Radioactivity | 放射性

📚 Radioactivity | 放射性

Radioactivity is a core topic in AQA A-Level Physics. It explores the spontaneous disintegration of unstable nuclei, the properties of nuclear radiation, and the mathematics of decay. This article provides a structured revision guide aligned with the AQA specification, covering essential definitions, equations, and practical applications.

放射性是AQA A-Level物理的核心内容，研究不稳定原子核的自发衰变、核辐射的性质以及衰变的数学规律。本文依据AQA考纲提供结构化复习指南，涵盖核心定义、方程与实际应用。

1. Atomic Structure and the Strong Nuclear Force | 原子结构与强核力

An atom consists of a dense nucleus containing protons (positively charged) and neutrons (neutral), surrounded by orbiting electrons. The proton number Z (atomic number) determines the element’s identity, while the nucleon number A (mass number) is the total number of protons and neutrons. Isotopes are atoms of the same element with the same number of protons but a different number of neutrons.

原子由致密的原子核（内含带正电的质子和电中性的中子）和绕核运动的电子组成。质子数Z（原子序数）决定了元素的种类，核子数A（质量数）是质子数与中子数之和。同位素是指质子数相同但中子数不同的同种元素的原子。

The strong nuclear force binds protons and neutrons together in the nucleus. It acts only over a very short range (approximately 1-3 fm). At separations around 1 fm, it is an attractive force that overcomes the electrostatic repulsion between protons. This delicate balance determines whether a nucleus is stable or radioactive.

强核力将质子和中子束缚在原子核内。它只在极短距离（约1-3飞米）内起作用。在约1飞米的间距上，强核力表现为吸引力，能够克服质子之间的静电排斥力。这种微妙的平衡决定了原子核是稳定的还是放射性的。

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

Radioactive decay is a random and spontaneous process. It is random because it is impossible to predict which individual nucleus will decay next; it is spontaneous because it cannot be influenced by external factors such as temperature, pressure, or chemical state. The decay process involves the nucleus emitting radiation to become a more stable configuration.

放射性衰变是一个随机且自发的进程。说它随机，是因为无法预测下一个衰变的是哪个原子核；说它自发，是因为它不受温度、压力或化学状态等外部因素影响。衰变过程中，原子核通过放出辐射转变为更稳定的状态。

When a nucleus undergoes decay, it is said to be unstable. The instability arises when the neutron-to-proton ratio falls outside the stable band (the “valley of stability” on the N-Z curve). For light elements, stability requires roughly equal numbers of protons and neutrons; for heavier elements, a greater proportion of neutrons is needed to mitigate proton-proton repulsion.

原子核发生衰变时即为不稳定态。当中子数与质子数之比偏离稳定带（N-Z曲线上的“稳定谷”）时就会出现不稳定。对于轻元素，稳定性要求质子数与中子数大致相等；对于重元素，则需要更高比例的中子来缓解质子间的排斥力。

3. Alpha, Beta and Gamma Radiation | α、β与γ辐射

There are three main types of nuclear radiation: alpha (α), beta (β) and gamma (γ). Each possesses distinct physical properties, penetrating power, and ionizing ability. A comparison is shown in the table below.

核辐射主要有三种类型：α射线、β射线和γ射线。每种辐射具有不同的物理性质、穿透能力和电离本领。下表进行比较。

Property	Alpha (α)	Beta (β)	Gamma (γ)
Nature	Helium nucleus (2 protons + 2 neutrons)	Fast-moving electron	Electromagnetic wave
Charge	+2e	-e	0
Speed	~5% of the speed of light	Up to 95% of the speed of light	Speed of light
Penetrating power	Stopped by paper or a few cm of air	Stopped by 3-5 mm of aluminium	Reduced by lead; never fully absorbed
Ionizing ability	Strongest (high charge, high mass)	Moderate	Weakest (no charge, no mass)

4. Alpha Decay and the Decay Equation | α衰变与衰变方程

Alpha decay occurs in heavy, proton-rich nuclei. The nucleus emits an alpha particle consisting of 2 protons and 2 neutrons, which is equivalent to a helium-4 nucleus. The daughter nucleus has a mass number reduced by 4 and an atomic number reduced by 2.

α衰变发生在质子过多的重原子核中。原子核放出一个由2个质子和2个中子组成的α粒子，相当于一个氦-4核。子核的质量数减少4，原子序数减少2。

ᵃ₂ₓX → ᵃ⁻⁴₂₋₂Y + ⁴₂He

For example, radium-226 decays to radon-222:

例如，镭-226衰变为氡-222：

²²⁶₈₈Ra → ²²²₈₆Rn + ⁴₂He

Alpha decay reduces the neutron-to-proton ratio, making the daughter nucleus more stable. The energy released appears as the kinetic energy of the alpha particle and the recoil energy of the daughter nucleus.

α衰变降低了中子与质子之比，使子核更加稳定。释放的能量表现为α粒子的动能和子核的反冲能。

5. Beta-Minus Decay and the Decay Equation | β⁻衰变与衰变方程

Beta-minus (β⁻) decay occurs in neutron-rich nuclei. A neutron transforms into a proton, emitting an electron (the beta particle) and an antineutrino. The mass number A remains unchanged, while the atomic number increases by 1.

β⁻衰变发生在中子过多的原子核中。一个中子转变为质子，同时放出一个电子（即β粒子）和一个反中微子。质量数A保持不变，原子序数增加1。

ⁿ₀ → p⁺ + e⁻ + ṽₑ

ᵃ₂ₓX → ᵃ₂₊₁Y + ⁰₋₁e + ṽₑ

A classic example is the decay of carbon-14 to nitrogen-14:

碳-14衰变为氮-14是经典实例：

¹⁴₆C → ¹⁴₇N + ⁰₋₁e + ṽₑ

The antineutrino (ṽₑ) carries away part of the energy to conserve momentum and energy. In the AQA specification, you are expected to know that the continuous beta spectrum results from the sharing of energy between the electron and the antineutrino.

反中微子（ṽₑ）带走部分能量以保证动量和能量守恒。在AQA考纲中，需掌握β连续能谱源于电子与反中微子之间的能量分配这一结论。

6. Gamma Emission | γ辐射发射

Gamma radiation is high-frequency electromagnetic radiation emitted from an excited nucleus. When a nucleus undergoes alpha or beta decay, the daughter nucleus is often left in an excited energy state. It transitions to a lower energy level by emitting a gamma photon. Gamma emission does not change the mass number or atomic number of the nucleus.

γ辐射是不稳定的原子核从激发态跃迁到较低能级时发出的高频率电磁波。当原子核发生α或β衰变后，子核往往处于激发态。子核通过发射γ光子跃迁至较低能级。γ发射不改变原子核的质量数或原子序数。

ᵃ₂ₓ* → ᵃ₂ₓ + γ

Because gamma rays have no mass and no charge, they are the most penetrating form of nuclear radiation. Their wavelengths are typically shorter than 10⁻¹² m, placing them at the high-energy end of the electromagnetic spectrum.

由于γ射线没有质量和电荷，它是穿透力最强的核辐射。其波长通常小于10⁻¹²米，位于电磁波谱的高能端。

7. Half-Life and the Decay Constant | 半衰期与衰变常数

The half-life (T½) of a radioactive isotope is the average time taken for half of the nuclei in a sample to decay, or equivalently, the time taken for the activity to fall to half of its initial value. It is related to the decay constant λ by the following equation:

放射性同位素的半衰期（T½）是指样品中一半原子核发生衰变所需的平均时间，也可等效视为活度降至初始值一半所需的时间。它与衰变常数λ的关系如下：

T½ = ln 2 / λ

The decay constant λ is the probability of a nucleus decaying per unit time, measured in s⁻¹. The number of undecayed nuclei N at time t is given by the exponential decay law:

衰变常数λ是单位时间内某个原子核发生衰变的概率，单位为s⁻¹。t时刻尚未衰变的原子核数N由指数衰变定律给出：

N = N₀ e^(−λt)

Similarly, the activity A (the rate of decay, measured in becquerel Bq, where 1 Bq = 1 decay per second) follows the same exponential form:

类似地，活度A（衰变率，单位为贝克勒尔Bq，1 Bq = 每秒1次衰变）遵循相同的指数形式：

A = A₀ e^(−λt)

When tackling calculations, always check whether the question asks for the number of undecayed nuclei N, the mass of remaining isotope, or the activity A. These are interconnected through N = m/m_atom and A = λN.

在解题时，务必注意题目要求的是未衰变的核数N、剩余同位素的质量还是活度A。它们之间通过N = m/m_atom和A = λN相互关联。

8. Exponential Decay Graphs and Logarithmic Plots | 指数衰变曲线与对数坐标图

The decay of a radioactive substance is exponential, meaning the rate of decay is proportional to the number of undecayed nuclei. The graph of N against t shows a continuously decreasing curve that approaches zero asymptotically but never quite reaches it.

放射性物质的衰变是指数型，即衰变速率与未衰变的核数成正比。N随t变化的曲线是连续递减的，渐近接近零但永不真正到达零。

To determine the half-life from a decay curve, locate the time at which N falls to N₀/2, then from N₀/2 to N₀/4, and so on. Each interval should be equal for an exponential decay, confirming a constant half-life. Alternatively, plot ln N against t: the graph is a straight line with gradient −λ and intercept ln N₀. This linear form is especially useful when the background count must be subtracted.

从衰变曲线求半衰期时，找到N降至N₀/2的时间，再从N₀/2降至N₀/4的时间，依此类推。指数衰变中相邻间隔相等，说明半衰期恒定。另一种方法是绘制ln N对t的图：所得为一条直线，斜率为−λ，截距为ln N₀。这种线性形式在需要扣除背景计数时尤为有用。

9. Background Radiation | 背景辐射

Background radiation is the low-level radiation that is always present in the environment. It originates from multiple sources, including cosmic rays from space, radon gas from rocks and soil, natural radioactive isotopes in food and building materials, and artificial sources such as medical procedures and nuclear weapons testing.

背景辐射是环境中始终存在的低水平辐射。其来源多种多样，包括来自太空的宇宙射线、岩石和土壤中的氡气、食物和建筑材料中的天然放射性同位素，以及医疗过程和核武器试验等人为来源。

In any radioactivity experiment, the measured count rate includes background radiation. The corrected count rate is obtained by subtracting the background count rate from the total measured count rate. A common examination question requires students to measure background radiation over a period of time, calculate the average, and then subtract it from experimental readings.

在任何放射性实验中，测得的计数率都包含背景辐射。修正后的计数率需从总测量计数率中减去背景计数率。考试中常见的要求是：在一段时间内测量背景辐射，计算平均值，然后从实验读数中扣减。

When measuring the half-life of a source with a long half-life, background radiation becomes a significant source of error. Always record the background count before and after the experiment to ensure accuracy. For short-lived sources, the half-life can be deduced by plotting the corrected activity on a logarithmic scale.

当测量的放射源半衰期较长时，背景辐射会成为显著的误差来源。实验前后都应记录背景计数以保证准确性。对于短寿命放射源，可在对数坐标上绘制修正后的活度曲线来推算半衰期。

10. Detecting Radiation | 辐射探测

The Geiger-Müller (GM) tube is the most commonly used detector in A-level practical work. It consists of a thin-walled tube filled with gas at low pressure. When ionizing radiation enters the tube, it creates a pulse of current that is amplified and recorded by a counter.

盖革-米勒（GM）管是A-level实验中最常用的探测器。它由一个薄壁管组成，管内充有低压气体。当电离辐射进入管内时产生电流脉冲，经放大后被计数器记录。

The GM tube detects alpha, beta and gamma radiation, but not equally efficiently. Alpha particles are stopped by the tube wall, so a thin mica window is used. Gamma radiation is weakly ionizing, so only a small proportion is detected. The counting efficiency of a GM tube for gamma radiation is typically around 1%.

GM管能探测α、β和γ辐射，但探测效率并不相同。α粒子会被管壁阻挡，因此需要使用薄的云母窗。γ辐射电离能力弱，只有小部分能被探测到。GM管对γ辐射的探测效率通常约为1%。

When recording counts, the reading includes both the background count rate and the count rate from the source. To obtain accurate results, the source should be placed at a fixed distance from the detector, and the count should be taken over a suitable time interval to reduce statistical fluctuations. For weak sources, longer counting times improve precision.

记录计数时，读数包括背景计数率和源自放射源的计数率。为获得准确结果，放射源应放置在距探测器固定距离处，并在合适的时间间隔内计数以减少统计涨落。对于弱源，延长计数时间可提高精确度。

11. Risks and Safety Measures | 辐射危害与安全措施

Ionizing radiation can damage living cells by ionizing atoms within DNA molecules, potentially causing cancer or genetic mutations. The severity of the biological effect depends on the type of radiation, the dose received, and the tissue exposed. Alpha radiation is the most hazardous when ingested or inhaled because its high ionizing power causes extensive local damage, even though it cannot penetrate the skin.

电离辐射通过电离DNA分子中的原子而损伤活细胞，可能引发癌症或基因突变。生物效应的严重程度取决于辐射类型、受照剂量和暴露的组织。α辐射一旦被摄入或吸入极为危险，因为其电离能力强、会对局部造成严重损伤，即便它无法穿透皮肤。

Key safety measures in the laboratory include:

实验室中的关键安全措施包括：

Use tongs or tweezers to handle radioactive sources, keeping them as far from the body as possible.

使用钳子或镊子夹取放射源，尽量远离身体。
Point sources away from the experimenter and others; never look directly down a source holder.

使放射源的出射方向远离实验者和他人的身体；绝不可直视源容器内部。
Minimise exposure time and maximise distance. The intensity of radiation decreases with the square of the distance from a point source (inverse square law).

尽量缩短暴露时间并加大距离。点源的辐射强度与距离的平方成反比（平方反比定律）。
Wear gloves and lab coats to prevent contamination, and wash hands after handling sources.

穿戴手套和实验服以防污染，接触放射源后要洗手。
Store radioactive sources in lead-lined containers when not in use, and never dispose of them with ordinary waste.

不使用时将放射源存放在铅衬容器中，切不可与普通垃圾混放丢弃。

12. Applications of Radioactivity | 放射性的应用

Radioactive isotopes have a wide range of applications in medicine, industry, and archaeology. In medicine, technetium-99m is used as a gamma tracer for imaging organs because its short half-life (about 6 hours) gives a high initial activity that declines quickly, minimising patient dose. Cobalt-60 sources deliver gamma radiation in radiotherapy for the treatment of tumours.

放射性同位素在医学、工业和考古领域有广泛的应用。在医学中，锝-99m用作γ示踪剂进行器官成像，因其半衰期短（约6小时），初始活度高但迅速衰减，可减少患者受到的剂量。钴-60源在放疗中用于发射γ射线治疗肿瘤。

In industry, beta emitters are used in thickness monitoring of paper or metal sheets: a detector on the opposite side measures the amount of radiation transmitted, and any change indicates a variation in thickness. Gamma sources are used to inspect welds and pipelines for internal flaws without damaging the object under test.

在工业中，β放射源用于纸张或金属箔的厚度监测：探测器在另一侧测量穿过材料的辐射量，任何变化都反映厚度的偏差。γ源用于无损检测焊缝和管道内部缺陷。

Carbon-14 dating uses the beta decay of carbon-14 to estimate the age of organic remains up to about 50,000 years old. In a living organism, the ratio of carbon-14 to carbon-12 remains constant because it is continuously replaced. After death, the carbon-14 decays without replenishment, and the measured activity enables the elapsed time to be calculated using the half-life of 5,730 years.

碳-14测年法利用碳-14的β衰变来推算约5万年以内有机遗存的年代。在生物存活期间，碳-14与碳-12的比值保持恒定，因为不断得到补充。死亡后，碳-14不再补充而持续衰减，通过测量剩余活度，用其5,730年的半衰期即可计算逝去的时间。

Published by TutorHao | Physics Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）

Radioactivity | 放射性