📚 Nuclear Radiation and Radioactive Decay | 核辐射与放射性衰变
In Edexcel A Level Physics, Topic 11 (Nuclear Radiation) explores the structure of the nucleus, the nature of radioactive emissions, and the mathematics of exponential decay. Understanding these ideas is essential for solving problems on half-life, activity and decay equations, and for evaluating the uses and the risks of ionising radiation in medicine, industry and everyday life. This revision guide works through the nuclear model, isotope notation, the three main types of emission, decay equations and conservation laws, the decay constant, exponential and graphical methods, background radiation, practical applications and radiation safety.
在 Edexcel A Level 物理中，第 11 章（核辐射）探讨原子核的结构、放射性发射的本质以及指数衰变的数学。理解这些概念，对求解半衰期、活度、衰变方程以及评估电离辐射在医学、工业和日常生活中的用途和风险至关重要。本复习指南将依次讲解核式模型、同位素符号、三种主要放射类型、衰变方程与守恒定律、衰变常数、指数与图像方法、本底辐射、实际应用以及辐射安全。
1. The Nuclear Model of the Atom | 原子的核式模型
Rutherford's alpha-scattering experiment fired alpha particles at a very thin gold foil. Most particles passed straight through, but a small number were deflected through large angles, and about 1 in 8000 bounced back towards the source.
卢瑟福的 α 散射实验将 α 粒子射向极薄的金箔。大多数粒子径直穿过，但少数粒子发生大角度偏转，大约每 8000 个中有 1 个被反弹回来。
Each feature of the scattering pattern carries a clear physical message. A straight-through path means the alpha particle met almost nothing; a large deflection means it passed close to a concentrated region of positive charge; a backward bounce means it struck something small, heavy and positively charged almost head-on.
散射图样的每一个特征都传递着明确的物理信息。径直穿过说明 α 粒子几乎没遇到任何东西；大角度偏转说明它从集中的正电荷区域附近经过；被反弹回来则说明它几乎正对着撞上了一个很小、很重且带正电的东西。
These results showed that the atom is mostly empty space, with a tiny, dense, positively charged nucleus at its centre and electrons orbiting around it. The nuclear model replaced the earlier plum pudding model, in which positive charge and electrons were imagined to be spread evenly throughout the whole atom.
这些结果表明原子大部分是空的，中心有一个极小、致密、带正电的原子核，电子绕核运动。核式模型取代了早期的葡萄干布丁模型——后者认为正电荷与电子均匀分布在整个原子之中。
The scale comparison is worth memorising: nuclear diameters are of the order of 10⁻¹⁵ m to 10⁻¹⁴ m, while atomic diameters are of the order of 10⁻¹⁰ m. Almost all of the mass of the atom is therefore concentrated in the nucleus, while the electrons occupy the rest of the volume.
值得记住的尺度对比是：原子核直径约为 10⁻¹⁵ m 至 10⁻¹⁴ m，而原子直径约为 10⁻¹⁰ m。因此原子的几乎全部质量都集中在原子核内，电子则占据其余的体积。
2. Isotopes and Nuclear Notation | 同位素与核素符号
Isotopes are atoms of the same element with the same number of protons (proton number Z) but different numbers of neutrons. They therefore have the same chemical properties but different physical properties such as mass and stability.
同位素是同一元素的原子，质子数（质子序数 Z）相同但中子数不同。因此它们化学性质相同，但质量、稳定性等物理性质不同。
The nucleon number counts protons plus neutrons, so the neutron number is found from N = A − Z.
核素符号将核子（质量）数 A 写在化学符号左上角作为上标，将质子（原子）序数 Z 写在左下角作为下标。核子数等于质子数与中子数之和，因此中子数可由 N = A − Z 求出。
itium). All carbon isotopes have Z = 6, but they contain 6, 7 and 8 neutrons respectively.
常见例子包括碳的 ¹²₆C 与 ¹⁴₆C、铀的 ²³⁵₉₂U 与 ²³⁸₉₂U，以及氢的三种同位素 ¹₁H、²₁H（氘）和 ³₁H（氚）。所有碳同位素的 Z 都是 6，但它们分别含有 6、7 和 8 个中子。
Because chemical behaviour depends on the electron arrangement, which depends on Z, isotopes of an element react in the same way. Their differing nuclear masses and stabilities mean that some isotopes are stable, while others are radioactive and decay at a characteristic rate.
由于化学性质取决于电子排布，而电子排布取决于 Z，同一元素的各同位素化学反应方式相同。它们核质量和稳定性的差异意味着有些同位素是稳定的，而另一些具有放射性，并按各自特有的速率衰变。
3. The Nature of Alpha, Beta and Gamma Radiation | α、β、γ 辐射的本质
An alpha particle is a helium nucleus: two protons and two neutrons bound together, written ⁴₂He. It carries a charge of +2e and is emitted by heavy, unstable nuclei in which the strong nuclear force can no longer hold the nucleus together comfortably.
α 粒子就是氦核：两个质子和两个中子结合在一起，记作 ⁴₂He。它带 +2e 的电荷，由那些强核力已难以稳定束缚的重核发射出来。
A beta-minus particle is a fast electron created inside the nucleus when a neutron transforms into a proton. The process also emits an antineutrino, which carries away some of the energy and momentum. This happens in neutron-rich nuclei.
β⁻ 粒子是在核内由一个中子转变为质子时产生的高速电子。该过程同时发射一个反中微子，带走部分能量和动量。这一过程发生在中子过多的核中。
A beta-plus particle (positron) is emitted when a proton converts into a neutron, releasing a positron and a neutrino; this occurs in proton-rich nuclei. Electron capture is a competing process in which an inner electron is absorbed by a proton, again converting it into a neutron and emitting a neutrino.
β⁺ 粒子（正电子）是在质子转变为中子时发射的，同时放出正电子和中微子；这发生在质子过多的核中。电子俘获是与之竞争的过程：内层电子被质子吸收，同样使质子转变为中子并放出中微子。
Gamma radiation is a high-energy photon emitted when a nucleus is left in an excited state after alpha or beta decay. Gamma emission changes neither the nucleon number nor the proton number; it simply allows the nucleus to lose surplus energy. A metastable state is labelled with the superscript m, as in ⁹⁹ᵐ₄₃Tc.
γ 辐射是原子核在 α 或 β 衰变后处于激发态时放出的高能光子。γ 发射既不改变核子数也不改变质子数，只是让原子核释放多余能量。亚稳态用上标 m 表示，例如 ⁹⁹ᵐ₄₃Tc。
4. Penetration, Ionising Power and Deflection | 穿透力、电离能力与偏转
The three emissions differ markedly in how far they travel, how strongly they ionise matter, and how they behave in electric and magnetic fields. A summary table is the quickest way to keep these properties straight.
三种放射在传播距离、电离物质的能力以及在电场和磁场中的行为方面差别很大。用一张汇总表来记忆这些性质最为快捷。
| Emission | 放射 | Nature | 本质 | Range / Stopped by | 射程 / 阻挡 | Ionising power | 电离能力 | Deflection | 偏转 |
|---|---|---|---|---|
| Alpha α | ⁴₂He nucleus, charge +2e | A few cm in air; paper or skin | Strongest | Small deflection towards − plate |
| Beta-minus β⁻ | Fast electron, charge −e | A few m in air; few mm of aluminium | Moderate | Large deflection towards + plate |
| Gamma γ | High-energy photon, no charge | Reduced by thick lead or concrete | Weakest | No deflection |
Alpha particles ionise strongly because of their large charge and relatively slow speed, so they lose energy quickly and have a short range. Gamma photons interact only occasionally with atoms, so they ionise weakly but penetrate deeply. Ionising power and penetrating power are therefore in inverse order.
α 粒子因电荷大、速度相对较慢而电离能力很强，因而能量损失快、射程短。γ 光子与原子的相互作用只是偶尔发生，因此电离能力弱但穿透力强。可见电离能力与穿透能力恰好顺序相反。
In an electric field the deflections follow the sign of the charge: alpha curves slightly towards the negative plate because of its large mass, beta curves sharply towards the positive plate because it is light, and gamma is undeflected because it has no charge. The same logic applies in a magnetic field, where the force is always perpendicular to the velocity.
在电场中，偏转方向由电荷正负决定：α 因质量大而略微向负极板弯曲，β 因质量小而明显向正极板弯曲，γ 不带电所以不偏转。在磁场中同理，洛伦兹力始终垂直于速度方向。
A point source spreads its radiation over a sphere, so intensity follows an inverse-square law with distance from the source. Doubling the distance from a point source reduces the intensity to one quarter, which is why distance is such an effective protective measure
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