Edexcel Physics: Radioactive Decay – Key Points | Edexcel 物理：放射性衰变考点精讲

📚 Edexcel Physics: Radioactive Decay – Key Points | Edexcel 物理：放射性衰变考点精讲

Radioactive decay is a fundamental nuclear process in which an unstable atomic nucleus loses energy by emitting radiation. For Edexcel Physics, understanding the random nature of decay, the properties of alpha, beta, and gamma emissions, and the mathematical models that describe activity and half-life is essential. This article consolidates all critical concepts, equations, and exam tips to help you master the topic.

放射性衰变是一种基本的核过程，不稳定原子核通过释放辐射损失能量。在 Edexcel 物理考试中，理解衰变的随机性、α、β、γ 辐射的性质以及描述活度和半衰期的数学模型至关重要。本文将整合所有关键概念、方程和考试技巧，帮助您全面掌握该主题。

1. The Nature of Radioactive Decay | 放射性衰变的本质

Radioactive decay is a spontaneous and random process. The term ‘random’ means that it is impossible to predict exactly when a particular nucleus will decay; only the probability of decay per unit time can be stated. The process is unaffected by external factors such as temperature, pressure, or chemical bonding.

放射性衰变是一个自发且随机的过程。“随机”意味着无法准确预测某个特定原子核何时会衰变；只能给出单位时间内衰变的概率。该过程不受温度、压力或化学键等外部因素影响。

Decay results in the emission of particles or electromagnetic radiation, transforming the parent nuclide into a daughter nuclide. The type of emission depends on the instability of the nucleus. A nucleus with too many neutrons may undergo beta-minus decay, while one with too many protons might undergo beta-plus decay or electron capture. Alpha decay typically occurs in very heavy nuclei.

衰变导致粒子或电磁辐射的发射，使母核素转变为子核素。发射的类型取决于原子核的不稳定性。中子过多的原子核可能发生 β⁻ 衰变，质子过多的可能发生 β⁺ 衰变或电子俘获。α 衰变通常发生在非常重的原子核中。

2. Alpha, Beta, and Gamma Radiation | α、β 和 γ 辐射

Edexcel requires you to know the properties and nature of the three main types of nuclear radiation. Alpha (α) particles are helium nuclei (⁴₂He), consisting of two protons and two neutrons. They are heavily ionising, have a range of a few centimetres in air, and can be stopped by a sheet of paper or human skin.

Edexcel 要求你了解三种主要核辐射的性质和本质。α 粒子是氦原子核（⁴₂He），由两个质子和两个中子组成。它们电离能力强，在空气中射程仅几厘米，可被一张纸或人体皮肤阻挡。

Beta-minus (β⁻) particles are fast-moving electrons emitted when a neutron converts into a proton. Beta-plus (β⁺) particles are positrons emitted when a proton converts into a neutron. Beta particles are moderately ionising, travel a few metres in air, and are stopped by a few millimetres of aluminium. Gamma (γ) radiation is a high-energy electromagnetic wave, weakly ionising, very penetrating, and requires several centimetres of lead or metres of concrete for significant absorption.

β⁻ 粒子是中子转变为质子时发射的快速电子。β⁺ 粒子是质子转变为中子时发射的正电子。β 粒子电离能力中等，在空气中传播几米，可被几毫米铝阻挡。γ 辐射是一种高能电磁波，电离能力弱，穿透力极强，需要几厘米铅或几米混凝土才能显著吸收。

Below is a summary table of the radiations:

Property	Alpha (α)	Beta (β⁻/β⁺)	Gamma (γ)
Nature	Helium nucleus ⁴₂He	Electron/Positron	EM wave (photon)
Charge	+2e	-e / +e	0
Ionising power	Strong	Medium	Weak
Penetration	Few cm in air, stopped by paper	~1 m in air, stopped by Al foil	Very far, reduced by thick Pb or concrete

下面是辐射类型对比表：（中文重复表格内容）

性质	α 粒子	β 粒子	γ 射线
本质	氦核 ⁴₂He	电子 / 正电子	电磁波（光子）
电荷	+2e	-e / +e	0
电离能力	强	中等	弱
穿透能力	空气几厘米，被纸阻挡	空气约1米，被铝箔阻挡	极远，需厚铅或混凝土减弱

3. Nuclear Equations and Conservation Laws | 核反应方程与守恒定律

Nuclear equations must balance both nucleon number (mass number A) and proton number (atomic number Z). For alpha decay of uranium-238: ²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He. Notice the sum of A is 238 = 234+4, and Z is 92 = 90+2.

核方程必须同时平衡核子数（质量数 A）和质子数（原子序数 Z）。以铀-238 的 α 衰变为例：²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He。注意到 A 的总和为 238=234+4，Z 的总和为 92=90+2。

For beta-minus decay of carbon-14: ¹⁴₆C → ¹⁴₇N + ⁰₋₁e. The emitted electron has A = 0 and Z = -1 to balance the increase in proton number. For beta-plus decay: ¹¹₆C → ¹¹₅B + ⁰₊₁e. A neutrino or antineutrino is also emitted in beta decays, but it is not required in the equation balancing for Edexcel AS.

碳-14 的 β⁻ 衰变：¹⁴₆C → ¹⁴₇N + ⁰₋₁e。发射的电子具有 A=0, Z=-1，以平衡质子数的增加。β⁺ 衰变：¹¹₆C → ¹¹₅B + ⁰₊₁e。β 衰变中还会释放中微子或反中微子，但在 Edexcel AS 的方程平衡中不需写出。

Gamma emission does not change A or Z; it often follows alpha or beta decay when the daughter nucleus is in an excited state. The equation includes the gamma photon (γ) with zero charge and zero mass number.

γ 发射不改变 A 或 Z；它通常发生在 α 或 β 衰变后子核处于激发态时。方程中包含 γ 光子，电荷和质量数均为零。

4. Decay Constant (λ) and Activity (A) | 衰变常数 (λ) 与活度 (A)

The decay constant λ is the probability of decay of a nucleus per unit time. It has units of s⁻¹. Activity A is the number of decays occurring per unit time in a sample, measured in becquerels (Bq), where 1 Bq = 1 decay per second.

衰变常数 λ 是单个原子核单位时间内衰变的概率，单位为 s⁻¹。活度 A 是样品中单位时间发生的衰变次数，以贝克勒尔 (Bq) 为单位，1 Bq = 每秒衰变1次。

The relationship between activity A, decay constant λ, and the number of unstable nuclei N is given by:

A = λN

This equation tells us that activity is directly proportional to the number of radioactive nuclei present. As N decreases, activity decreases.

活度 A、衰变常数 λ 和不稳定核数 N 之间的关系为：

A = λN

该方程表明活度与现存放射性核数成正比。N 减少，活度也随之减少。

You must also be aware that the activity of a source is often measured after correcting for background radiation. The experimental determination of λ can be done by measuring A at different times and using the exponential relationship.

你还需注意，源的活度通常在扣除本底辐射后才进行计算。实验测定 λ 可通过测量不同时刻的 A 并利用指数关系完成。

5. Exponential Decay Law | 指数衰变定律

Radioactive decay follows an exponential law because the number of decays per unit time is proportional to the number of nuclei present. The number of undecayed nuclei N at time t is given by:

N = N₀ e⁻λt

where N₀ is the initial number of nuclei. This can also be expressed for activity: A = A₀ e⁻λt, since A ∝ N.

放射性衰变遵循指数定律，因为单位时间内的衰变数与现存核数成正比。t 时刻未衰变的核数 N 为：

N = N₀ e⁻λt

其中 N₀ 为初始核数。该式也可用活度表示：A = A₀ e⁻λt，因为 A ∝ N。

The exponential decay curve shows a rapid initial drop that flattens over time. When solving problems, always identify whether you are given N or A, and ensure units of time match λ (often s⁻¹, but can be year⁻¹ in carbon dating).

指数衰变曲线显示初始快速下降，随时间推移趋于平缓。解题时，需明确题目给出的是 N 还是 A，并确保时间单位与 λ 匹配（通常为 s⁻¹，碳定年中可为 year⁻¹）。

6. Half-life (T½) and Its Determination | 半衰期 (T₁/₂) 及其测定

Half-life T₁/₂ is the time taken for half of the unstable nuclei in a sample to decay, or for the activity to halve. The relationship between half-life and decay constant is derived from the exponential equation by setting N = N₀/2 at t = T₁/₂:

T₁/₂ = ln 2 / λ ≈ 0.693 / λ

半衰期 T₁/₂ 是样品中一半不稳定核发生衰变所需的时间，或活度减半所需的时间。半衰期与衰变常数的关系由指数方程导出，设 t = T₁/₂ 时 N = N₀/2 可得：

T₁/₂ = ln 2 / λ ≈ 0.693 / λ

You can determine half-life from experimental data by reading the time for activity to fall from a value to half that value on an A–t graph. For more accurate analysis, a log-linear graph may be plotted, since taking natural logs of A = A₀ e⁻λt gives:

ln A = ln A₀ – λt

The gradient of the ln A versus t graph is -λ, allowing λ to be found, and then T₁/₂.

你可以通过实验数据确定半衰期，在 A–t 图上读取活度从某一数值降至一半的时间。为了更精确分析，可绘制对数-线性图，对 A = A₀ e⁻λt 取自然对数得：

ln A = ln A₀ – λt

ln A 对 t 图的斜率为 -λ，由此可求出 λ 再求 T₁/₂。

7. Carbon Dating and Radioactive Dating | 碳定年法及其他放射性定年

Carbon-14 (¹⁴C) dating is a classic application of radioactive decay. Living organisms maintain a constant ratio of ¹⁴C to ¹²C through exchange with the atmosphere. Upon death, the ¹⁴C decays with half-life ~5730 years, and the remaining proportion allows the age to be estimated using N = N₀ e⁻λt.

碳-14 (¹⁴C) 定年是放射性衰变的一个经典应用。活体生物通过与大气交换，保持¹⁴C/¹²C比例恒定。死亡后，¹⁴C 以约 5730 年的半衰期衰变，通过剩余的¹⁴C比例可利用 N = N₀ e⁻λt 估算年龄。

In Edexcel questions, you might be given the measured activity of a sample and asked to calculate age. Remember that the ratio is compared to the assumed atmospheric ratio at the time of death. Calibration curves from tree rings are used to refine dates. The method is valid up to about 50 000 years.

在 Edexcel 考题中，可能给出样品的实测活度，要求计算年龄。需记住，比例是与假设死亡时的大气比例进行比较。树轮校正曲线用于精确定年。该方法有效期约 5 万年。

Other dating methods include potassium-argon dating (K-40 to Ar-40) for geological samples, exploiting longer half-lives. The same exponential principles apply.

其他定年方法包括钾-氩定年（⁴⁰K 衰变为 ⁴⁰Ar），用于地质样品，利用了更长的半衰期。同样遵循指数原理。

8. Background Radiation and its Correction | 本底辐射及其扣除

Background radiation is the ionising radiation present in the environment from natural sources (cosmic rays, rocks, radon gas) and artificial sources (medical, nuclear accidents). When conducting experiments on radioactive decay, the measured count rate includes background radiation, which must be subtracted to get the true count rate of the source.

本底辐射是环境中存在的电离辐射，来自天然源（宇宙射线、岩石、氡气）和人造源（医疗、核事故）。进行放射性衰变实验时，测得的计数率包含本底辐射，必须减去它以得到源的真实计数率。

Correction is done by measuring the background count rate over a long period with the source removed, finding an average. Then subtract this average from each measured count rate. This corrected value is proportional to the activity of the source.

扣除方法是：移除源，长时间测量本底计数率，取平均值。然后将该平均值从每次测得的计数率中减去。校正后的值正比于源的活度。

Exam questions often give data with uncorrected counts and expect you to perform the correction before plotting or calculation. Always check if the count rate is given as ‘gross’ or ‘net’.

考题经常给出未经校正的计数数据，期望你在绘图或计算前先进行扣除。务必注意计数率是“总值”还是“净值”。

9. Applications, Hazards, and Safety Precautions | 应用、危害与安全预防

Radioactive isotopes have numerous applications: medical tracers (technetium-99m emits low-energy gamma), radiotherapy (cobalt-60), industrial thickness monitoring (beta sources for paper), and smoke detectors (americium-241 emits alpha). The choice of isotope depends on half-life and radiation type.

放射性同位素应用广泛：医学示踪剂（锝-99m 发出低能 γ 射线）、放射治疗（钴-60）、工业测厚（使用 β 源测纸张厚度）、烟雾探测器（镅-241 发射 α 粒子）。选择同位素取决于半衰期和辐射类型。

Exposure to ionising radiation can damage cells and cause mutations or cancer. Alpha sources are particularly hazardous if ingested because of their strong ionisation. Safety measures include using sealed sources, minimising exposure time, increasing distance (inverse square law for gamma), and using lead shielding. Always handle sources with forceps and store them in lead-lined containers.

电离辐射会损伤细胞，引发突变或癌症。α 源一旦被摄入，因其强电离性尤其危险。安全措施包括使用密封源、缩短暴露时间、增加距离（γ 服从平方反比定律）、使用铅屏蔽。始终用镊子夹持源，并存放在铅衬容器中。

The inverse square law for gamma radiation: intensity I ∝ 1/x², where x is distance from point source. This law can be verified by measuring count rate at various distances after background correction.

γ 辐射的平方反比定律：强度 I ∝ 1/x²，其中 x 为距离点源的距离。可通过在不同距离测量校正后的计数率来验证该定律。

10. Common Exam Mistakes and Graphical Analysis | 常见考试错误与图像分析

Many students confuse the random nature of decay with the predictable exponential pattern. Remember: individual decays are random, but the large-scale behaviour is deterministic. Do not say ‘decay is spontaneous and predictable’ – it is predictable only in a statistical sense.

许多学生将衰变的随机性与可预测的指数模式混淆。记住：单个衰变是随机的，但大量原子的整体行为是确定的。不要说“衰变是自发且可预测的”——只有在统计意义上才可预测。

Another common error is misapplying A = λN. Ensure N is the actual number of unstable nuclei, not the mass in grams. If given mass m and molar mass M, use N = (m / M) × Nₐ. Also, ensure λ is in correct time units.

另一个常见错误是误用 A = λN。确保 N 是不稳定核的实际数量，而不是以克计的质量。如果给出质量 m 和摩尔质量 M，应使用 N = (m/M) × Nₐ。另外，确保 λ 的时间单位正确。

When plotting graphs for half-life, use clearly labelled axes. For an exponential decay graph (A vs t), T₁/₂ is constant and can be found from several halvings. For the log graph, ensure you use natural log (ln) and explain the gradient. Avoid using log₁₀ unless specifically required, as the relationship becomes T₁/₂ ≈ 0.301×(decade time).

在绘制半衰期相关图形时，坐标轴要清楚标记。对于指数衰变图（A 对 t），T₁/₂ 恒定，可从多次减半求得。对于对数图，确保使用自然对数 (ln) 并解释斜率。除非题目特别要求，避免使用 log₁₀，因为关系会变为 T₁/₂ ≈ 0.301×(十倍衰减时间)。

Typical exam question: “A sample has an initial activity of 240 Bq. After 48 hours, it is 15 Bq. Calculate λ and T₁/₂.” Use A = A₀ e⁻λt ⇒ 15 = 240 e⁻λ×48×3600 ⇒ solve for λ, then T₁/₂ = ln2/λ. Always convert time to seconds unless λ is in hour⁻¹.

典型考题：“某样品初始活度为 240 Bq，48 小时后活度为 15 Bq。计算 λ 和 T₁/₂。” 使用 A = A₀ e⁻λt ⇒ 15 = 240 e⁻λ×48×3600，解出 λ，然后 T₁/₂ = ln2/λ。除非 λ 单位为 h⁻¹，否则时间要转换成秒。

11. Mass-Energy Equivalence in Decay | 衰变中的质能等价

Deep understanding of radioactive decay also touches on mass-energy equivalence. The total mass of the products is slightly less than the mass of the parent nucleus; this mass defect Δm is converted into kinetic energy of the products according to E = Δm c². This is the origin of the discrete energy spectra of alpha particles.

深入理解放射性衰变还需涉及质能等价。产物的总质量略小于母核质量；这个质量亏损 Δm 根据质能方程 E = Δm c² 转化为产物的动能。这解释了 α 粒子分立能谱的来源。

In Edexcel A level, you might calculate the energy released in a decay given atomic masses. Remember to use unified atomic mass unit u = 1.66×10⁻²⁷ kg and c = 3.00×10⁸ m/s. The energy equivalence of 1 u is 931.5 MeV. This topic links nuclear physics with particle physics.

在 Edexcel A-level 考试中，可能会给出原子质量，要求计算衰变释放的能量。记得使用原子质量单位 u = 1.66×10⁻²⁷ kg，c = 3.00×10⁸ m/s。1 u 的能量当量是 931.5 MeV。该主题将核物理与粒子物理联系起来。

12. Summary and Key Equations Checklist | 总结与关键方程清单

Before the exam, ensure you can recall and apply the following equations:

考前务必确保能回忆并应用以下各公式：

A = λN – activity law
A = λN – 活度定律
N = N₀ e⁻λt, A = A₀ e⁻λt – exponential decay
N = N₀ e⁻λt, A = A₀ e⁻λt – 指数衰变
T₁/₂ = ln2 / λ – half-life relation
T₁/₂ = ln2 / λ – 半衰期关系
E = Δm c² – energy released
E = Δm c² – 释放的能量
I ∝ 1/x² (gamma radiation)
I ∝ 1/x² (γ 辐射)

Mastering radioactive decay means understanding both the qualitative concepts and the quantitative models. Practice with past paper questions involving graphs, carbon dating, and background correction to build confidence.

掌握放射性衰变意味着既理解定性概念，又掌握定量模型。通过练习涉及图像、碳定年法和本底扣除的历年真题来建立信心。

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Edexcel Physics: Radioactive Decay – Key Points | Edexcel 物理：放射性衰变 考点精讲