📚 A-Level WJEC Physics: Radioactive Decay Revision | 放射性衰变考点精讲
Radioactive decay is a fundamental concept in the WJEC A-Level Physics specification, describing how unstable nuclei spontaneously transform into more stable configurations by emitting particles or electromagnetic radiation. A thorough understanding of decay types, exponential mathematics, half-life, activity, and practical applications such as radioactive dating is essential for success in both the written examination and practical assessments. This revision guide breaks down every key point, pairing clear English explanations with their Chinese counterparts to reinforce bilingual comprehension.
放射性衰变是WJEC A-Level物理课程的核心内容，描述不稳定原子核通过释放粒子或电磁辐射自发转变为更稳定结构的过程。深入理解衰变类型、指数数学、半衰期、活度以及放射性测年等实际应用，对于笔试和实验考核都至关重要。本考点精讲将每个关键点拆解为双语对照，帮助您牢固掌握。
1. Types of Radioactive Decay | 衰变类型
Unstable nuclei can undergo several distinct decay modes. Alpha (α) decay involves the emission of a helium nucleus (²⁴₂He), reducing the mass number by 4 and the atomic number by 2. Beta-minus (β⁻) decay occurs when a neutron converts into a proton, emitting an electron (⁰₋₁e) and an antineutrino (ν̅); this increases the atomic number by 1 while leaving the mass number unchanged. Beta-plus (β⁺) decay happens in proton-rich nuclei, where a proton becomes a neutron, releasing a positron (⁰₊₁e) and a neutrino (ν), decreasing the atomic number by 1. Gamma (γ) decay follows alpha or beta decays, releasing excess energy as a high-energy photon without altering mass or atomic numbers.
不稳定原子核可发生几种不同的衰变模式。α衰变释放氦核（⁴₂He），质量数减少4，原子序数减少2。β⁻衰变发生于中子转化为质子时，释放电子（⁰₋₁e）和反中微子（ν̅），原子序数增加1而质量数不变。β⁺衰变发生在富质子核中，质子转化为中子，释放正电子（⁰₊₁e）和中微子（ν），原子序数减少1。γ衰变通常跟随α或β衰变，以高能光子形式释放多余能量，不改变质量数和原子序数。
| Decay | Particle | Effect on A, Z | Penetration |
|---|---|---|---|
| α | ⁴₂He | A ↓4, Z ↓2 | Low (stopped by paper) |
| β⁻ | ⁰₋₁e | A →, Z ↑1 | Medium (stopped by Al) |
| β⁺ | ⁰₊₁e | A →, Z ↓1 | Medium (annihilation) |
| γ | photon | no change | High (reduced by thick Pb) |
nium-238: ²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He, and the beta decay of carbon-14: ¹⁴₆C → ¹⁴₇N + ⁰₋₁e + ν̅.
理解这些特征变化对于书写平衡的核反应方程至关重要。例如，铀-238的衰变：²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He，以及碳-14的β衰变：¹⁴₆C → ¹⁴₇N + ⁰₋₁e + ν̅。
2. Decay Equations and Conservation Laws | 衰变方程与守恒定律
In all nuclear processes, total charge and mass number (nucleon number) are strictly conserved. Write the parent nuclide on the left and the daughter plus emissions on the right, ensuring the sum of upper indices (mass numbers) and lower indices (atomic numbers) are equal on both sides. For beta decays, an antineutrino or neutrino carries away some energy and momentum, ensuring the conservation of lepton number. Gamma emission has no effect on these numbers but adjusts the energy state of the nucleus.
在所有核反应过程中，总电荷数和质量数（核子数）严格守恒。将母核写在左侧，子核和发射粒子写在右侧，确保两边的上标之和（质量数）与下标之和（原子序数）分别相等。在β衰变中，反中微子或中微子带走部分能量和动量，保证了轻子数守恒。γ发射对这些数字无影响，但调整核的能量状态。
The law of conservation of momentum also applies: the emitted particle and the recoiling daughter nucleus move in opposite directions with momenta of equal magnitude. When solving problems, always check that the equation balances numerically and that the emitted particle matches the decay type predicted by the N-Z ratio.
动量守恒定律同样适用：发射粒子与反冲子核以大小相等、方向相反的动量运动。解题时，始终检查方程数值是否平衡，发射粒子是否符合N-Z比所预言的衰变类型。
3. Activity and the Becquerel | 活度与贝克勒尔
a radioactive sample is defined as the number of decays per unit time. Mathematically, A = – y constant unique to each nuclide. As N decreases exponentially, activity follows the same exponential trend.
放射性样品的活度（A）定义为单位时间内的衰变次数。数学上，A = –dN/dt，其中N为尚未衰变的原子核数目。其SI单位是贝克勒尔（Bq），相当于每秒一次衰变。活度与现存的不稳定核数目成正比：A = λN，其中λ是每个核素特有的衰变常数。随着N呈指数衰减，活度也遵循相同的指数趋势。
from measured count rate to obtain the true activity of a source. Detectors like Geiger-Mür tubes record counts, which are then converted to activity by accounting for the detector' A = λN allows you to relate half-life, decay constant, and the amount of material present.
在实际实验中，必须从测量计数率中减去背景计数率才能得到放射源的真实活度。盖格-米勒管等探测器记录计数，再通过考虑探测效率转换为活度。掌握A = λN能帮助您将半衰期、衰变常数和材料数量联系起来。
4. Half-life and the Decay Constant | 半衰期与衰变常数
active source. The relationship is derived directly from the exponential decay law: when N = N₀/2, e⁻λT½ = 1/2.
半衰期（T½）是样品中一半放射性核发生衰变所需的时间。它与衰变常数的关系为 T½ = ln 2 / λ。衰变常数λ表示单个核在单位时间内发生衰变的概率。λ越大意味着半衰期越短，放射源活度越高。该关系从指数衰变定律直接推导得出：当N = N₀/2时，e⁻λT½ = 1/2。
A common misconception is that after two half-lives all nuclei have decayed; actually, 1/4 of the original nuclei remain. Half-life is independent of the initial number of nuclei and is a characteristic of the isotope, making it a powerful tool for dating and identification.
常见的误解是经过两个半衰期后所有核都已衰变；实际上，还有原核数的1/4剩余。半衰期与初始核数目无关，是同位素的特征属性，这使其成为测年和识别的有力工具。
5. Exponential Decay Law | 指数衰变规律
proportional to the number present, leading to a first-order differential equation dN/dt = –λN.
经过时间t后尚未衰变的原子核数目N遵循指数衰减规律：N = N₀ e⁻λᵗ，其中N₀为初始核数目。同位素的质量m和活度A也服从相同的数学形式：m = m₀ e⁻λᵗ，A = A₀ e⁻λᵗ。这一规律的根源在于每次衰变相互独立，且衰变速率与当前数目成正比，导致一阶微分方程 dN/dt = –λN。
N = N₀ e⁻λᵗ
A = A₀ e⁻λᵗ
To linearise the data, take the natural logarithm: ln N = ln N₀ – λt. A plot of ln(N) against time yields a straight line with gradient – WJEC practical contexts, where students measure count rates and deduce the decay constant.
对数据线性化可取自对数：ln N = ln N₀ – λt。以ln(N)对时间作图将得到一条直线，其斜率为–λ，截距为ln N₀。这在WJEC的实验背景中常被考查，学生需要测量计数率并推导出衰变常数。
6. Determining Half-life from Graphs | 从图像确定半衰期
tency, which confirms the decay is truly exponential. If the graph is plotted on semi-log paper or transformed to a log-linear plot, the half-life can be extracted from the gradient: λ = –gradient, and T½ = ln2 / λ.
若将活度或计数率对时间作图，得到一条指数衰减曲线。要直接求出半衰期，可在曲线上任选一点，记录时刻，然后找出活度降为一半时的时间，两者之差即为T½。重复几个不同起点以确认一致性，这验证了衰减确实是指数型的。如果使用半对数纸绘图或转换为对数-线性图，则可从斜率提取半衰期：λ = –斜率，T½ = ln2 / λ。
WJEC exam questions frequently provide a table of count rate vs time and ask candidates to plot the data, determine the half-life, and comment on uncertainties. Remember to correct for background radiation before analysis, otherwise the gradient will be skewed and half-life underestimated.
WJEC考题常提供计数率-时间数据表，要求考生作图、确定半衰期并评述不确定度。务必在分析之前扣除背景辐射，否则斜率将发生偏移，半衰期会被低估。
7. Radioactive Dating | 放射性测年
n2) × ln(N₀ / N), where N₀ is the initial activity (approximated by the activity of a modern sample) and N is the current activity. Other isotopes, such as uranium-238 to lead-206, are used for dating rocks over geological timescales.
碳-14测年是指数衰变的经典应用。活生物体与大气交换碳元素，保持稳定的¹⁴C与¹²C比例。死亡后摄入停止，¹⁴C以5730年的半衰期衰变。样品年代由公式 t = (T½ / ln2) × ln(N₀ / N) 计算，其中N₀为初始活度（可用现代样品活度近似），N为当前活度。其他同位素，如铀-238至铅-206，用于地质时间尺度的岩石测年。
t = (T½ / ln 2) × ln(N₀ / N)
Reliability depends on assuming that the initial ¹⁴C/¹²C ratio has remained constant and that the sample has not been contaminated. For WJEC, you should be able to manipulate the decay equations to solve for t, given appropriate data, and discuss the limitations of the method.
可靠性取决于假设初始¹⁴C/¹²C比保持恒定以及样品未被污染。在WJEC考试中，您应能运用衰变方程求解年代t，并根据给定数据讨论方法的局限性。
8. Background Radiation and Safety | 背景辐射与安全
Background radiation originates from cosmic rays, rocks (e.g., granite), radon gas, food, and medical procedures. It contributes a count rate that must be subtracted from all measurements. Radiation safety follows three core principles: time, distance, and shielding. Minimise exposure time, maximise distance from the source (inverse-square law for gamma), and use appropriate absorbers (paper for alpha, aluminium for beta, lead/concrete for gamma). In addition, sealed sources should be handled with tongs and never pointed at people.
背景辐射来自宇宙射线、岩石（如花岗岩）、氡气、食物和医疗过程。它产生的计数率必须从所有测量中扣除。辐射安全遵循三大原则：时间、距离和屏蔽。尽可能缩短暴露时间，增大与源的距离（γ射线遵循平方反比律），并使用适当的吸收体（α用纸、β用铝、γ用铅/混凝土）。此外，密封源应用长柄钳操作，切勿指向他人。
Dosimeters monitor cumulative exposure, and the effective dose is measured in sieverts (Sv). You should recall that ionising radiation can damage DNA and cause cancer, but the risk is minimised by sticking to the ALARA principle – 'as low as reasonably achievable'. WJEC may ask about safety precautions in a laboratory context involving radioactive sources.
剂量计监测累积暴露量，有效剂量以希沃特（Sv）为单位。您应记住电离辐射可损伤DNA并引发癌症，但坚持ALARA原则——"尽可能合理地低"——可将风险降至最低。WJEC可能考查在实验室中使用放射源的安全预防措施。
9. Nuclear Stability and the N-Z Curve | 核稳定性与N-Z曲线
neutron number (N) against proton number (Z) for stable isotopes reveals a characteristic 'band of stability' line. Nuclides above the stability band have too many neutrons and often undergo β⁻ decay; those below the band are proton-rich and tend to undergo β⁺ decay or electron capture. Very heavy nuclei (Z > 82) often decay via alpha emission, shedding both protons and neutrons to move closer to stability.
稳定同位素的中子数（N）对质子数（Z）图呈现一条特征性的"稳定带"。轻的稳定核位于N ≈ Z线附近，但随着Z增大，需要更多的中子来克服增大的质子间静电斥力，曲线因此弯向N = Z线上方。位于稳定带以上的核素有过多中子，常发生β⁻衰变；位于带以下的核素富含质子，倾向于发生β⁺衰变或电子俘获。极重核（Z>82）常通过释放α粒子进行衰变，同时减少质子和中子以趋向稳定。
sotopes is limited and why technetium (Z=43) and promethium (Z=61) have no stable isotopes—they fall in a gap of the stability band.
理解N-Z曲线使您能够预测未知同位素可能的衰变模式，并解释为何某些原子核不稳定。该曲线也说明了为什么稳定同位素的数量有限，以及为什么锝（Z=43）和钷（Z=61）没有稳定同位素——它们位于稳定带的空隙中。
10. Binding Energy and Decay Energy | 结合能与衰变能
c². For alpha decay to occur spontaneously, the mass of the parent must be greater than the total mass of the products. This is equivalent to a positive Q-value, and the released energy is shared as kinetic energy of the alpha particle and the recoil nucleus.
虽然结合能是独立子题目，但它与放射性衰变直接相关。衰变中释放的能量（Q值）来源于母核与子核及发射粒子总质量之间的差异，通过 E = mc² 转换。要使α衰变自发发生，母核质量必须大于产物总质量。这等价于正Q值，释放的能量以α粒子和反冲核的动能形式分配。
mass units u) to energy using the conversion 1 u ≈ 931.5 MeV, and pay attention to units.
在WJEC考题中，您可能需要运用给定的原子质量计算衰变释放的能量或判断某一衰变是否在能量上可行。务必使用转换关系 1 u ≈ 931.5 MeV 将质量亏损（以原子质量单位u计）换算为能量，并注意单位。
ΔE = Δm c²
The binding energy per nucleon curve explains why both fusion of light nuclei and fission of heavy nuclei release energy, but radioactive decay of an individual unstable nucleus simply releases the excess energy necessary to reach a more stable configuration.
比结合能曲线解释了为什么轻核聚变和重核裂变都能释放能量，而单个不稳定核的放射性衰变仅仅是释放达到更稳定构型所需的多余能量。
Published by TutorHao | Physics Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图