📚 Radioactive Decay for AQA A Level Physics | A-Level AQA 物理：放射性衰变 考点精讲
Radioactive decay is a random and spontaneous process in which an unstable atomic nucleus loses energy by emitting radiation. In the AQA A Level Physics specification, you are expected to understand the nature of α, β⁻, β⁺ and γ radiation, write balanced nuclear equations, apply the exponential decay law, calculate activity and half‑life, interpret decay graphs, and appreciate the uses and dangers of ionising radiation. This article will walk you through every key point, pairing clear English explanations with matching Chinese translations so that you can master the topic thoroughly.
放射性衰变是一个随机且自发的过程，不稳定的原子核通过发射辐射来释放能量。在AQA A Level物理考纲中，你需要掌握α、β⁻、β⁺和γ射线的本质，能够书写平衡的核反应方程，应用指数衰变规律，计算活度和半衰期，解读衰变图像，并理解电离辐射的应用与危害。本文将逐一讲解所有核心考点，用清晰的英文说明和对应的中文解释帮助你扎实掌握这一主题。
1. The Nature of Radioactive Decay | 放射性衰变的本质
Radioactive decay is the spontaneous disintegration of an unstable nucleus, resulting in the release of particles or electromagnetic radiation. The process is unaffected by external conditions such as temperature or pressure because it arises from imbalances within the nuclear forces. An individual decay event is completely random – we cannot predict which nucleus will decay next, only the probability of decay within a certain time interval.
放射性衰变是不稳定原子核自发地分裂，释放出粒子或电磁辐射的过程。该过程不受温度、压力等外部条件的影响，因为它源于核力内部的不平衡。单个衰变事件是完全随机的——我们无法预测哪一个原子核会在下一刻衰变，只能知道在一定时间间隔内的衰变概率。
In AQA Physics, we distinguish between four main types of radiation emitted during decay: alpha (α) particles, beta‑minus (β⁻) particles, beta‑plus (β⁺) particles, and gamma (γ) rays. Each has a different penetrating power, ionising ability, and behaviour in electric and magnetic fields.
在AQA物理中，我们需要区分衰变过程中发射的四种主要辐射：α粒子、β⁻粒子、β⁺粒子和γ射线。它们的贯穿本领、电离能力和在电场、磁场中的行为各不相同。
2. Alpha, Beta and Gamma Radiation | α、β和γ辐射
An alpha particle is a helium nucleus, consisting of two protons and two neutrons. It has a charge of +2e and a relatively large mass number of 4. Because of its strong ionising power, an α particle loses energy quickly over a short distance in air and can be stopped by a few centimetres of air or a sheet of paper. Alpha decay typically occurs in heavy nuclei such as uranium‑238.
α粒子是一个氦原子核，由两个质子和两个中子组成。它带+2e电荷，质量数为4，相对较大。由于电离能力很强，α粒子在空气中很短距离内就迅速损失能量，能被几厘米空气或一张纸阻挡。α衰变通常发生在铀‑238等重核中。
Beta‑minus decay occurs when a neutron inside the nucleus transforms into a proton, emitting a fast‑moving electron (β⁻) and an antineutrino. The emitted electron has a charge of −1e and a much smaller mass, giving it greater penetrating power than alpha. β⁻ particles can travel a few metres in air and are stopped by a few millimetres of aluminium. In beta‑plus decay, a proton changes into a neutron, emitting a positron (β⁺) and a neutrino. The positron is the antimatter counterpart of the electron, with the same mass but a charge of +1e. Both types of beta decay conserve charge and nucleon number in the process.
β⁻衰变发生在核内一个中子转变为质子时，同时发射出一个高速电子（β⁻）和一个反中微子。发射出的电子带−1e电荷，质量远小于α粒子，因此贯穿本领更强。β⁻粒子在空气中可行进几米，被几毫米厚的铝板阻挡。在β⁺衰变中，一个质子转变为中子，发射出一个正电子（β⁺）和一个中微子。正电子是电子的反物质对应体，质量相同但带+1e电荷。两种β衰变在过程中均守恒电荷数和核子数。
Gamma rays are high‑energy electromagnetic photons emitted when an excited nucleus loses energy after a previous decay. They have no charge and no mass, so they are weakly ionising but highly penetrating. Gamma radiation can pass through many centimetres of lead and requires thick concrete or lead shielding to reduce intensity significantly. Often gamma emission accompanies alpha or beta decay as the daughter nucleus returns to its ground state.
γ射线是高能电磁光子，在之前的衰变之后，当激发态原子核损失能量时发出。它不带电荷、没有静止质量，电离能力弱但贯穿能力极强。γ射线可以穿透几厘米厚的铅，需要用厚水泥或铅屏蔽才能显著降低强度。γ射线通常伴随α或β衰变，使子核回到基态时发射出来。
3. Writing Nuclear Decay Equations | 书写核衰变方程
Nuclear equations must balance both mass number (A) and atomic (proton) number (Z). The general form for alpha decay is: AZ X → A−4Z−2 Y + 42 α. For example, uranium‑238 decays to thorium‑234: 23892 U → 23490 Th + 42 He.
核反应方程必须配平质量数（A）和原子序数（Z）。α衰变的通用形式为：AZ X → A−4Z−2 Y + 42 α。例如，铀‑238衰变为钍‑234：23892 U → 23490 Th + 42 He。
In beta‑minus decay, a neutron becomes a proton, so A remains the same but Z increases by 1: AZ X → AZ+1 Y + 0−1 e + ν̄. For carbon‑14: 146 C → 147 N + 0−1 e + ν̄.
β⁻衰变中，一个中子变为质子，因此A不变，Z增加1：AZ X → AZ+1 Y + 0−1 e + ν̄。例如碳‑14：146 C → 147 N + 0−1 e + ν̄。
For beta‑plus decay, a proton changes into a neutron, so Z decreases by 1: AZ X → AZ−1 Y + 0+1 e + ν. An example is the decay of fluorine‑18: 189 F → 188 O + 0+1 e + ν.
β⁺衰变中，质子变为中子，因此Z减少1：AZ X → AZ−1 Y + 0+1 e + ν。例如氟‑18衰变：189 F → 188 O + 0+1 e + ν。
Gamma emission is often added to the decay equation with the symbol γ after the daughter nucleus, showing that the nucleus loses energy but does not change A or Z. For instance, 6027 Co → 6028 Ni + 0−1 e + ν̄ + γ.
γ辐射通常在衰变方程中在子核后加上γ符号，表明核损失能量但不改变A和Z。例如：6027 Co → 6028 Ni + 0−1 e + ν̄ + γ。
4. Random Nature and Probability | 随机性与概率
The decay of a particular nucleus is unpredictable, but for a large number of identical nuclei the behaviour is governed by probability. The decay constant λ (lambda) is the probability that an individual nucleus will decay per unit time. A larger λ means a faster decay rate. The activity A of a sample is the number of disintegrations per second, measured in becquerels (Bq), where 1 Bq = 1 decay per second.
单个原子核的衰变是不可预测的，但对于大量相同的原子核，其行为遵循概率规律。衰变常数λ是单个原子核在单位时间内发生衰变的概率。λ越大，衰变速率越快。一个样品的活度A是每秒衰变次数，以贝克勒尔（Bq）为单位，1 Bq = 1次衰变/秒。
Because the process is random, the count rate measured by a Geiger–Müller tube shows statistical fluctuations. When plotting a graph of count rate against time, the points will scatter around a smooth exponential curve. It is essential to correct for background radiation by subtracting the background count from all readings.
由于过程是随机的，盖革‑米勒管测得的计数率会表现出统计涨落。绘制计数率‑时间图像时，数据点将围绕一条光滑的指数曲线上下散布。必须通过从所有读数中减去本底计数来校正本底辐射。
5. The Exponential Law of Decay | 指数衰变规律
The number of undecayed nuclei N remaining after time t is given by the exponential law:
N = N₀ e−λt
时间t后剩余的未衰变原子核数N由指数规律给出：N = N₀ e−λt
Here, N₀ is the initial number of undecayed nuclei, λ is the decay constant, and t is the elapsed time. The same relationship holds for activity A, because activity is directly proportional to the number of radioactive nuclei present at that instant: A = A₀ e−λt. Similarly, mass and count rate (corrected for background) also decay exponentially.
式中，N₀为初始未衰变核数，λ为衰变常数，t为经过的时间。活度A也遵循同样的关系，因为活度与当时存在的放射性核数成正比：A = A₀ e−λt。同理，质量和校正本底后的计数率也呈指数衰减。
On a graph of N against t, the curve approaches zero asymptotically but never quite reaches it within a finite time. The curve has a constant‑ratio property: after each half‑life, the value halves.
在N‑t图像上，曲线渐近地趋近于零，但在有限时间内永远不会完全达到零。该曲线具有恒定比例的性质：每经过一个半衰期，数值减半。
6. Half‑Life and Decay Constant | 半衰期与衰变常数
The half‑life T₁/₂ is the average time taken for the number of undecayed nuclei (or the activity) to reduce to half of its initial value. Using the exponential law, when N = N₀/2, we have e−λT₁/₂ = 1/2, which yields:
T₁/₂ = ln 2 / λ
半衰期T₁/₂是未衰变原子核数量（或活度）减少到初始值一半所需的平均时间。利用指数规律，当N = N₀/2时，有e−λT₁/₂ = 1/2，从而推导出：T₁/₂ = ln 2 / λ
This derivation connects the macroscopic half‑life to the microscopic decay constant. For example, the isotope technetium‑99m has a half‑life of about 6 hours, which means its decay constant λ = ln 2 / (6 × 3600) ≈ 3.21 × 10⁻⁵ s⁻¹. You should be able to calculate half‑life from graphs or from given data, and use the formula to find λ or remaining nuclei after a certain number of half‑lives.
这个推导将宏观半衰期与微观衰变常数联系起来。例如，同位素锝‑99m的半衰期约为6小时，这意味着其衰变常数λ = ln 2 / (6 × 3600) ≈ 3.21 × 10⁻⁵ s⁻¹。你需要能够从图像或给定数据中计算半衰期，并运用该公式求λ或经过一定数量半衰期后剩余的核数。
A common exam task is to work out the fraction remaining after n half‑lives: (1/2)ⁿ. For instance, after 3 half‑lives, 1/8 of the original radioactive nuclei remain, and 7/8 have decayed.
常见的考试题型是计算经过n个半衰期后剩余的分数：(1/2)ⁿ。例如，经过3个半衰期后，还剩原有放射性核的1/8，已衰变了7/8。
7. Activity and Counting Rates | 活度与计数率
Activity (A) is the rate at which nuclei decay, defined as the number of disintegrations per unit time. It is connected to the decay constant and the number of radioactive nuclei by the equation:
A = λ N
活度A是原子核衰变的速率，定义为单位时间内的衰变次数。它与衰变常数和放射性核数目之间的关系为：A = λ N
Because A ∝ N, the activity‑time graph also follows an exponential decay with the same half‑life. In practical experiments, you measure count rate C (counts per second), which is proportional to the activity after corrections for detector efficiency and background radiation. The relationship C = k A, where k is the detection efficiency factor, allows you to determine half‑life from the slope of a graph of ln(count rate) against time.
由于A ∝ N，活度‑时间图像也遵循指数衰减，且半衰期相同。在实际实验中，我们测量的是计数率C（每秒计数），在校正探测器效率和本底辐射后，计数率与活度成正比。关系式C = k A中，k为探测效率因子，借此可以从ln(计数率)‑时间图像的斜率求出半衰期。
In the AQA required practical, you might use a GM tube to measure the count rate from a radioactive sample over time and plot a graph to determine the half‑life. Always remember to subtract the background count rate before calculating activity or plotting graphs.
在AQA要求的实验考核中，你可能需要利用盖革管测量放射性样品在一段时间内的计数率，并通过作图确定半衰期。务必记住在计算活度或绘制图像之前减去本底计数率。
8. Graphical Analysis of Decay | 衰变的图像分析
Exponential decay can be analysed using three main graphs:
- N versus t: a smooth, curved line that halves in value every half‑life. The curve never touches the x‑axis.
- ln N versus t: because N = N₀ e−λt, taking natural logs gives ln N = ln N₀ − λt. This is the equation of a straight line with gradient −λ and y‑intercept ln N₀.
- Activity A versus t shows the same shape as N v t, and likewise, ln A v t is linear with gradient −λ.
指数衰变可以用三种主要图像来分析：
- N‑t图：一条平滑曲线，每经过一个半衰期数值减半，曲线永远不会触及x轴。
- ln N‑t图：由N = N₀ e−λt取自然对数得ln N = ln N₀ − λt，这是一条斜率为−λ、截距为ln N₀的直线。
- 活度A‑t图形状与N‑t图相同；同样，ln A‑t图是斜率为−λ的直线。
This linear relation is extremely useful for determining λ or verifying the exponential nature of the data. In the examination, you may be given data points and asked to plot a suitable graph to find T₁/₂ or λ. Always label axes, choose sensible scales, and draw a best‑fit line.
这种线性关系对于求λ或验证数据的指数性质非常有用。在考试中，你可能被给出一组数据，要求绘制适当的图像来找到T₁/₂或λ。务必标注坐标轴、选择合适的比例并画出最佳拟合线。
9. Carbon Dating | 碳年代测定法
Carbon‑14 dating is a classic application of half‑life. Living organisms constantly exchange carbon with the atmosphere, maintaining a steady ratio of radioactive 14C to stable 12C. When an organism dies, the intake stops and the 14C decays with a half‑life of about 5730 years. By measuring the current activity of a sample and comparing it with the activity of a fresh sample, the age can be estimated:
t = (T₁/₂ / ln 2) × ln (A₀ / A)
碳‑14测年法是半衰期的一个经典应用。活体生物不断与大气交换碳元素，维持放射性14C与稳定12C的比例恒定。当生物死亡后，摄入停止，14C以约5730年的半衰期衰变。通过测量样品的当前活度并与新鲜样品的活度比较，可以估算出年代：t = (T₁/₂ / ln 2) × ln (A₀ / A)
Because 14C dating relies on extremely low counting rates, careful background subtraction and long counting times are needed. The method is reliable for ages up to about 50 000 years, beyond which the activity becomes too weak to measure accurately.
由于碳‑14测年依赖于极低的计数率，需要仔细扣除本底并采用长计数时间。该方法对约5万年以内的年代可靠，超过该范围后活度过低而无法精确测量。
10. Radioactive Decay and Half‑Life Calculations | 放射性衰变与半衰期计算
Typical AQA numerical questions ask you to find the remaining number of nuclei, the elapsed time for a given fraction to decay, or the decay constant. You will often combine N = N₀ e−λt with λ = ln 2 / T₁/₂. For instance, if an isotope has a half‑life of 8 days and a sample initially contains 1.0 × 10¹² nuclei, you can find the number remaining after 24 days (three half‑lives) directly as (1/2)³ × 1.0 × 10¹² = 1.25 × 10¹¹. Alternatively, calculate λ and then use the exponential formula.
常见的AQA计算题要求你求出剩余核数目、衰减某一分数所需的时间或衰变常数。你通常会结合使用N = N₀ e−λt和λ = ln 2 / T₁/₂。例如，若某同位素的半衰期为8天，某样品初始含有1.0 × 10¹²个原子核，可以直接得出24天（即3个半衰期）后剩余核数为(1/2)³ × 1.0 × 10¹² = 1.25 × 10¹¹。或者，先求出λ再代入指数公式。
Always keep units consistent: T₁/₂ and t must be in the same time unit. Use natural logs conveniently by taking ln of both sides of the decay equation. When solving for t, rearrange to t = (ln (N₀/N)) / λ. This appears in many exam questions.
务必保持单位一致：T₁/₂和t必须使用相同的时间单位。利用衰变方程两边取自然对数可以简便求解。求t时，整理为t = (ln (N₀/N)) / λ。这在许多考题中都会出现。
11. Hazards, Shielding and Safety | 危害、屏蔽与安全
Alpha sources are extremely dangerous if inhaled or ingested because they cause intense localised ionisation inside the body, but they are easily stopped by dead skin cells or a few centimetres of air. Beta particles can penetrate skin and cause burns, while gamma rays are deeply penetrating and can ionise cells throughout the body, increasing the risk of cancer. The inverse‑square law for gamma intensity means that doubling the distance from a point source reduces the intensity to one‑quarter, so distance is an effective safety measure.
α放射源如果被吸入或摄入体内极其危险，因为它们会在体内造成强烈的局部电离，但α粒子很容易被皮肤角质层或几厘米空气阻挡。β粒子能穿透皮肤并造成灼伤，而γ射线穿透深度极大，能电离全身细胞，增加癌症风险。γ强度的平方反比定律意味着与点源的距离加倍，强度降至原来的四分之一，因此距离是一种有效的安全措施。
Laboratory safety rules include using forceps to handle sources, pointing sources away from the body, storing sources in lead‑lined containers, and never eating or drinking near radioactive materials. AQA questions often ask you to explain which type of shielding is appropriate for each type of radiation.
实验室安全守则包括使用镊子操作放射源、将源指向远离身体的方向、将源储存在铅衬容器中，以及不得在放射源附近饮食。AQA考试常要求你解释针对每种辐射应使用哪种屏蔽方式。
12. Applications of Radioactive Isotopes | 放射性同位素的应用
Radioactive tracers in medicine: short‑lived gamma‑emitting isotopes such as technetium‑99m are injected into the body, and a gamma camera detects the radiation to image organs. Gamma emitters are chosen because they can escape the body with minimal ionising damage, and short half‑lives limit the patient’s dose.
医学放射性示踪剂：短寿命的γ发射同位素如锝‑99m被注入体内，伽马相机检测辐射来对器官成像。选择γ放射源是因为它们能够逸出体外且电离损伤最小，同时短半衰期限制了患者所受剂量。
Industrial applications include measuring thickness of materials using beta sources, detecting leaks in pipes, and sterilising medical equipment with intense gamma radiation from cobalt‑60. In smoke detectors, a tiny americium‑241 alpha source ionises air, and smoke particles disrupt the current, triggering the alarm.
工业应用包括利用β源测量材料厚度、检测管道泄漏，以及使用钴‑60强γ辐射对医疗设备进行消毒。在烟雾探测器中，微量的镅‑241 α源电离空气，烟雾颗粒干扰电流从而触发报警。
Understanding these applications helps you link the physical properties of each type of radiation (penetrating power, ionising ability, half‑life) to real‑world uses, a key skill for AQA written papers.
理解这些应用有助于你将每种辐射的物理性质（贯穿本领、电离能力和半衰期）与实际应用联系起来，这是AQA笔试中的一项关键技能。
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