📚 Radioactive Decay Essentials for IB & AQA Physics | IB AQA 物理：放射性衰变 考点精讲
Radioactive decay is a spontaneous process by which an unstable atomic nucleus loses energy by emitting radiation. Understanding the types of decay, decay equations, half‑life and activity is essential for both IB and AQA physics exams. This article concisely covers all key points, from the nature of α, β and γ radiation to exponential decay laws and real‑world applications.
放射性衰变是不稳定原子核通过释放辐射而自发损失能量的过程。理解衰变类型、衰变方程、半衰期和活度对 IB 和 AQA 物理考试至关重要。本文精炼涵盖所有考点，从 α、β、γ 射线的性质到指数衰变规律与实际应用。
1. What is Radioactivity? | 什么是放射性？
Radioactivity is the spontaneous disintegration of an unstable nucleus accompanied by the emission of particles or electromagnetic radiation. The process is unaffected by temperature, pressure or chemical environment because it originates in the nucleus.
放射性是不稳定原子核自发地瓦解并伴随发射粒子或电磁辐射的过程。由于该过程源自原子核，它不受温度、压力或化学环境的影响。
The decay of a single nucleus is a random event; we cannot predict exactly when a particular nucleus will decay. However, for a large number of nuclei, the overall decay rate follows a predictable statistical pattern.
单个原子核的衰变是随机事件；我们无法准确预测某个原子核何时衰变。然而，对于大量原子核，整体衰变率遵循可预测的统计规律。
Unstable nuclei have an excess of protons or neutrons (or too much energy) and decay towards a stabler configuration. The original nucleus is called the parent, and the resulting nucleus is the daughter.
不稳定的原子核含有过多的质子或中子（或能量过高），通过衰变趋向更稳定的结构。原来的原子核称为母核，生成的原子核称为子核。
2. Types of Radioactive Decay | 放射性衰变类型
There are four main types of radiation emitted in nuclear decays: alpha (α), beta‑minus (β⁻), beta‑plus (β⁺) and gamma (γ). Each differs in charge, mass, penetrating ability and ionising power.
核衰变中主要放出四种辐射：α 射线、β⁻ 射线、β⁺ 射线和 γ 射线。它们的电荷、质量、穿透能力和电离本领各不相同。
| Property | Alpha (α) | Beta‑minus (β⁻) | Beta‑plus (β⁺) | Gamma (γ) |
|---|---|---|---|---|
| Nature | Helium‑4 nucleus, ₂⁴He²⁺ | Electron, ₋₁⁰e | Positron, ₊₁⁰e | High‑energy photon |
| Charge | +2e | –1e | +1e | 0 |
| Mass (u) | 4 | 1/1836 | 1/1836 | 0 |
| Penetration | Stopped by paper or few cm of air | Stopped by a few mm of aluminium | Stopped by a few mm of aluminium (annihilates quickly) | Reduced by many cm of lead or metres of concrete; never fully stopped |
| Ionising ability | High | Medium | Medium | Low |
下表总结了各种辐射的性质：α 粒子穿透力最弱但电离能力最强；γ 射线穿透力最强但电离能力最弱。
3. Alpha Decay | α 衰变
In alpha decay, a heavy unstable nucleus emits an alpha particle (helium‑4 nucleus). The daughter nucleus has a mass number decreased by 4 and an atomic number decreased by 2.
在 α 衰变中，重不稳定核放出一个 α 粒子（氦‑4 核）。子核的质量数减少 4，原子序数减少 2。
A typical equation is the decay of uranium‑238:
一个典型方程是铀‑238 的衰变：
₂₃₈⁹²U → ₂₃₄⁹⁰Th + ₂⁴He
Mass number: 238 = 234 + 4 (conserved). Proton number: 92 = 90 + 2 (conserved).
质量数：238 = 234 + 4（守恒）。质子数：92 = 90 + 2（守恒）。
Alpha particles travel only a few centimetres in air and are easily absorbed by a sheet of paper. They are highly ionising, making them dangerous if ingested or inhaled.
α 粒子在空气中仅行进数厘米，一张纸即可将其吸收。它们电离能力很强，如果被摄入或吸入则非常危险。
4. Beta-Minus (β⁻) Decay | β⁻ 衰变
Beta‑minus decay occurs in neutron‑rich nuclei. A neutron turns into a proton, an electron (β⁻) and an antineutrino. The atomic number increases by 1 while the mass number remains unchanged.
β⁻ 衰变发生于富中子原子核。一个中子转变为质子、一个电子（β⁻）和一个反中微子。原子序数增加 1，质量数保持不变。
Example: carbon‑14 decay:
例子：碳‑14 衰变：
₆¹⁴C → ₇¹⁴N + ₋₁⁰e + ν̅ₑ
The antineutrino (ν̅ₑ) carries away energy and momentum, ensuring conservation laws are satisfied. Without it, the beta particle would have a single energy, but in reality it shows a continuous spectrum.
反中微子（ν̅ₑ）带走能量和动量，确保守恒定律满足。没有它，β 粒子会有单一能量，但实际呈现连续谱。
5. Beta-Plus (β⁺) Decay | β⁺ 衰变
In proton‑rich nuclei, beta‑plus decay occurs: a proton transforms into a neutron, a positron (β⁺) and a neutrino. The atomic number decreases by 1, while the mass number stays the same.
在富质子原子核中会发生 β⁺ 衰变：一个质子转变为中子、一个正电子（β⁺）和一个中微子。原子序数减少 1，质量数不变。
Example: sodium‑22 decay:
例子：钠‑22 衰变：
₁₁²²Na → ₁₀²²Ne + ₊₁⁰e + νₑ
The positron is the antiparticle of the electron. It quickly annihilates with an electron, producing two gamma photons of 511 keV each, used in PET scans.
正电子是电子的反粒子，迅速与电子湮灭，产生两个各 511 keV 的 γ 光子，这被用于 PET 扫描。
6. Gamma Decay | γ 衰变
Gamma decay follows α or β decay when the daughter nucleus is left in an excited state. The nucleus emits a high‑energy photon (gamma ray) as it de‑excites down to its ground state. There is no change in mass number or atomic number.
γ 衰变通常跟随在 α 或 β 衰变之后，此时子核处于激发态。原子核退激到基态时放出高能光子（γ 射线）。质量数和原子序数均不改变。
Example: the beta decay of cobalt‑60 produces an excited nickel‑60 nucleus that then emits two gamma photons:
例子：钴‑60 的 β 衰变产生激发的镍‑60 核，随后释放两个 γ 光子：
₆₀Co → ₆₀Ni* + β⁻ + ν̅ₑ → ₆₀Ni + γ + γ
Gamma rays are the most penetrating electromagnetic radiation and require thick lead or concrete for shielding. They are weakly ionising.
γ 射线穿透力最强的电磁辐射，需用厚铅板或混凝土屏蔽。其电离能力很弱。
7. Decay Equations and Conservation Laws | 衰变方程与守恒定律
Every nuclear decay equation must conserve both mass number (total number of nucleons) and proton number (atomic number, charge). Additionally, energy and momentum are conserved, which is why neutrinos or antineutrinos were postulated.
每个核衰变方程都必须同时满足质量数（核子总数）和质子数（原子序数，电荷）守恒。此外，能量与动量也守恒，正因如此人们才提出了中微子或反中微子。
When writing equations, place the mass number as a left superscript and the proton number as a left subscript. Ensure the sums match on both sides.
书写方程时将质量数作为左上标，质子数作为左下标，并确保两边相加相等。
For gamma emission, the nucleus is shown in an excited state with an asterisk: X* → X + γ.
对于 γ 发射，母核带星号表示激发态：X* → X + γ。
8. Half-Life Concept | 半衰期概念
The half‑life, T½, is the time taken for half the unstable nuclei in a sample to decay, or equivalently for the activity to reduce to half its initial value. It is a constant for a given isotope and cannot be altered by physical or chemical means.
半衰期 T½ 是指样品中一半不稳定原子核发生衰变所需的时间，或等价地，活度降至初始值一半所需的时间。对给定同位素它是一个常数，无法用物理或化学手段改变。
Half‑life values range from fractions of a second to billions of years. For example, uranium‑238 has a half‑life of about 4.5 × 10⁹ years, while polonium‑214 has a half‑life of 164 µs.
半衰期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 的半衰期为 164 微秒。
Since decay is random, half‑life is a statistical average; the larger the number of nuclei, the closer the observed decay matches the theoretical curve.
由于衰变随机，半衰期是统计平均值；原子核数量越大，实际观察越接近理论曲线。
9. Exponential Decay Law | 指数衰变律
The number of undecayed nuclei N remaining after time t follows the exponential law:
经过时间 t 后尚未衰变的原子核数 N 遵循指数规律：
N = N₀ e–λt
where N₀ is the initial number, λ is the decay constant (probability of decay per unit time). The SI unit of λ is s⁻¹.
其中 N₀ 是初始数目，λ 是衰变常量（单位时间衰变概率），其 SI 单位是 s⁻¹。
The half‑life and decay constant are related by:
半衰期与衰变常量的关系为：
T½ = ln2 / λ ≈ 0.693 / λ
Activity A, measured in becquerel, is proportional to N: A = λN. It therefore also decays exponentially: A = A₀ e–λt.
活度 A（以贝克勒尔为单位）与 N 成正比：A = λN，因此也呈指数衰减：A = A₀ e–λt。
10. Activity and the Becquerel | 活度与贝克勒尔
Activity is the number of decays occurring per second in a radioactive sample. One becquerel (Bq) is defined as one decay per second.
活度是放射性样品每秒发生的衰变数。一贝克勒尔（Bq）定义为每秒一次衰变。
Although the becquerel is small, practical samples often have activities of MBq or GBq. Detectors measure the count rate, which after background subtraction is proportional to activity.
尽管 Bq 很小，实际样品常达到 MBq 或 GBq 级别。探测器测量的是计数率，减去背景后与活度成正比。
When plotting the exponential decay, both N and A halve every half‑life. After n half‑lives, the fraction remaining is (½)n.
绘制指数衰变曲线时，N 和 A 每过一个半衰期减半。经过 n 个半衰期后，剩余比例为 (½)n。
11. Background Radiation and Corrections | 背景辐射与修正
Background radiation arises from cosmic rays, terrestrial rocks, building materials, and even food. It gives a constant, random count rate that must be subtracted from measured rates when examining a source.
背景辐射来源于宇宙射线、地球岩石、建筑材料甚至食物。它产生一个基本恒定的随机计数率，在测量放射源时必须从读数中扣除。
To measure the half‑life of a source in the lab, record the corrected count rate Ccorr = Cmeasured – Cbackground. Plot a graph of Ccorr against time and read T½ directly.
在实验室测量放射源的半衰期时，记录修正计数率 Ccorr = Cmeasured – Cbackground。绘制 Ccorr 对时间的图像，直接读出 T½。
Safety: always handle sources with tongs, keep them pointed away, and store in lead‑lined containers.
安全要求：始终用长柄钳操作放射源，方向远离人体，存放在铅衬容器中。
12. Applications and Safety | 应用与安全
Radioactive isotopes have many uses. Carbon‑14 dating relies on the known half‑life (5730 years) to estimate the age of organic remains. The isotope ratio C‑14 / C‑12 in dead tissue decays predictably.
放射性同位素用途广泛。碳‑14 测年依靠已知半衰期（5730 年）来估计有机物遗存的年代。死亡组织中 C‑14 / C‑12 的比例按规律衰减。
In medicine, technetium‑99m (γ emitter, T½=6 h) is used as a tracer for imaging. Iodine‑131 (β⁻ and γ) treats thyroid disorders. PET scans use β⁺ emitters like fluorine‑18.
医学上，锝‑99m（γ 放射源，T½=6 小时）用作成像示踪剂。碘‑131（β⁻ 和 γ）治疗甲状腺疾病。PET 扫描使用 β⁺ 放射源如氟‑18。
Industrial thickness gauges use the attenuation of β particles by the material being measured. Sterilisation of medical equipment employs intense gamma sources.
工业测厚仪利用材料对 β 粒子的衰减来工作。医疗器械灭菌使用强 γ 放射源。
Precautions include minimising exposure time, maximising distance (inverse‑square law), using shielding appropriate to the radiation type, and never allowing ingestion or inhalation.
防护措施包括：缩短接触时间、增大距离（平方反比定律）、选择与辐射类型匹配的屏蔽，并严禁吞入或吸入放射性物质。
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