📚 Experimental Investigation of Nuclear Energy: Radioactive Decay and Half-Life | 核能实验探究：放射性衰变与半衰期
Nuclear energy is rooted in the transformations that occur within atomic nuclei, and A-Level physics students often explore these principles through controlled laboratory experiments. This article reviews the key experimental approaches used to investigate radioactive decay, absorption of radiation, and the determination of half-life, all within the context of the Oxford AQA International A-Level specification.
核能的基础在于原子核内部发生的转变，A-Level 物理学生通常通过受控的实验室实验来探索这些原理。本文旨在回顾用于研究放射性衰变、辐射吸收以及测定半衰期的关键实验方法，所有内容均基于 Oxford AQA International A-Level 教学大纲的要求。
1. Introduction to Nuclear Energy Experiments | 核能实验简介
Practical investigations in nuclear physics allow students to directly observe the stochastic nature of radioactive decay and to verify fundamental laws such as the inverse square law and exponential decay. These experiments deepen the understanding of concepts like activity, decay constant, and half-life, which are essential for grasping how nuclear energy is harnessed.
核物理的实践探究使学生能够直接观察放射性衰变的随机性质，并验证诸如平方反比定律和指数衰变等基本规律。这些实验加深了对活度、衰变常数和半衰期等概念的理解，而这些概念对于掌握核能如何被利用至关重要。
Typical experiments include measuring the count rate from a gamma source at various distances, absorbing radiation with different materials, and capturing the decay curve of a short-lived isotope such as protactinium-234. Each experiment reinforces the connection between mathematical models and physical reality.
典型的实验包括在不同距离处测量伽马源的计数率、用不同材料吸收辐射，以及捕获短寿命同位素（例如镤-234）的衰变曲线。每个实验都强化了数学模型与物理现实之间的联系。
2. Safety Considerations in Radiation Experiments | 辐射实验的安全注意事项
Before handling any radioactive source, strict safety rules must be followed. Always use tongs or forceps to maintain distance, never point a source at anyone, and keep exposure time to a minimum. Sources must be stored in lead-lined containers when not in use.
在处理任何放射源之前，必须遵守严格的安全规则。务必使用镊子或钳子以保持距离，切勿将源指向任何人，并尽可能缩短暴露时间。不使用时，源必须存放在铅衬容器中。
The inverse square law and absorption experiments require a collimated beam to reduce stray radiation. The laboratory should be well ventilated, and students must wear lab coats and, if necessary, film badges to monitor cumulative exposure.
平方反比定律和吸收实验需要使用准直束以减少杂散辐射。实验室应保持良好通风，学生必须穿着实验服，并在必要时佩戴胶片徽章以监测累积照射量。
For experiments involving protactinium-234 derived from a uranyl nitrate solution, organic solvents are used; therefore, additional chemical safety precautions are required, including the use of fume hoods and protective gloves.
对于涉及从硝酸铀酰溶液中提取镤-234 的实验，会使用有机溶剂；因此，需要额外的化学安全防护措施，包括使用通风橱和防护手套。
3. Equipment: The Geiger-Müller Tube and Counter | 设备：盖革-米勒管与计数器
The central device for detecting nuclear radiation in school laboratories is the Geiger-Müller (GM) tube, coupled to a scaler or ratemeter. The GM tube consists of a cylindrical cathode and a thin central anode wire, filled with low-pressure gas. An applied high voltage (typically 300–500 V) causes each ionising particle to trigger an avalanche discharge, producing a countable pulse.
学校实验室中探测核辐射的核心设备是盖革-米勒（GM）管，连接至定标器或速率计。GM 管由一个圆柱形阴极和一根细的中心阳极丝组成，内部充有低压气体。施加的高压（通常为 300–500 V）使得每个电离粒子触发雪崩放电，产生可计数的脉冲。
A GM tube exhibits a plateau region where the count rate is nearly independent of small voltage variations. Before starting any experiment, it is good practice to determine the operating voltage by plotting a plateau curve and selecting a point in the middle of the plateau.
GM 管存在一个坪区，在该区域内计数率几乎不随电压的微小变化而改变。在开始任何实验之前，最好通过绘制坪曲线来确定工作电压，并选择坪区中点对应的电压值。
4. Measuring Background Radiation | 测量本底辐射
All radiation measurements are superimposed on a background count arising from cosmic rays, naturally occurring radioisotopes in building materials, and radon gas. To obtain the net count rate due to the source alone, the background count must be recorded and subtracted.
所有辐射测量都叠加了一个本底计数，它来自宇宙射线、建筑材料中天然存在的放射性同位素以及氡气。为了获得仅由源产生的净计数率，必须记录并扣除本底计数。
The typical procedure involves taking a long-duration background count (e.g., 10 minutes) without a source present, then calculating the background rate C_bg in counts per second. This value is subtracted from every subsequent measurement.
典型步骤是在没有源的情况下进行长时间的本底计数（例如 10 分钟），然后计算以每秒计数衡量的本底率 C_bg。所有后续测量结果都减去该值。
Uncertainty in the background count follows Poisson statistics; the standard deviation is the square root of the total number of counts. Therefore, longer background measurements reduce the fractional uncertainty.
本底计数的误差遵循泊松统计；标准差是总计数数量的平方根。因此，较长的本底测量时间可以降低相对误差。
5. Experiment 1: Inverse Square Law for Gamma Radiation | 实验一：伽马辐射的平方反比定律
Gamma rays emitted from a point source spread out uniformly in all directions. The intensity I, or the count rate C detected by a GM tube, is inversely proportional to the square of the distance d from the source: C ∝ 1/d².
点源发射的伽马射线在所有方向上均匀扩散。强度 I，或 GM 管检测到的计数率 C，与到源的距离 d 的平方成反比：C ∝ 1/d²。
In the laboratory, a sealed gamma source (e.g., cobalt-60 or caesium-137) is placed in a holder, and a collimator ensures a narrow beam. The GM tube is positioned at different distances d, and the count rate is recorded for a constant time interval each time.
在实验室中，将密封的伽马源（例如钴-60 或铯-137）置于支架上，并使用准直器确保窄束。GM 管放置在不同距离 d 处，每次在相同的时间间隔内记录计数率。
After subtracting the background count, a graph of C against 1/d² should yield a straight line through the origin, confirming the inverse square relationship. Deviations at small distances may arise because the source is not a true point source.
扣除本底计数后，绘制 C 与 1/d² 的关系图应得到一条通过原点的直线，从而证实平方反比关系。在短距离处的偏差可能由于源并非真正的点源所致。
6. Experiment 2: Absorption of Radiation by Matter | 实验二：物质对辐射的吸收
When a beam of beta particles or gamma rays passes through matter, its intensity decreases exponentially with thickness x: I = I₀ e⁻μˣ, where μ is the linear attenuation coefficient. The half-value thickness x₁/₂ is the thickness required to reduce the intensity by half and is given by x₁/₂ = ln2/μ.
当一束 β 粒子或 γ 射线穿过物质时，其强度随厚度 x 呈指数衰减：I = I₀ e⁻μˣ，其中 μ 是线性衰减系数。半值厚度 x₁/₂ 是将强度减半所需的厚度，由 x₁/₂ = ln2/μ 给出。
In this experiment, thin aluminium or lead plates of known thickness are placed between the source and the detector. The corrected count rate is measured for each added thickness, keeping the geometry constant.
在本实验中，将已知厚度的薄铝板或铅板放置在源和探测器之间。每次增加厚度时测量经修正的计数率，并保持几何条件不变。
Plotting ln(C) against x yields a straight line with gradient −μ, from which μ and x₁/₂ can be determined. This exercise helps students appreciate how shielding materials are selected for nuclear reactors and medical applications.
绘制 ln(C) 随 x 的变化图可得到一条斜率为 −μ 的直线，从中可以确定 μ 和 x₁/₂。该练习有助于学生理解如何为核反应堆和医疗应用选择屏蔽材料。
7. Experiment 3: Determining the Half-Life of Protactinium-234 | 实验三：测定镤-234 的半衰期
A classic A-Level experiment uses a solvent extraction technique to isolate protactinium-234 from a uranyl nitrate solution. Uranium-238 decays to thorium-234, which then beta-decays to protactinium-234 (half-life approximately 70 seconds). Protactinium is extracted into an organic layer and its decay can be followed in real time.
一个经典的 A-Level 实验利用溶剂萃取技术从硝酸铀酰溶液中分离出镤-234。铀-238 衰变成钍-234，钍-234 再经 β 衰变成镤-234（半衰期约为 70 秒）。镤被萃取到有机层中，可以实时跟踪其衰变过程。
After shaking the mixture and allowing the layers to separate, the organic phase, which now contains protactinium, is placed near the GM tube. The count rate is recorded every 10 or 15 seconds without interruption.
摇动混合物并待分层后，将含有镤的有机相放置在 GM 管附近。每间隔 10 或 15 秒不中断地记录计数率。
The recorded data, after background subtraction, are used to plot a decay curve. The exponential nature is verified, and the half-life is found by reading the time interval over which the count rate halves several times and taking an average.
经本底扣除后，记录的数据用于绘制衰变曲线。验证其指数性质，并通过多次读取计数率减半所需的时间间隔并取平均值来求得半衰期。
8. Data Analysis and Graphical Methods | 数据分析与绘图方法
For the protactinium experiment, a more accurate half-life is obtained by linearising the exponential decay equation. Since A = A₀ e⁻λᵗ, where A is the activity (proportional to corrected count rate C), taking the natural logarithm gives ln(C) = ln(C₀) − λt.
对于镤实验，通过对指数衰变方程进行线性化可以得到更准确的半衰期。由于 A = A₀ e⁻λᵗ，其中 A 为活度（与修正后的计数率 C 成正比），取自然对数可得 ln(C) = ln(C₀) − λt。
Plotting ln(C) versus time t yields a straight line of slope −λ. The decay constant λ is extracted, and the half-life is calculated as T₁/₂ = ln2 / λ. This method reduces the influence of random fluctuations compared to direct reading from the curve.
绘制 ln(C) 随时间 t 的变化图可得到斜率为 −λ 的直线。提取出衰变常数 λ，然后通过 T₁/₂ = ln2 / λ 计算半衰期。与直接从曲线上读取相比，该方法可减少随机涨落的影响。
In absorption experiments, the linear fit of ln(C) against x is similarly robust. Students should be able to calculate uncertainties in gradient and intercept using standard techniques.
在吸收实验中，ln(C) 随 x 变化的线性拟合同样可靠。学生应能运用标准方法计算斜率和截距的误差。
9. Sources of Uncertainty and Error | 误差与不确定度来源
Random uncertainties in radiation experiments are dominated by counting statistics. The standard uncertainty on a count of N is √N, so the fractional uncertainty becomes smaller at larger count totals. To improve precision, students should accumulate at least 400 counts for each measurement or extend the counting time.
辐射实验中的随机误差主要由计数统计主导。N 计数量的标准不确定度为 √N，因此计数总量越大，相对误差越小。为提高精密度，学生每次测量应至少累积 400 个计数，或延长计数时间。
Systematic errors may arise from the dead time of the GM tube at very high count rates, inaccurate distance measurement, scattering from surroundings, and incomplete separation of protactinium. Dead time correction may be necessary if the observed count rate exceeds a few hundred per second.
系统误差可能源自 GM 管在极高计数率下的死时间、距离测量不准确、周围环境的散射以及镤的不完全分离。若观测到的计数率超过每秒数百个，则可能需要进行死时间校正。
Controlling geometry is vital; the source, absorber sheets, and detector window must be aligned precisely. Even small misalignments can alter the effective thickness and the solid angle.
控制几何条件至关重要；源、吸收片和探测器窗口必须精确对直。即使是微小的未对准也可能改变有效厚度和立体角。
10. Conclusion and Real-World Context | 总结与真实世界背景
These experimental investigations provide tangible evidence for the abstract models students encounter in nuclear physics. From verifying the inverse square law to measuring the short half-life of protactinium-234, each activity develops practical skills and reinforces theoretical concepts central to nuclear energy.
这些实验探究为学生遇到的核物理抽象模型提供了切实的证据。从验证平方反比定律到测量镤-234 的短暂半衰期，每项活动都培养了实践技能，并强化了对核能至关重要的理论概念。
Understanding how radiation interacts with matter is fundamental for the safe operation of nuclear power plants, the design of radiation shielding, and medical imaging techniques. The half-life concept governs the management of nuclear waste and the radiological safety of workers and the public.
理解辐射如何与物质相互作用，对于核电站的安全运行、辐射屏蔽设计以及医学成像技术至关重要。半衰期的概念支配着核废料的管理以及工作人员和公众的辐射安全。
Through careful experimental design and rigorous data analysis, A-Level students gain not only exam-ready knowledge but also an appreciation of how science informs the responsible use of nuclear energy.
通过精心的实验设计和严格的数据分析，A-Level 学生不仅获得了应试知识，还体会到科学如何为核能的负责任利用提供依据。
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