📚 Radioactive Decay | 放射性衰变
Radioactive decay is a fundamental nuclear process in which an unstable atomic nucleus loses energy by emitting radiation. This spontaneous transformation changes the composition of the nucleus, often converting one element into another. Understanding decay modes, half‑life, activity, and the exponential law is essential for IB and CCEA Physics examinations, where students must model decay mathematically, interpret decay curves, and apply concepts to real‑world contexts from carbon dating to nuclear safety.
放射性衰变是一个基本的核过程，不稳定的原子核通过发射辐射来释放能量。这种自发转变会改变原子核的组成，常常将一种元素转变为另一种元素。理解衰变模式、半衰期、放射性活度以及指数衰变规律对于 IB 和 CCEA 物理考试至关重要，考生需要能够建立衰变的数学模型、解读衰变曲线，并将概念应用于从碳定年到核安全的实际情境。
1. The Nature of Radioactive Decay | 放射性衰变的本质
Radioactive decay occurs because some nuclear configurations are energetically unfavourable. The nucleus contains protons and neutrons held together by the residual strong force. When the neutron‑to‑proton ratio lies outside the band of stability, the nucleus becomes radioactive. Decay is a quantum‑mechanical tunnelling process combined with weak interaction effects, and it cannot be triggered, slowed down, or predicted for a single nucleus — only statistical behaviour is deterministic.
放射性衰变的发生是由于某些原子核的组态在能量上不占优势。原子核由质子和中子组成，依靠残余强相互作用力结合在一起。当中子‑质子比超出稳定带的范围时，原子核便具有放射性。衰变是一个量子力学隧穿效应与弱相互作用共同作用的过程，不能被触发、减缓，单个原子核的衰变时刻无法预测——只有统计行为是确定的。
2. Alpha (α) Decay | α 衰变
In α‑decay, a heavy nucleus emits an alpha particle (two protons and two neutrons, i.e. a ⁴₂He nucleus). The parent nucleus loses two protons and two neutrons, so its mass number drops by 4 and its atomic number drops by 2. Alpha particles have a short range in air (a few centimetres) and are stopped by a sheet of paper. They are strongly ionising because of their +2e charge and relatively large mass. A typical α‑decay equation: ²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He.
在 α 衰变中，一个重原子核发射一个 α 粒子（两个质子和两个中子，即一个 ⁴₂He 核）。母体核失去两个质子和两个中子，因此质量数减少 4，原子序数减少 2。α 粒子在空气中的射程很短（几厘米），一张纸就能将其阻挡。由于带有 +2e 电荷且质量相对较大，它们的电离能力很强。一个典型的 α 衰变方程：²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He。
3. Beta‑minus (β⁻) and Beta‑plus (β⁺) Decay | β⁻ 与 β⁺ 衰变
β⁻ decay occurs in neutron‑rich nuclei. A neutron transforms into a proton, emitting an electron (β⁻ particle) and an antineutrino. The atomic number increases by 1 while the mass number remains unchanged. Example: ¹⁴₆C → ¹⁴₇N + e⁻ + ν̅ₑ. β⁺ decay happens in proton‑rich nuclei: a proton converts into a neutron, releasing a positron (β⁺) and a neutrino. The atomic number decreases by 1. Beta particles are moderately ionising and can travel a few metres in air; they are stopped by a few millimetres of aluminium. In both cases, the emitted energy is shared between the beta particle and the neutrino, resulting in a continuous energy spectrum.
β⁻ 衰变发生在中子过剩的原子核中。一个中子转变成一个质子，同时发射一个电子（β⁻ 粒子）和一个反中微子。原子序数增加 1，而质量数保持不变。例如：¹⁴₆C → ¹⁴₇N + e⁻ + ν̅ₑ。β⁺ 衰变发生在质子富裕的核中：一个质子转变成一个中子，释放一个正电子（β⁺）和一个中微子。原子序数减少 1。β 粒子的电离能力中等，在空气中可穿行几米；几毫米厚的铝片就能将其阻挡。两种情况下，发射的能量都在 β 粒子和中微子之间分配，从而形成连续能谱。
4. Gamma (γ) Emission | γ 辐射
Gamma radiation often follows α or β decay when the daughter nucleus is left in an excited state. The nucleus falls to a lower energy level by emitting a high‑energy photon — a gamma ray. Gamma emission does not change the proton or neutron numbers; it simply removes excess energy. Gamma rays are the least ionising but the most penetrating of the three radiations; thick lead or several metres of concrete can attenuate them significantly. Cobalt‑60 is a well‑known γ‑ray source: ⁶⁰₂₇Co → ⁶⁰₂₈Ni + e⁻ + ν̅ₑ + γ.
γ 辐射通常伴随 α 或 β 衰变发生，此时子核处在激发态。原子核通过发射高能光子——伽马射线，跃迁到较低能级。γ 发射不改变质子数或中子数，仅仅释放多余能量。在三种辐射中，γ 射线的电离能力最弱，但穿透能力最强；厚铅板或几米厚的混凝土才能显著将其衰减。钴‑60 是著名的 γ 射线源：⁶⁰₂₇Co → ⁶⁰₂₈Ni + e⁻ + ν̅ₑ + γ。
5. Penetrating Power and Ionising Ability | 穿透力与电离能力
Understanding the comparative properties of α, β, and γ radiation is crucial for both experimental design and radiation protection. The table below summarises their range in air, typical shielding, and ionising power.
理解 α、β 和 γ 辐射的对比特性对于实验设计和辐射防护都至关重要。下表总结了它们在空气中的射程、常用屏蔽材料以及电离能力。
| Radiation | Range in air | Typical shielding | Ionising ability |
|---|---|---|---|
| Alpha (α) | A few cm | Paper / skin | Very high |
| Beta (β) | About 1 m | 3–5 mm aluminium | Moderate |
| Gamma (γ) | Many metres | Thick lead / concrete | Low |
6. The Decay Constant and Activity | 衰变常数与活度
The probability that a single nucleus decays per unit time is called the decay constant, λ (lambda). Its unit is s⁻¹. For a sample containing N undecayed nuclei, the activity A is the number of decays per second: A = λN. Activity is measured in becquerels (Bq), where 1 Bq = 1 decay per second. Because A is proportional to N, the activity of a source also follows exponential decay. Students should be able to differentiate between the physical decay constant and the half‑life and to calculate the count rate from background‑corrected measurements.
单个原子核在单位时间内发生衰变的概率称为衰变常数，记作 λ（拉姆达），单位为 s⁻¹。对于一个含有 N 个未衰变原子核的样品，活度 A 是每秒衰变次数：A = λN。活度的单位是贝克勒尔 (Bq)，1 Bq = 每秒 1 次衰变。由于 A 与 N 成正比，放射源的活度同样遵循指数衰减。考生应能区分物理衰变常数与半衰期，并能根据扣除本底后的计数测量值算得活度。
7. Exponential Decay Law | 指数衰变定律
The number of undecayed nuclei N at time t is given by the exponential law:
N = N₀ e⁻⁽λᵗ⁾
Where N₀ is the original number of nuclei. Taking natural logarithms yields a linear relationship: ln N = ln N₀ − λt. The same equation describes the activity: A = A₀ e⁻⁽λᵗ⁾. Graphs of ln(N) against t give a straight line of slope −λ. This is a standard method for determining the decay constant from experimental data. IB and CCEA papers frequently ask candidates to use these equations or to find half‑life from a decay graph.
在 t 时刻未衰变的原子核数 N 由指数定律给出：N = N₀ e⁻⁽λᵗ⁾，其中 N₀ 为初始原子核数。两边取自然对数后得到线性关系：ln N = ln N₀ − λt。同样的方程也适用于活度：A = A₀ e⁻⁽λᵗ⁾。作出 ln(N) 随 t 变化的图线可得到一条斜率为 −λ 的直线，这是根据实验数据确定衰变常数的标准方法。IB 和 CCEA 试卷常要求考生运用这些方程，或者根据衰变曲线求出半衰期。
8. Half‑Life and Its Calculation | 半衰期及其计算
Half‑life (T₁/₂) is the time taken for half of the radioactive nuclei in a sample to decay, or for the activity to halve. It is related to the decay constant by:
T₁/₂ = ln 2 / λ
Because ln 2 ≈ 0.693, this gives T₁/₂ = 0.693/λ. Half‑life is independent of the amount of material and is a characteristic property of each radioisotope. Worked examples often involve determining the remaining mass or activity after an integer number of half‑lives: after n half‑lives, the fraction remaining is (½)ⁿ. More generally, if the time elapsed is t, the fraction remaining is (½)^(t/T₁/₂).
半衰期 (T₁/₂) 是指样品中一半放射性原子核发生衰变，或活度减半所需要的时间。它与衰变常数的关系为：T₁/₂ = ln 2 / λ。由于 ln 2 ≈ 0.693，可写成 T₁/₂ = 0.693/λ。半衰期与物质的数量无关，是每种放射性同位素的特征属性。典型例题常涉及经过整数个半衰期后剩余质量或活度的计算：经过 n 个半衰期后，剩余分数为 (½)ⁿ。更一般地，若经过的时间为 t，剩余分数为 (½)^(t/T₁/₂)。
9. Carbon Dating and Radioactive Dating | 碳定年与放射性测年
Radiocarbon dating uses the β⁻ decay of ¹⁴C (half‑life ≈ 5730 years) to estimate the age of organic remains. Living organisms maintain a constant ¹⁴C to ¹²C ratio through exchange with the atmosphere; after death, the ¹⁴C decays exponentially with no replenishment. By measuring the current ¹⁴C activity and comparing it with the initial level, the time since death can be calculated. Other isotopes such as ²³⁸U (half‑life 4.5 × 10⁹ years) are used to date rocks. IB and CCEA candidates must be able to apply the decay equations to such dating problems and discuss the limitations, e.g. changes in atmospheric ¹⁴C concentration.
放射性碳定年法利用 ¹⁴C 的 β⁻ 衰变（半衰期约为 5730 年）来估算有机遗物的年代。活着的生物体通过与大气交换保持恒定的 ¹⁴C 与 ¹²C 比例；死亡后，¹⁴C 按指数规律衰变而无法得到补充。通过测量当前 ¹⁴C 活度并与初始水平对比，便可计算出死亡至今的时间。其他同位素如 ²³⁸U（半衰期 4.5 × 10⁹ 年）被用来确定岩石的年代。IB 和 CCEA 考生必须能够将衰变方程应用到此类测年问题中，并讨论其局限性，例如大气中 ¹⁴C 浓度的变化。
10. Nuclear Stability and the N–Z Plot | 核稳定性与 N–Z 图
The stability of nuclides is elegantly summarised by a plot of neutron number N against proton number Z. Stable nuclei lie in a narrow band: for light nuclei, N ≈ Z; for heavier nuclei, N > Z to counteract the increasing electrostatic repulsion among protons. Nuclei above the stability band are neutron‑rich and tend to undergo β⁻ decay; nuclei below the band are proton‑rich and undergo β⁺ decay or electron capture. Very heavy nuclei (Z > 83) often undergo α decay. The N–Z plot helps predict the decay mode of an unknown isotope, a common requirement in examination questions.
核素稳定性可以通过中子数 N 对质子数 Z 的图线简洁地概括。稳定核素位于一条狭窄的带内：对于轻核，N ≈ Z；对于较重核，N > Z 以抵消质子间不断增强的静电排斥。稳定带上方的核素中子过剩，倾向于发生 β⁻ 衰变；带下方的核素质子过剩，发生 β⁺ 衰变或电子俘获。很重的核素（Z > 83）常发生 α 衰变。N–Z 图有助于预测未知同位素的衰变模式，这是考试中的常见要求。
11. Safety, Background Radiation, and Applications | 安全、本底辐射与应用
All measurements of radioactivity must account for background radiation from cosmic rays, terrestrial sources, and radon gas. The corrected count rate is obtained by subtracting the background count rate from the measured rate. Radioactive sources are handled with tongs, stored in lead containers, and kept as far as possible from the body. Applications of radioisotopes include medical imaging (e.g. technetium‑99m), radiotherapy (e.g. cobalt‑60), industrial thickness gauging (β sources), and smoke detectors (α sources). Candidates may be asked to choose an appropriate isotope for a given use based on half‑life, emission type, and activity.
所有放射性测量都必须考虑来自宇宙射线、陆地来源和氡气的本底辐射。修正后的计数率等于实测计数率减去本底计数率。放射源需要用钳子操作，储存在铅罐中，并尽量远离身体。放射性同位素的应用包括医学成像（如锝‑99m）、放射治疗（如钴‑60）、工业厚度测量（β 源）以及烟雾探测器（α 源）。考题可能要求学生根据半衰期、发射类型和活度为特定用途选择合适的同位素。
12. Common Exam Pitfalls and Data‑Handling Skills | 常见易错点与数据处理技巧
Many students confuse mass number and atomic number when writing decay equations — always check that the sum of mass numbers and the sum of atomic numbers balance on both sides. When plotting decay data, do not forget to include error bars if uncertainties are given, and draw the best‑fit straight line for ln N vs t graphs. In half‑life questions, note whether the time given corresponds to an integer number of half‑lives; if not, use the exponential equation. Always express the unit of activity in Bq and give half‑life with its proper time unit. Finally, when using the N–Z plot, identify the direction of decay arrows correctly: β⁻ moves diagonally down‑right (ΔZ = +1, ΔN = −1), β⁺ moves diagonally up‑left, and α moves two steps left and two down.
许多学生在书写衰变方程时混淆质量数和原子序数——务必检查等号两边质量数之和与原子序数之和是否平衡。在绘制衰变数据图时，如果给出了不确定度，不要忘记加上误差棒，并在 ln N 对应 t 的图上画出最佳拟合直线。在半衰期问题中，要注意给定的时间是否对应整数个半衰期；如果不是，则需使用指数方程。活度的单位始终用 Bq 表示，半衰期要标注正确的时间单位。最后，在使用 N–Z 图时，要正确标出衰变箭头的方向：β⁻ 向右下对角移动（ΔZ = +1, ΔN = −1），β⁺ 向左上对角移动，而 α 衰变先向左两步再向下两步。
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