📚 Radioactivity: Nuclear Decay, Half-Life and Applications | 放射性：核衰变、半衰期与应用
Radioactivity is the spontaneous and random emission of radiation from the nucleus of an unstable atom. In AQA A-level Physics 3.3, you must link the type of radiation to nuclear structure, write balanced decay equations, use activity and half-life, and explain both hazards and uses of radioisotopes. This guide builds each of those ideas from the nuclear model to exam-style calculations and risk contexts.
放射性是不稳定原子的原子核自发、随机发射辐射的现象。在 AQA A-level 物理 3.3 中，你需要把辐射类型与核结构联系起来，写出平衡的衰变方程，使用活度和半衰期，并解释放射性同位素的危害与用途。本文从核模型出发，逐步扩展到考试计算与风险情境。
1. The Structure of the Atom and the Nuclear Model | 原子的结构与核模型
Rutherford's alpha-scattering experiment directed alpha particles at a thin gold foil. Most passed straight through, showing that the atom is mostly empty space, while a small number were deflected through large angles, showing that the positive charge and almost all the mass are concentrated in a tiny nucleus. This nuclear model underpins every nuclear decay process.
卢瑟福的 α 粒子散射实验将 α 粒子射向薄金箔。大部分粒子直线穿过，表明原子内大部分是空的；少数发生大角度偏转，表明正电荷和几乎全部质量集中在一个极小的原子核中。这个核模型是所有核衰变过程的基础。
The nucleus contains protons and neutrons, collectively called nucleons. The proton number Z determines the element, while the nucleon number A is the total number of protons and neutrons. Isotopes have the same Z but different A, and some isotopes are unstable because their proton-to-neutron ratio lies outside the stable range.
原子核由质子和中子组成，统称为核子。质子数 Z 决定元素种类，核子数 A 是质子与中子的总数。同位素具有相同的 Z 但不同的 A；某些同位素不稳定，是因为其质子与中子比例超出了稳定范围。
The radius of a nucleus is of the order 10⁻¹⁵ m, whereas the atomic radius is about 10⁻¹⁰ m. This huge difference in scale explains why alpha particles almost always pass through the electron cloud without deflection and only interact strongly when they approach a nucleus.
原子核半径约为 10⁻¹⁵ m，而原子半径约为 10⁻¹⁰ m。尺度上的巨大差异解释了为什么 α 粒子几乎总能穿过电子云而不偏转，只有接近原子核时才会发生强烈相互作用。
2. Types of Nuclear Radiation | 核辐射的类型
Nuclear radiation is classified into three main types: alpha particles, beta particles, and gamma rays. They differ in nature, charge, ionising power, penetration, and deflection in electric and magnetic fields.
核辐射主要分为三类：α 粒子、β 粒子和 γ 射线。它们在本质、电荷、电离能力、穿透能力以及在电场和磁场中的偏转情况各不相同。
| Property | Alpha α | Beta β | Gamma γ |
|---|---|---|---|
| Nature | Helium nucleus ⁴₂He | Fast electron or positron | Electromagnetic photon |
| Charge | +2e | −1e (β⁻) or +1e (β⁺) | 0 |
| Ionising ability | Very high | Medium | Low |
| Penetration | A few cm in air; stopped by paper | A few mm in aluminium | Reduced by cm of lead or metres of concrete |
| Deflection in fields | Slightly deflected towards the negative plate in an electric field; opposite direction to β⁻ in a magnetic field | Strongly deflected towards the positive plate for β⁻, opposite for β⁺; opposite direction to α in a magnetic field | Not deflected in electric or magnetic fields |
| Speed | About 5% of the speed of light | Up to about 99% of the speed of light | Speed of light c |
Alpha emission occurs mostly in very heavy nuclei, beta emission occurs when the neutron-to-proton ratio is too high or too low, and gamma emission usually follows alpha or beta decay as the daughter nucleus loses excess energy.
α 衰变主要发生在很重的原子核中；β 衰变发生在中子与质子比例过高或过低时；γ 发射通常在 α 或 β 衰变之后发生，因为子核需要释放多余能量。
3. Ionising Power, Penetration and Deflection | 电离能力、穿透能力与偏转
Ionising power is the ability of radiation to remove electrons from atoms, creating ion pairs. Alpha particles have the highest ionising power because they are relatively massive, highly charged, and interact strongly over a short range. Beta particles have medium ionising power, and gamma rays have the lowest ionising power because they are uncharged photons.
电离能力是辐射从原子中移走电子、产生离子对的能力。α 粒子电离能力最强，因为它质量较大、电荷较高，并在短距离内强烈相互作用。β 粒子电离能力中等，γ 射线电离能力最弱，因为它是无电荷的光子。
Penetrating power is roughly the opposite of ionising power. Alpha particles are stopped by a few centimetres of air or a sheet of paper. Beta particles are stopped by a few millimetres of aluminium. Gamma rays need several centimetres of lead or metres of concrete to reduce their intensity significantly.
穿透能力大致与电离能力相反。α 粒子可被几厘米空气或一张纸阻挡；β 粒子可被几毫米铝阻挡；γ 射线需要数厘米铅或数米混凝土才能显著降低强度。
For a point source, gamma intensity follows an inverse-square law with distance:
对于点源，γ 射线强度随距离遵循平方反比定律：
I = I₀ / r²
This relationship is important in radiation safety: doubling the distance from a source reduces the intensity to one quarter. In an electric field, alpha particles are deflected towards the negative plate, beta particles towards the positive plate if they are β⁻, and gamma rays are undeflected. In a magnetic field, alpha and beta particles curve in opposite directions, while gamma rays remain straight.
这一关系在辐射安全中很重要：距离源加倍，强度降为原来的四分之一。在电场中，α 粒子向负极板偏转，β⁻ 粒子向正极板偏转，γ 射线不偏转。在磁场中，α 与 β 粒子向相反方向弯曲，而 γ 射线保持直线。
4. Nuclear Decay Equations and Conservation Laws | 核衰变方程与守恒定律
In every nuclear decay equation, the total nucleon number A and the total charge Z must be conserved. This means you balance the mass numbers at the top and the atomic numbers at the bottom. Energy and momentum are also conserved, and the released energy appears as kinetic energy of the products and as photon energy.
在每个核衰变方程中，总核子数 A 与总电荷数 Z 必须守恒。也就是说，你要平衡上方的质量数与下方的原子序数。能量和动量也守恒，释放的能量表现为产物的动能以及光子能量。
In alpha decay, the nucleus emits a helium nucleus, so A decreases by 4 and Z decreases by 2. For example:
在 α 衰变中，原子核发射一个氦核，因此 A 减少 4，Z 减少 2。例如：
²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He
In beta-minus decay, a neutron changes into a proton and an electron is emitted, so A stays the same and Z increases by 1. An antineutrino is also emitted, which conserves energy and momentum. For example:
在 β⁻ 衰变中，一个中子转变为质子并发射一个电子，因此 A 不变，Z 增加 1。同时发射一个反中微子，以守恒能量与动量。例如：
¹⁴₆C → ¹⁴₇N + ⁰₋₁e + ν̄
In beta-plus decay, a proton changes into a neutron and a positron is emitted, so A stays the same and Z decreases by 1. A neutrino is also emitted. For example:
在 β⁺ 衰变中，一个质子转变为中子并发射一个正电子，因此 A 不变，Z 减少 1。同时发射一个中微子。例如：
²²₁₁Na → ²²₁₀Ne + ⁰₊₁e + ν
Gamma emission does not change A or Z. It usually occurs when a daughter nucleus is left in an excited state and drops to a lower energy state by emitting a high-energy photon.
γ 发射不改变 A 或 Z。它通常发生在子核处于激发态时，通过发射高能光子跃迁到较低能态。
5. Activity, Decay Constant and the Exponential Law | 活度、衰变常数与指数定律
ty is not the same as count rate: count rate is what a detector records, and it is always lower than the true activity because of geometry, absorption, and detector efficiency.
活度 A 是原子核衰变的速率，单位为贝可勒尔，1 Bq = 每秒 1 次衰变。活度不等于计数率：计数率是探测器记录到的值，由于几何位置、吸收和探测效率，它总是低于真实活度。
A = ΔN / Δt
The decay constant λ is the probability that a given nucleus decays per unit time. It is a constant for a particular isotope and is not affected by temperature, pressure, or chemical state. Activity is proportional to the number of undecayed nuclei N:
衰变常数 λ 是某个原子核在单位时间内衰变的概率。对特定同位素它是常数，不受温度、压强或化学状态影响。活度与未衰变核数 N 成正比：
A = λN
Because decay is random, the number of undecayed nuclei decreases exponentially with time:
由于衰变是随机的，未衰变核数随时间呈指数减少：
N = N₀e−λt
Since activity is proportional to N, activity also decays exponentially:
因为活度与 N 成正比，活度也按指数规律衰减：
A = A₀e−λt
These equations are central to AQA 3.3 calculations, especially when a question gives an initial activity, a decay constant or half-life, and asks for a later activity or the time elapsed.
这些方程是 AQA 3.3 计算的核心，尤其当题目给出初始活度、衰变常数或半衰期，并要求计算后来活度或经过时间时。
6. Half-Life and Exponential Decay | 半衰期与指数衰减
The half-life t½ is the time taken for the number of undecayed nuclei, or the activity, to halve. Half-life is constant for a given isotope and is independent of external conditions. After n half-lives, the remaining fraction is ½ⁿ, so:
半衰期 t½ 是未衰变核数或活度减半所需的时间。对给定同位素半衰期是常数，与外界条件无关。经过 n 个半衰期后，剩余比例为 ½ⁿ，因此：
N = N₀ / 2ⁿ
A = A₀ / 2ⁿ
The decay constant and half-life are linked by:
衰变常数与半衰期的关系为：
t½ = ln 2 / λ ≈ 0.693 / λ
A graph of activity against time for a radioactive isotope is an exponential decay curve. A graph of ln A against time is a straight line with gradient −λ. This is a common exam skill: you plot ln A on the y-axis and time on the x-axis, then use the gradient to find λ and hence the half-life.
放射性同位素活度随时间变化的图像是指数衰减曲线。ln A 随时间变化的图像是一条直线，斜率为 −λ。这是常见考试技能：以 ln A 为纵轴、时间为横轴作图，用斜率求 λ，再求半衰期。
Half-life values vary enormously. Some isotopes have half-lives of fractions of a second, while others have half-lives of billions of years. This determines whether an isotope is suitable for a medical tracer, a dating technique, or a long-term industrial source.
半衰期的数值差异极大。有些同位素半衰期只有几分之一秒，有些则长达数十亿年。这决定了某同位素是否适合用作医疗示踪剂、测年技术或长期工业源。
7. Decay Chains, Background Radiation and Detection | 衰变链、本底辐射与探测
A radioactive decay chain is a series of decays in which each unstable nucleus decays into another unstable nucleus, until a stable isotope is reached. For example, uranium-238 decays through a long chain that eventually produces stable lead-206. Each step has its own half-life and radiation type.
放射性衰变链是一系列衰变，其中每个不稳定核衰变成另一个不稳定核，直到到达稳定同位素。例如，铀-238 经过长链衰变，最终生成稳定的铅-206。每一步都有自己的半衰期和辐射类型。
Background radiation is ionising radiation present in the environment from natural and artificial sources. Natural sources include radon gas from rocks, cosmic rays, and radioactive isotopes in food and drink. Artificial sources include medical procedures, nuclear weapons tests, and nuclear power. When measuring activity, you must subtract the background count rate.
本底辐射是环境中来自天然和人工源的电离辐射。天然源包括岩石释放的氡气、宇宙射线以及食物和饮水中的放射性同位素。人工源包括医疗程序、核武器试验和核电。测量活度时，必须扣除本底计数率。
A Geiger-Muller tube detects ionising radiation by producing a pulse of current when radiation ionises gas inside the tube. The count rate is the number of pulses per second. To improve reliability, you take repeated readings and calculate a mean. To find the corrected count rate, subtract the background count rate from the measured count rate.
盖革-米勒管通过辐射电离管内气体产生电流脉冲来探测电离辐射。计数率是每秒脉冲数。为提高可靠性，应重复读数并计算平均值。要得到校正计数率，需从测得计数率中减去本底计数率。
8. Hazards of Ionising Radiation | 电离辐射的危害
Ionising radiation can damage living cells by breaking chemical bonds and ionising molecules, especially DNA. This can cause mutations, uncontrolled cell division, and cancer. High doses can cause acute radiation sickness, burns, and organ failure. The risk depends on the type of radiation, the activity of the source, the distance, the shielding, and the duration of exposure.
电离辐射可通过破坏化学键和电离分子来损伤活细胞，尤其是 DNA。这可能导致突变、细胞分裂失控和癌症。高剂量可造成急性辐射病、灼伤和器官衰竭。风险取决于辐射类型、源活度、距离、屏蔽以及暴露时间。
Alpha particles are the most dangerous if inhaled or ingested,
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