exponential. If you plot ln N (or ln A) against t, you obtain a straight line with a negative gradient equal to –λ. This is a very useful graphical method for determining λ.
在N-t图上，曲线为下降的指数函数。如果绘制ln N（或ln A）对t的图，将得到一条斜率为–λ的直线。这是确定λ的非常有用的图像方法。
7. Half-Life | 半衰期
The half-life T½ is the time taken for the number of undecayed nuclei (or the activity) to fall to half of its initial value. It is related to the decay constant by:
半衰期T½是指未衰变核的数目（或活度）降至初始值一半所需的时间。它与衰变常数的关系为：
T½ = (ln 2) / λ
This relation is derived by setting N = N₀/2 in the exponential law: N₀/2 = N₀ e−λT½ → e−λT½ = 1/2 → –λT½ = ln(1/2) → T½ = ln 2 / λ.
此关系由指数定律推导而来：令N = N₀/2，则 N₀/2 = N₀ e−λT½ → e−λT½ = 1/2 → –λT½ = ln(1/2) → T½ = ln 2 / λ。
f about 4.5×10⁹ years, while polonium-214 has a half-life of only 1.6×10⁻⁴ s. Carbon-14 (T½ ≈ 5730 years) is widely used in dating archaeological samples.
不同同位素的半衰期差异极大，从几分之一秒到数十亿年不等。例如铀-238的半衰期约为4.5×10⁹年，而钋-214的半衰期仅为1.6×10⁻⁴秒。碳-14（T½ ≈ 5730年）广泛应用于考古断代。
8. Background Radiation and Detection | 背景辐射与探测
Background radiation is the ionising radiation present in the environment from natural and artificial sources. Natural sources include cosmic rays, radon gas, and radioactive materials in rocks and soil. Artificial sources come from medical procedures, nuclear power and fallout. When measuring the activity of a sample, the background count rate must be subtracted.
背景辐射是环境中存在的电离辐射，来自天然和人工来源。天然来源包括宇宙射线、氡气以及岩石和土壤中的放射性物质。人工来源包括医疗程序、核能及沉降物。测量样品活度时，必须扣除本底计数率。
Common detectors include the Geiger–Müller (GM) tube, which gives a count rate; the scintillation counter, which produces light flashes; and the cloud chamber, which shows particle tracks. GM tubes are widely used in school laboratories but cannot distinguish between types of radiation unless used with absorbers.
常见的探测器有盖革-米勒 (GM) 计数管（给出计数率）、闪烁计数器（产生光脉冲）和云室（显示粒子径迹）。GM管广泛用于学校实验室，但若不借助吸收材料则无法区分辐射类型。
To identify the type of radiation, you can place a series of absorbers between the source and the detector: if the count drops dramatically with paper, it is alpha; if it drops with a few mm of aluminium, it is beta; if it persists through aluminium but is reduced by lead, it is gamma.
鉴别辐射类型时，可在源与探测器间依次加入吸收片：若加入纸张后计数大幅下降则为α；若几毫米铝使其下降则为β；若能穿过铝而仅被铅减弱则为γ。
9. Uses of Radioisotopes | 放射性同位素的应用
Radioactive isotopes have numerous applications in medicine, industry and research. In medicine, technetium-99m (γ emitter, T½ rgans. Iodine-131 (β and γ) is used to treat thyroid disorders because the thyroid gland absorbs iodine. Radiotherapy employs focused gamma rays to destroy cancerous cells.
放射性同位素在医学、工业和研究中有大量应用。在医学上，锝-99m（γ放射源，半衰期6小时）用作示踪剂来成像器官。碘-131（β和γ）用于治疗甲状腺疾病，因为甲状腺会吸收碘。放射治疗利用聚焦的γ射线摧毁癌细胞。
In industry, gamma sources are used to inspect welds and pipelines through radiography. Beta sources are used in thickness gauges for paper or metal foil production. Carbon-14 dating determines the age of organic materials up to about 50000 years by measuring the remaining 14C activity.
在工业中，γ源被用于射线照相术检查焊缝和管道。β源用于纸张或金属箔生产中的厚度测量。碳-14断代通过测量残留的14C活度，可确定有机材料的年代，上限约5万年。
Smoke alarms use a weak alpha source (americium-241) to ionise air; the presence of smoke disrupts the current, triggering the alarm. Tracers in agriculture and hydrology study the flow of water and uptake of fertilisers.
烟雾报警器利用弱α源（镅-241）电离空气；烟雾的存在干扰电流从而触发警报。农业和水文学中的示踪剂用于研究水流和肥料吸收。
10. Radiation Hazards and Safety | 辐射危害与安全
Ionising radiation can damage living cells by breaking chemical bonds and altering DNA. High doses can cause radiation sickness, burns and increased risk of cancer. Alpha sources are particularly dangerous if ingested or inhaled because, although they have little penetrating power, they cause intense local ionisation inside the body.
电离辐射可通过破坏化学键和改变DNA来损伤活细胞。高剂量可导致辐射病、灼伤并增加患癌风险。α源若被摄入或吸入则尤其危险，因为尽管其穿透力很弱，但在体内会引起强烈的局部电离。
Safety precautions include minimising exposure time, maximising distance from the source, and using shielding appropriate to the radiation type. Sources must never be touched with bare hands, and should be handled using tongs or remote manipulators. Storage should be in lead-lined containers, and working areas monitored regularly.
安全措施包括尽量减少照射时间、尽量远离放射源，并采用适应辐射类型的屏蔽材料。严禁裸手接触放射源，应使用镊子或远程操作器。存储应置于铅衬容器中，工作区应定期监测。
The principles of radiation protection are time, distance and shielding. Monitoring badges such as film badges or thermoluminescent dosimeters (TLDs) are worn by radiation workers to record accumulated dose. The effective dose is measured in sieverts (Sv).
辐射防护的三原则是时间、距离和屏蔽。辐射工作人员佩戴胶片徽章或热释光剂量计等监测徽章来记录累积剂量。有效剂量单位是西弗特 (Sv)。
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