📚 Mastering Nuclear Equations and Radioactive Decay | 核方程式的平衡与放射性衰变
Understanding radioactive decay and being able to balance nuclear equations is a core skill in IGCSE Edexcel Science. In this article, we will explore the structure of the nucleus, the main types of ionising radiation, and how to construct and balance equations for alpha, beta and gamma emissions. You will learn the conservation rules that govern all nuclear processes and practise with worked examples designed to reinforce your exam technique.
在IGCSE Edexcel科学课程中，理解放射性衰变并掌握核方程式的平衡是一项核心技能。本文将带你探索原子核的结构、三种主要的电离辐射，以及如何构建和配平α、β和γ衰变的方程式。你将学习支配所有核过程的守恒规则，并通过考试风格的示例加以练习，从而巩固解题技巧。
1. Atomic Structure and Isotopes | 原子结构与同位素
Atoms consist of a central nucleus containing protons and neutrons, surrounded by electrons in energy levels. The nucleus carries almost all the mass of an atom. Protons have a positive charge, neutrons are neutral, and electrons have a negative charge of equal magnitude. The number of protons defines the element and is called the atomic (proton) number, Z. The total number of protons and neutrons is the mass (nucleon) number, A.
原子由一个包含质子和中子的中央原子核，以及分层排布的电子组成。原子核几乎承载了原子的所有质量。质子带正电，中子不带电，电子带负电且电量与质子相等。质子数决定了元素的种类，称为原子序数（质子数）Z；质子数和中子数的总和称为质量数（核子数）A。
Isotopes are atoms of the same element that have the same proton number but different numbers of neutrons. For example, carbon-12 (¹²₆C) and carbon-14 (¹⁴₆C) are isotopes. Nuclide notation shows the chemical symbol with the mass number as a superscript and the atomic number as a subscript: ᴬZX. This notation is essential when writing nuclear equations.
同位素是指质子数相同而中子数不同的同种原子。例如碳 ‑12（¹²₆C）和碳 ‑14（¹⁴₆C）就是同位素。核素符号将化学符号与质量数（上标）和原子序数（下标）组合在一起，记作 ᴬZX。书写核方程式时，这种表示方法必不可少。
2. Types of Radioactive Emission | 放射性辐射的种类
Unstable nuclei emit ionising radiation to become more stable. There are three primary types: alpha (α) particles, beta (β⁻) particles and gamma (γ) rays. An alpha particle consists of two protons and two neutrons – it is identical to a helium nucleus, ⁴₂He. A beta-minus particle is a fast-moving electron emitted from a nucleus when a neutron converts into a proton, written as ⁰₋₁e. Gamma radiation is a high-frequency electromagnetic wave with no mass or charge, often emitted after alpha or beta decay to release surplus energy.
不稳定的原子核通过发射电离辐射来变得更稳定。主要分为三种类型：α粒子、β⁻粒子和γ射线。α粒子由两个质子和两个中子组成，等同于一个氦核 ⁴₂He。β⁻粒子是原子核内一个中子转变为质子时释放的高速电子，记作 ⁰₋₁e。γ辐射是高频率的电磁波，无质量、不带电，经常在α或β衰变后释放剩余能量。
3. Nature and Properties of Alpha Particles | α粒子的特性
Alpha particles have a large mass and a charge of +2e. They are strongly ionising because their double positive charge can easily pull electrons away from atoms they pass. However, they only travel a few centimetres in air and can be stopped by a sheet of paper or the outer layer of human skin. In electric and magnetic fields, alpha particles are deflected in directions that indicate their positive charge, and their large mass results in a smaller deflection compared with beta particles.
α粒子质量较大，带+2e的电荷。由于双正电荷容易从途经的原子中剥离电子，因此α粒子的电离能力很强。但它们在空气中仅能前进数厘米，一张纸或人体皮肤表层即可将其阻挡。在电场和磁场中，α粒子的偏转方向表明其带正电，且因其质量大，偏转幅度比β粒子小。
4. Nature and Properties of Beta Particles | β粒子的特性
Beta-minus particles are high-speed electrons carrying a charge of –1e. Their mass is extremely small – about 1/2000 of a proton. Beta radiation is moderately ionising, much less than alpha but more than gamma. It can travel several metres in air and requires a few millimetres of aluminium to stop it. Electric and magnetic fields deflect beta particles in the opposite direction to alpha particles, and the light mass leads to a much greater deflection, confirming their negative charge.
β⁻粒子是高速电子，带–1e电荷，质量极小——约为质子的1/2000。β辐射的电离能力中等，远弱于α，但强于γ。它在空气中可传播数米，需要用几毫米厚的铝板才能阻挡。电场和磁场使β粒子向与α粒子相反的方向偏转，因其质量小，偏转幅度更大，这证实了其负电性质。
5. Nature and Properties of Gamma Rays | γ射线的特性
Gamma rays are electromagnetic waves of very short wavelength and no charge. They are the least ionising radiation because they interact with matter only occasionally, transferring energy in discrete bursts. Conversely, gamma rays are highly penetrating; thick lead or several metres of concrete are required to significantly reduce their intensity. They are not deflected by electric or magnetic fields, which demonstrates their neutral character.
γ射线是波长极短且不带电的电磁波。它们的电离能力最弱，因为γ射线只偶尔与物质相互作用，以离散的能量爆发形式传递能量。反之，γ射线穿透力极强；需要厚铅板或数米厚的混凝土才能显著降低其强度。它们在电场和磁场中不发生偏转，证明自身呈电中性。
6. Comparison Table of Radiations | 三种辐射对比表
| Property | 性质 | Alpha (α) | Beta (β⁻) | Gamma (γ) |
|---|---|---|---|
| Nature | 本质 | Helium nucleus ⁴₂He | Electron ⁰₋₁e | Electromagnetic wave |
| Charge | 电荷 | +2e | –1e | 0 |
| Relative ionising power | 相对电离能力 | High | Moderate | Low |
| Penetrability | 穿透力 | Stopped by paper | Stopped by thin aluminium | Reduced by thick lead |
| Deflection in fields | 场中偏转 | Small, towards negative plate | Large, towards positive plate | No deflection |
7. Conservation Laws for Nuclear Equations | 核方程式的守恒定律
All nuclear equations must obey two simple conservation rules: the total mass number (A) on the left must equal the total mass number on the right, and the total atomic number (Z) must also balance. These rules stem from the conservation of nucleon number and charge. Unlike chemical equations, the identity of the elements can change because the nucleus transmutes into a different element.
所有核方程式必须遵循两条简单的守恒规律：方程左边的总质量数A必须等于右边的总质量数，原子序数Z的总和也必须配平。这些规律源自核子数守恒和电荷守恒。与化学方程式不同的是，元素的种类可以发生改变，因为原子核会嬗变成不同的元素。
nd Z = 0, so it does not affect the mass or atomic numbers but only removes energy from the nucleus.
配平时，可先用代数表示未知核素，或按步骤进行：先确保质量数配平，再调整原子序数。如果原子序数不符，就需要相应调整释放的辐射或子核。请记住，γ辐射的A = 0、Z = 0，因此不影响质量数和原子序数，仅带走原子核的能量。
8. Balancing Alpha Decay Equations | α衰变方程式的配平
In alpha decay, an unstable nucleus emits an alpha particle, so the daughter nucleus has its mass number reduced by 4 and its atomic number reduced by 2. This is because the helium nucleus ⁴₂He carries away two protons and two neutrons. For example, the decay of uranium-238 can be written as:
在α衰变中，不稳定的原子核发射一个α粒子，因此子核的质量数减少4，原子序数减少2。这是因为氦核 ⁴₂He 带走了两个质子和两个中子。例如铀‑238的衰变可写作：
²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He
e daughter nuclide by its proton number using the periodic table. Another common example is the decay of polonium-210 to lead-206:
检查是否配平：质量数 238 = 234 + 4；原子序数 92 = 90 + 2。元素由铀（Z = 92）变为钍（Z = 90）。务必根据周期表用质子数确定子核元素。另一个常见例子是钋‑210衰变为铅‑206：
²¹⁰₈₄Po → ²⁰⁶₈₂Pb + ⁴₂He
9. Balancing Beta-Minus Decay Equations | β⁻衰变方程式的配平
Beta-minus decay occurs when a neutron inside the nucleus turns into a proton, an electron (beta particle) and an antineutrino. The electron and antineutrino are immediately ejected. As a result, the mass number stays the same, while the atomic number increases by 1. The generic equation for a beta emitter X is:
β⁻衰变发生在核内一个中子转变为质子、电子（β粒子）和反中微子之时。电子和反中微子随即被射出。因此，质量数保持不变，原子序数却增加1。β放射源X的通式如下：
ᴬZX → ᴬZ₊₁Y + ⁰₋₁e + ν̅ₑ
For instance, carbon-14 undergoes beta decay to form nitrogen-14. The balanced equation is:
例如，碳‑14发生β衰变生成氮‑14。配平后的方程式为：
¹⁴₆C → ¹⁴₇N + ⁰₋₁e
The mass numbers are 14 = 14 + 0, and atomic numbers are 6 = 7 + (– rticle is written as an electron, it originates from the nucleus, not the electron shells.
质量数为 14 = 14 + 0，原子序数为 6 = 7 + (–1)，符合守恒。反中微子不带电荷且质量可忽略，在IGCSE阶段通常略去。尽管β粒子写作电子形式，但它源于原子核，而非核外电子层。
10. Gamma Emission and Isomeric Transitions | γ发射与同核异能跃迁
Gamma decay does not alter the mass number or atomic number; it simply releases excess energy from an excited nucleus. This often happens after a preceding alpha or beta decay has left the daughter nucleus in an excited state. The excited form of the same nuclide is called a nuclear isomer. For example, technetium-99m (⁹⁹ᵐTc) is a widely used gamma emitter in medical imaging.
γ衰变不改变质量数和原子序数，仅从激发态原子核释放多余能量。这种情况常发生在α或β衰变将子核留在激发态之后。同一种核素的激发形态称为核同质异能素。例如，锝‑99m（⁹⁹ᵐTc）是医学影像中广泛使用的γ放射源。
To indicate gamma emission in equations, simply add the Greek letter gamma or write '+ γ' after the daughter nuclide. For example, the decay of metastable barium-137m can be shown as:
在方程式中表示γ发射时，只需在子核后加上希腊字母γ或写“+ γ”。例如，亚稳态钡‑137m的衰变可表示为：
¹³⁷₅₆Ba* → ¹³⁷₅₆Ba + γ
The mass and atomic numbers remain unchanged. This type of emission does not transmute the element, but it plays an important role in reducing the energy of the nucleus to a stable ground state.
质量和原子序数均保持不变。此类发射不会使元素嬗变，但在降低原子核能量至稳定基态方面发挥着重要作用。
11. Worked Examples and Common Pitfalls | 实例分析与常见错误
214, and on the right 214 + A = 214, so A = 0. The atomic number: 83 = 84 + Z, giving Z = –1. The particle with mass number 0 and atomic number – a particle if they only look at the mass number without checking the atomic number change.
示例1：写出²¹⁴₈₃Bi → ²¹⁴₈₄Po + X 中缺失的粒子。左侧质量数为214，右侧为214 + A = 214，故A = 0。原子序数：83 = 84 + Z，得Z = –1。质量数为0且原子序数为–1的粒子是β粒子 ⁰₋₁e。因此X为一个β粒子。很多学生仅看质量数未变就错误推断为α粒子，忽略了原子序数的变化。
rent is ²²⁴₈₈Ra. The equation is ²²⁴₈₈Ra → ²²⁰₈₆Rn + ⁴₂He. Always check that the equation balances both ways.
示例2：某未知原子核发射一个α粒子后生成氡‑220（²²⁰₈₆Rn）。试确定母核。由于α粒子使子核增加质量数4和原子序数2，逆向求解：母核质量数 = 220 + 4 = 224，原子序数 = 86 + 2 = 88。镭(Ra)的Z = 88，故母核为²²⁴₈₈Ra。方程式为 ²²⁴₈₈Ra → ²²⁰₈₆Rn + ⁴₂He。务必双向检验配平。
for a beta particle, it is easily misread; always treat ⁰₋₁e as a single particle with Z = –1.
要避免的常见错误包括：忘记原子序数必须守恒、混淆α和β的符号、以及核素符号书写不规范。β粒子的原子序数被写作负下标，容易被误读；应始终将 ⁰₋₁e 当作Z = –1的单一粒子处理。
12. Applications and Summary | 应用与总结
Nuclear equations are not only an exam essential but also the language used to describe natural radioactivity, nuclear medicine, carbon dating and power generation. Understanding how to balance them gives you insight into how elements transform in nuclear reactors, how smoke detectors utilise alpha particles, and how sterilisation of medical equipment uses gamma rays.
核方程式不仅是考试重点，也是描述自然放射性、核医学、碳定年和发电所用的语言。理解如何配平这些方程式，能让你深入了解元素如何在核反应堆中转变、烟雾探测器如何利用α粒子，以及医疗器械消毒如何运用伽马射线。
To excel in IGCSE Edexcel Science, practise writing the full nuclide notation for isotopes, memorise the properties of alpha, beta and gamma, and apply the two conservation rules systematically. With a clear, step-by-step approach and attention to detail, balancing nuclear equations will become second nature.
想要在IGCSE Edexcel科学考试中脱颖而出，就要练习完整书写同位素的核素符号，熟记α、β、γ的性质，并系统运用两条守恒规则。只要方法清晰、逐步推进并注重细节，平衡核方程式将成为你的第二天性。
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