Radioactivity and Nuclear Decay for Edexcel A Level Physics | 放射性衰变与核辐射

📚 Radioactivity and Nuclear Decay for Edexcel A Level Physics | 放射性衰变与核辐射

Radioactivity is the spontaneous disintegration of an unstable atomic nucleus, resulting in the emission of ionising radiation. In the Edexcel A Level Physics specification, this topic links nuclear structure, decay equations, half-life calculations and the safe use of radioisotopes in medicine and industry. A good understanding of these ideas is essential for both written papers and practical-based questions on activity, background radiation and risk assessment.

放射性是不稳定原子核自发衰变并发射电离辐射的过程。在 Edexcel A Level 物理考试大纲中，这一主题将核结构、衰变方程、半衰期计算以及放射性同位素在医学和工业中的安全应用联系在一起。扎实掌握这些概念对于笔试以及涉及活度、背景辐射和风险评估的题目都至关重要。

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1. The Nature of Radioactivity | 放射性的本质

An unstable nucleus becomes more stable by emitting radiation. Stability depends mainly on the balance between protons and neutrons, often described by the N/Z ratio, where N is the neutron number and Z is the proton number. Light stable nuclei tend to have N approximately equal to Z, but heavier stable nuclei require a greater proportion of neutrons to reduce electrostatic repulsion between protons.

不稳定的原子核通过发射辐射变得更稳定。稳定性主要取决于质子与中子之间的平衡，通常用 N/Z 比来描述，其中 N 是中子数，Z 是质子数。较轻的稳定核往往 N 与 Z 大致相等，但较重的稳定核需要更高比例的中子，以减弱质子之间的静电排斥力。

If a nucleus lies outside the band of stability, it will undergo radioactive decay. The three main types of radiation emitted are alpha particles, beta particles and gamma rays. Each type has a different nature, charge, penetrating power and ionising ability.

如果原子核位于稳定带之外，它就会发生放射性衰变。所发射的辐射主要有三种：α 粒子、β 粒子和 γ 射线。每种辐射的性质、电荷、穿透能力和电离能力各不相同。

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2. Types of Nuclear Radiation | 核辐射的类型

Alpha radiation consists of helium nuclei, each containing two protons and two neutrons. An alpha particle is therefore written as ⁴₂He²⁺ or simply ⁴₂He. Beta radiation can be beta-minus, which is a fast electron written as ⁰₋₁e, or beta-plus, which is a positron written as ⁰₊₁e. Gamma radiation is high-energy electromagnetic radiation with no mass and no charge, often emitted after alpha or beta decay when a daughter nucleus is left in an excited state.

α 辐射由氦核组成，每个氦核含有两个质子和两个中子。因此 α 粒子写作 ⁴₂He²⁺，或简写为 ⁴₂He。β 辐射可以是 β⁻，它是一种快速电子，写作 ⁰₋₁e；也可以是 β⁺，它是一种正电子，写作 ⁰₊₁e。γ 辐射是一种高能电磁辐射，没有质量也没有电荷，通常在 α 或 β 衰变后子核处于激发态时发射。

The table below summarises the key properties of the three radiations.

下表总结了这三种辐射的主要性质。

Property | 性质	Alpha α | α 粒子	Beta β | β 粒子	Gamma γ | γ 射线
Nature | 本质	Helium nucleus ⁴₂He | 氦核 ⁴₂He	Fast electron or positron | 快速电子或正电子	Electromagnetic wave | 电磁波
Charge | 电荷	+2e | +2e	-e or +e | -e 或 +e	0 | 0
Penetrating power | 穿透能力	Low, stopped by paper or skin | 低，纸张或皮肤可阻挡	Medium, stopped by a few mm of aluminium | 中等，几毫米铝可阻挡	High, reduced by several cm of lead | 高，几厘米铅只能减弱
Ionising ability | 电离能力	Very high | 非常高	Medium | 中等	Low | 低

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3. Penetrating Power and Ionising Ability | 穿透力与电离能力

Ionising ability and penetrating power are inversely related. Alpha particles are the most ionising because they have a large mass, a double positive charge and a relatively slow speed. They lose energy rapidly in collisions with air molecules, so their range in air is only a few centimetres and they are stopped by a sheet of paper.

电离能力与穿透能力成反比。α 粒子电离能力最强，因为它们质量大、带两个正电荷且速度相对较慢。它们在空气中与分子碰撞时迅速损失能量，因此在空气中的射程只有几厘米，一张纸就能将其阻挡。

Beta particles are much less ionising than alpha particles but more penetrating. Their range in air is typically around one metre, and they can pass through paper but are stopped by a few millimetres of aluminium. Gamma rays are weakly ionising but highly penetrating. They are electromagnetic waves, so they can travel long distances in air and require several centimetres of lead or thick concrete for significant reduction.

β 粒子的电离能力比 α 粒子弱得多，但穿透能力更强。它们在空气中的射程通常约为一米，可以穿过纸张，但会被几毫米厚的铝片阻挡。γ 射线电离能力较弱，但穿透能力很强。它们是电磁波，因此可以在空气中传播很长的距离，需要几厘米厚的铅板或厚混凝土才能显著减弱。

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4. Nuclear Decay Equations | 核衰变方程

In every nuclear decay equation, both the total nucleon number A and the total proton number Z must be conserved. Alpha decay reduces the mass number by 4 and the proton number by 2. For example, uranium-238 decays by alpha emission to thorium-234:

在每一个核衰变方程中，总核子数 A 和总质子数 Z 都必须守恒。α 衰变使质量数减少 4，质子数减少 2。例如，铀-238 通过 α 衰变生成钍-234：

²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He

Beta-minus decay occurs when a neutron in the nucleus changes into a proton, an electron and an antineutrino. The electron is emitted as a beta-minus particle. The proton number increases by 1, but the mass number stays the same. Carbon-14 decays by beta-minus emission to nitrogen-14:

β⁻ 衰变发生在原子核内的一个中子转变为质子、电子和反中微子时。该电子以 β⁻ 粒子形式发射。质子数增加 1，但质量数保持不变。碳-14 通过 β⁻ 衰变生成氮-14：

¹⁴₆C → ¹⁴₇N + ⁰₋₁e + ν̅ₑ

Beta-plus decay occurs when a proton changes into a neutron, a positron and a neutrino. The positron is emitted as a beta-plus particle. The proton number decreases by 1, while the mass number remains unchanged. Fluorine-18 is a common positron emitter used in PET scans.

β⁺ 衰变发生在一个质子转变为中子、正电子和中微子时。正电子以 β⁺ 粒子形式发射。质子数减少 1，而质量数保持不变。氟-18 是 PET 扫描中常用的正电子发射体。

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5. Alpha Decay in Detail | α 衰变详解

Alpha decay is the preferred decay mode for many heavy nuclei with proton numbers greater than 83, such as uranium, radium and polonium. The emission of an alpha particle removes two protons and two neutrons from the parent nucleus, which reduces both the electrostatic repulsion and the N/Z imbalance, thereby increasing nuclear stability.

α 衰变是许多质子数大于 83 的重核（如铀、镭和钋）优先选择的衰变方式。发射一个 α 粒子会从母核中带走两个质子和两个中子，这既减少了静电排斥力，也改善了 N/Z 比失衡，从而提高了核稳定性。

Alpha particles are emitted with discrete kinetic energies, typically between 4 MeV and 9 MeV. Because the energy is discrete, alpha spectra are line spectra. This was important historical evidence for the existence of discrete nuclear energy levels.

α 粒子以离散的动能发射，通常在 4 MeV 至 9 MeV 之间。由于能量是离散的，α 能谱为线状谱。这是历史上证明原子核存在离散能级的重要证据。

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6. Beta-minus and Beta-plus Decay | β⁻ 与 β⁺ 衰变

Beta-minus decay is common in neutron-rich nuclei, where the N/Z ratio is too high. Inside the nucleus, a down quark in a neutron changes into an up quark, transforming the neutron into a proton. This is mediated by the weak interaction and produces an electron and an electron antineutrino.

β⁻ 衰变常见于中子过多的核素，此时 N/Z 比过高。在原子核内部，中子里的一个下夸克变为上夸克，使中子转变为质子。这一过程由弱相互作用介导，并产生一个电子和一个电子反中微子。

Beta-plus decay is common in proton-rich nuclei, where the N/Z ratio is too low. A proton changes into a neutron, emitting a positron and an electron neutrino. Positron emitters are used in medical imaging because the emitted positron annihilates with an electron to produce two gamma photons travelling in opposite directions.

β⁺ 衰变常见于质子过多的核素，此时 N/Z 比过低。一个质子转变为中子，发射一个正电子和一个电子中微子。正电子发射体用于医学成像，因为发射出的正电子与电子湮灭，产生两个沿相反方向运动的 γ 光子。

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7. Gamma Emission and Energy Levels | γ 发射与能级

After alpha or beta decay, the daughter nucleus is often in an excited state. The nucleus can lose this excess energy by emitting a gamma photon. Gamma emission does not change the proton number or the mass number, so it is usually represented by the same nuclide symbol before and after emission.

α 或 β 衰变后，子核通常处于激发态。原子核可以通过发射 γ 光子来释放多余的能量。γ 发射不会改变质子数或质量数，因此发射前后的核素符号通常相同。

The gamma photon energy is equal to the difference between two nuclear energy levels. For example, cobalt-60 undergoes beta-minus decay to an excited nickel-60 nucleus, which then emits two gamma photons with energies of about 1.17 MeV and 1.33 MeV. This gamma radiation is widely used in radiotherapy and industrial radiography.

γ 光子的能量等于两个核能级之间的能量差。例如，钴-60 经 β⁻ 衰变生成激发态的镍-60 核，随后发射两个能量约为 1.17 MeV 和 1.33 MeV 的 γ 光子。这种 γ 辐射广泛用于放射治疗和工业射线照相。

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8. Half-life and Exponential Decay | 半衰期与指数衰减

Radioactive decay is a random and spontaneous process. The number of undecayed nuclei N in a sample decreases exponentially with time t according to the equation:

放射性衰变是一个随机且自发的过程。样品中未衰变的原子核数 N 随时间 t 按指数规律减少，遵循方程：

N = N₀ e^(−λt)

where N₀ is the initial number of nuclei and λ is the decay constant, measured in s⁻¹. The decay constant represents the probability of decay per unit time for a given nucleus.

其中 N₀ 是初始原子核数，λ 是衰变常数，单位为 s⁻¹。衰变常数表示一个给定原子核在单位时间内发生衰变的概率。

The half-life T½ is the time taken for the number of undecayed nuclei to fall to half its initial value. It is related to the decay constant by:

半衰期 T½ 是未衰变原子核数减少到初始值一半所需的时间。它与衰变常数的关系为：

T½ = ln 2 / λ

Half-lives 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 only 1.6 × 10⁻⁴ s.

半衰期从不到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 的半衰期仅为 1.6 × 10⁻⁴ 秒。

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9. Activity and the Decay Constant | 活度与衰变常数

The activity A of a radioactive source is the number of decays per unit time. It is measured in becquerels, where 1 Bq equals one decay per second. Activity is proportional to the number of undecayed nuclei, as shown by the equation:

放射源的活度 A 是单位时间内发生的衰变次数。其单位为贝克勒尔，1 Bq 等于每秒一次衰变。活度与未衰变原子核数成正比，如下式所示：

A = λN

Because N decreases exponentially, the activity also decreases exponentially with time. This means the count rate from a detector, after correcting for background radiation, follows the same exponential law:

由于 N 呈指数下降，活度也随时间呈指数下降。这意味着探测器测得的计数率，在扣除背景辐射后，遵循相同的指数规律：

C = C₀ e^(−λt)

In experiments, students often plot ln C against t. This produces a straight line with gradient −λ and y-intercept ln C₀, allowing the decay constant and half-life to be determined.

在实验中，学生通常绘制 ln C 对 t 的图像。该图像为一条直线，斜率为 −λ，y 轴截距为 ln C₀，由此可以求出衰变常数和半衰期。

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10. Background Radiation and Sources | 背景辐射与来源

Background radiation is the ionising radiation that is always present in the environment. Its main sources include radon gas from rocks and soil, cosmic rays from space, medical procedures such as X-rays and nuclear medicine, and naturally occurring radioactive isotopes in food and building materials.

背景辐射是环境中始终存在的电离辐射。其主要来源包括来自岩石和土壤的氡气、来自太空的宇宙射线、X 射线和核医学等医疗程序，以及食物和建筑材料中天然存在的放射性同位素。

In any experiment measuring radioactive decay, the background count rate must be subtracted from the measured count rate to obtain the corrected count rate from the source alone. Background radiation also sets a lower limit on the activity that can be detected reliably.

在任何测量放射性衰变的实验中，都必须从测得的计数率中扣除背景计数率，才能得到仅由放射源产生的修正计数率。背景辐射还决定了能够可靠检测到的最低活度。

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11. Uses of Radioisotopes in Medicine and Industry | 放射性同位素在医学和工业中的用途

Radioisotopes have many important applications. In medicine, gamma emitters such as technetium-99m are used as tracers because gamma rays can escape the body and be detected externally. Technetium-99m has a half-life of about 6 hours, which is long enough for imaging but short enough to limit patient dose.

放射性同位素有许多重要应用。在医学上，锝-99m 等 γ 发射体被用作示踪剂，因为 γ 射线可以穿出体外并被外部探测器检测。锝-99m 的半衰期约为 6 小时，既足够完成成像，又足够短以限制患者的辐射剂量。

Gold-198 is another medical radioisotope, used in the treatment of certain cancers. It decays by beta-minus emission with a half-life of about 2.7 days and also emits gamma radiation, allowing its distribution to be monitored. Small grains of gold-198 can be implanted directly into a tumour to deliver a localised radiation dose.

金-198 是另一种医用放射性同位素，用于治疗某些癌症。它以 β⁻ 衰变方式衰变，半衰期约为 2.7 天，同时还发射 γ 辐射，因此可以监测其分布。可将微小的金-198 颗粒直接植入肿瘤内，以提供局部辐射剂量。

In industry, gamma sources such as cobalt-60 are used to inspect metal welds and detect cracks in pipelines. Alpha sources such as americium-241 are used in smoke detectors because alpha particles ionise air molecules and allow a small current to flow. When smoke enters the detector, it absorbs alpha particles and reduces the current, triggering the alarm.

在工业上，钴-60 等 γ 源用于检查金属焊缝和检测管道裂纹。镅-241 等 α 源用于烟雾探测器，因为 α 粒子电离空气分子，允许微小电流通过。当烟雾进入探测器时，它会吸收 α 粒子并减小电流，从而触发报警。

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12. Safety, Hazards and Risk Assessment | 安全、危害与风险评估

Ionising radiation can damage living cells by breaking chemical bonds and causing mutations in DNA. High doses can cause radiation burns, radiation sickness and an increased risk of cancer. The hazard from a radioactive source depends on the type of radiation, its activity, the distance from the source and the duration of exposure.

电离辐射会破坏化学键并引起 DNA 突变，从而损伤活细胞。高剂量可导致辐射灼伤、辐射病并增加癌症风险。放射源的危害取决于辐射类型、活度、与源的距离以及受照时间。

The main safety precautions are to keep sources in lead-lined containers, handle them with long tongs, point them away from people, minimise exposure time and never bring a source close to the eyes. In school experiments, sealed sources with low activity are always used, and the background count rate is recorded before and after the experiment.

主要的安全预防措施包括：将放射源存放在铅衬容器中、使用长柄钳操作、使源远离人员、尽量减少受照时间，并且绝不可将源靠近眼睛。在学校实验中，始终使用低活度密封源，并在实验前后记录背景计数率。

Risk assessments must consider the inverse square law for gamma radiation, which states that intensity I decreases with distance r according to I ∝ 1/r². Doubling the distance from a gamma source reduces the intensity to one quarter, so increasing distance is a very effective way to reduce exposure.

风险评估必须考虑 γ 辐射的平方反比定律，即强度 I 随距离 r 按 I ∝ 1/r² 减小。离 γ 源的距离加倍，强度会降至原来的四分之一，因此增大距离是减少受照量的非常有效的方法。

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