📚 Experimental Investigations into Particles, Radiation and Radioactivity | 粒子、辐射与放射性的实验探究
Experimental work is central to understanding the behaviour of particles, the nature of radiation, and the principles of radioactivity. In the Oxford AQA International AS Physics course, practical investigations help bridge the gap between theoretical concepts and observable phenomena. This article outlines key experiments, from using a Geiger–Müller tube to simulating decay, reinforcing statistical analysis and safe laboratory practice.
实验操作是理解粒子行为、辐射本质以及放射性原理的核心。在 Oxford AQA 国际 AS 物理课程中，实践探究帮助弥合理论概念与可观察现象之间的差距。本文概述了一系列关键实验，从使用盖革‑米勒管到模拟衰变，强化统计分析和安全的实验室操作。
1. Introduction to Particle and Radiation Experiments | 粒子与辐射实验简介
Particle and radiation experiments allow us to detect and measure emissions from radioactive sources. These investigations reveal the different penetrating abilities of alpha, beta, and gamma radiation, the random nature of decay, and the exponential decrease in activity over time. Careful experimental design, including control of distances, shielding, and time intervals, is essential for obtaining reliable data.
粒子与辐射实验使我们能够探测和测量来自放射源的发射。这些探究揭示了α、β和γ辐射不同的穿透能力、衰变的随机性以及活度随时间的指数衰减。仔细的实验设计，包括对距离、屏蔽和时间间隔的控制，对于获得可靠数据至关重要。
2. Using a Geiger–Müller Tube and Counter | 使用盖革‑米勒管与计数器
A Geiger–Müller (GM) tube is the primary detector for ionising radiation. The tube contains a low‑pressure gas and a high voltage between a central wire anode and the outer cathode. When radiation enters the tube through a thin mica window, it ionises gas atoms, triggering an avalanche of electrons. Each avalanche produces a brief current pulse, which is counted by a scaler or connected to a data logger. The tube must be operated at its plateau voltage, where small voltage changes do not affect the count rate, and the dead time of the detector should be taken into account for high count rates.
盖革‑米勒管（GM 管）是电离辐射的主要探测器。管中含有低压气体，中心丝状阳极与外层阴极之间施加高压。当辐射通过薄云母窗进入管内时，使气体原子电离，触发电子的雪崩效应。每次雪崩产生一个短暂的电流脉冲，由定标器计数或通过数据记录器采集。管必须在坪电压下工作，此时电压的小幅变化不影响计数率；对于高计数率，还需考虑探测器的死时间。
Before any measurement, the background count must be recorded for a period of several minutes with no source present. The average background count rate is then subtracted from subsequent source measurements. The GM tube should be held securely in a stand, and sources handled with long‑handled tongs to maximise distance from the body.
在任何测量之前，必须在不放源的情况下记录数分钟的背景计数。然后将平均背景计数率从后续源测量中扣除。GM 管应稳固地固定在支架上，使用长柄钳操作放射源，以增加与身体的距离。
3. Measuring Background Radiation | 测量背景辐射
Background radiation comes from cosmic rays, naturally occurring radon gas, and terrestrial sources. In the laboratory, it provides a constant contribution to the measured count rate. To determine the background count rate, set up the GM tube without any source and record the total counts over a period of at least 300 s. Repeat the measurement several times and calculate the mean background count per second. The standard deviation of the counts can be compared with the square root of the mean count, √N, to illustrate the Poisson nature of random events.
背景辐射来自宇宙射线、天然存在的氡气和地球上的源。在实验室中，它对实测计数率提供一个恒定贡献。为测定背景计数率，在不放任何源的情况下架设好 GM 管，记录至少 300 s 内的总计数。重复测量多次，计算每秒平均背景计数。可将计数的标准偏差与平均计数的平方根 √N 进行比较，以说明随机事件的泊松特性。
A low background count rate is typical, often around 0.5 to 2 counts per second, but it can fluctuate. This measurement is an essential baseline for all quantitative radiation experiments.
典型的背景计数率较低，通常约为每秒 0.5 到 2 个计数，但会有波动。这一测量是所有定量辐射实验的基本基线。
4. Investigating Absorption of Alpha Particles | 研究α粒子的吸收
Alpha particles are highly ionising but have a very short range in air and are easily stopped by a sheet of paper. Using a sealed americium‑241 source, which emits alpha particles of energy about 5.5 MeV, the GM tube can be placed close to the source (within 2–3 cm). A series of very thin absorbers, such as different thicknesses of tissue paper or varying numbers of sheets, are interposed. The count rate drops sharply as the absorber thickness increases, falling to the background level once the thickness exceeds the range of the alpha particles in that material.
α粒子电离能力很强，但在空气中的射程很短，易被一张纸挡住。使用发射能量约 5.5 MeV α粒子的镅‑241 密封源，将 GM 管放置在靠近源的位置（2–3 cm 以内）。放置一系列极薄的吸收体，例如不同厚度的薄纸或不同张数，观察计数率的变化。随着吸收体厚度增加，计数率急剧下降；一旦厚度超过α粒子在该材料中的射程，计数率即降至本底水平。
Plotting count rate against absorber thickness reveals a steep cutoff rather than a gradual exponential decline, confirming that alpha particles have a definite range. The experiment should be conducted with the source and detector fixed to maintain consistent geometry.
绘制计数率随吸收体厚度变化的图像，可以看到陡峭的截止，而非缓慢的指数下降，这证实了α粒子具有确定的射程。实验应在源和探测器固定的条件下进行，以保持一致的几何条件。
5. Investigating Absorption of Beta Particles | 研究β粒子的吸收
Beta particles have a greater penetrating power than alpha particles and can pass through several millimetres of aluminium. A strontium‑90 source provides beta particles with a maximum energy of 0.546 MeV (plus a minor gamma component that can often be ignored). Place aluminium absorbers of known thickness (e.g. 0.5 mm, 1.0 mm, 1.5 mm …) between the source and the GM tube. For each thickness, record the count rate after background subtraction.
β粒子的穿透能力比α粒子强，可以穿过数毫米的铝。使用锶‑90 源提供最大能量为 0.546 MeV 的β粒子（另有一可忽略的微小γ成分）。在源和 GM 管之间放置已知厚度的铝吸收片（如 0.5 mm、1.0 mm、1.5 mm……），每增加一厚度，记录减去本底后的计数率。
The count rate decreases approximately exponentially with absorber thickness x, described by I = I₀ e⁻μˣ, where μ is the linear absorption coefficient. A graph of ln(count rate) against thickness yields a straight line, from which μ can be found. The half‑thickness, x½ = ln2 / μ, indicates the thickness needed to halve the beta intensity.
计数率随吸收体厚度 x 大致呈指数下降，可用 I = I₀ e⁻μˣ 描述，其中 μ 为线性吸收系数。以 ln(计数率) 对厚度作图得到一条直线，由此可求出 μ。半值厚度 x½ = ln2 / μ，表示使β强度减半所需的厚度。
Because beta particles are electrons, they can be scattered by the absorber, so the geometry must be kept fixed. It is also important to monitor the high‑voltage stability of the GM tube throughout the measurement.
由于β粒子是电子，可能会被吸收体散射，因此几何条件必须保持固定。同时，还必须监控整个测量过程中 GM 管的高压稳定性。
6. Investigating Absorption of Gamma Radiation | 研究γ射线的吸收
Gamma radiation is highly penetrating and requires dense materials such as lead for significant attenuation. A cobalt‑60 source (emitting gamma photons of 1.17 MeV and 1.33 MeV) or a caesium‑137 source (662 keV) is suitable. Lead sheets of different thicknesses are placed between the source and the GM tube, maintaining a fixed distance. The recorded count rate, after subtracting background, follows an exponential attenuation law I = I₀ e⁻μˣ more closely than betas.
γ辐射穿透性极强，需要使用铅等致密材料才能产生显著的衰减。钴‑60 源（发射 1.17 MeV 和 1.33 MeV 的γ光子）或铯‑137 源（662 keV）均适用。在源和 GM 管之间放置不同厚度的铅片，保持固定距离。减去本底后的计数率比β更严格地遵循指数衰减定律 I = I₀ e⁻μˣ。
A log‑linear graph enables determination of the linear attenuation coefficient μ and the half‑value thickness. By comparing the attenuation coefficients for different materials (e.g. aluminium vs. lead), students appreciate the dependence of gamma absorption on both photon energy and atomic number of the absorber.
通过半对数坐标图可确定线性衰减系数 μ 和半值厚度。通过比较不同材料（如铝与铅）的衰减系数，学生可以认识到γ吸收依赖于光子能量和吸收体原子序数的关系。
7. Statistical Nature of Radioactive Decay | 放射性衰变的统计性质
Radioactive decay is a random process, so repeated measurements of the same source under identical conditions yield different count totals. To demonstrate this, set up a long‑lived source (e.g. a weak beta source) and record the number of counts detected in successive equal time intervals, such as 10 s intervals for 100 trials. The observed frequencies of different count values can be plotted as a histogram and compared with a Poisson distribution.
放射性衰变是一个随机过程，因此在相同条件下对同一源进行重复测量会得到不同的总计数值。为展示这一点，设置一个长寿命源（如弱β源），记录连续相等时间间隔内探测到的计数，例如 100 次、每次 10 s 的计数。将不同计数值出现的频率绘制成直方图，并与泊松分布进行比较。
σ = √N
The standard deviation of the counts should be approximately equal to the square root of the mean count, σ ≈ √N̄, confirming the Poisson nature. This experiment reinforces the need to average counts over long periods to reduce uncertainty and introduces the concept of counting statistics.
计数的标准偏差应约等于平均计数的平方根，即 σ ≈ √N̄，从而证实泊松特性。该实验强化了需要通过长时间平均计数以减小不确定度的要求，并引入了计数统计概念。
8. Determining Half‑life from Decay Curves | 通过衰变曲线测定半衰期
To measure half‑life, a source with a reasonably short half‑life is needed. A common school experiment uses a uranium compound from which protactinium‑234 (half‑life about 70 s) is chemically extracted into an organic layer. The GM tube is positioned to monitor the beta emissions from the decaying protactinium. Counts are recorded in successive 10 s intervals immediately after preparation, continuing for several minutes.
要测量半衰期，需要半衰期较短的源。常见的学校实验使用铀化合物，从中将镤‑234（半衰期约 70 s）化学萃取到有机层中。GM 管放置好以监测衰变的镤发出的β射线。制备后立即在连续的 10 s 间隔内记录计数，持续数分钟。
N = N₀ e⁻λᵗ , λ = ln2 / T₁/₂
The corrected count rate (after background subtraction) is plotted against time. An exponential curve is fitted, and the half‑life is read directly as the time for the count rate to halve. The accuracy of the determined half‑life can be compared with the accepted value, and uncertainties in the timing and count statistics can be discussed.
将校正后的计数率（减去本底）对时间作图，拟合指数曲线，直接从图中读取计数率减半所需的时间即为半衰期。可将测得的半衰期与公认值进行比较，并讨论计时和计数统计中的不确定度。
9. Simulating Radioactive Decay | 模拟放射性衰变
A physical simulation provides an excellent analogy for the random nature of decay. A common method uses a large number of dice (e.g. 100 or more). The dice are thrown, and any die showing a specific number, say ‘6’, is considered to have ‘decayed’ and is removed. The remaining dice are thrown again for the next ‘time interval’, and the process is repeated until few dice remain.
物理模拟很好地类比了衰变的随机性。常见方法是使用大量骰子（如 100 个或更多）。掷骰子，任何显示特定数字（如 6）的骰子视为“已衰变”并移除。剩下的骰子再次掷出，作为下一个“时间间隔”，重复这一过程，直至剩余很少的骰子。
Number remaining N = N₀ (5/6)ⁿ
The number of undecayed dice can be plotted against throw number, giving an exponential decay curve. By comparing this with the theoretical curve N = N₀ e⁻λᵗ, one can extract a ‘decay constant’. This simulation deepens understanding of half‑life and the probabilistic nature of decay without using radioactive materials.
未衰变骰子数对投掷次数作图，得到一条指数衰减曲线。通过与理论曲线 N = N₀ e⁻λᵗ 比较，可提取出“衰变常数”。该模拟在不使用放射性物质的情况下加深了对半衰期和衰变概率本质的理解。
10. Observing Particle Tracks with a Cloud Chamber | 用云室观察粒子轨迹
A diffusion cloud chamber allows direct visualisation of ionising radiation tracks. A chamber containing alcohol vapour is cooled at the bottom, creating a supersaturated layer. A small radioactive source (e.g. a needle tipped with a speck of thorium ore) is placed inside. As alpha or beta particles pass through the vapour, they leave trails of condensed droplets, which can be photographed or observed.
扩散云室能够直接观察电离辐射的径迹。内部含有酒精蒸气的云室底部冷却，形成一层过饱和蒸气。放入一个小的放射源（如针尖上的一粒钍矿石）。当α或β粒子穿过蒸气时，会留下冷凝液滴的痕迹，可拍照或直接观察。
Alpha tracks appear as short, thick, straight lines due to their high ionisation density and short range. Beta tracks are thin, twisted, and longer, reflecting their lower mass and greater scattering. This qualitative experiment provides striking evidence of the differing properties of radiation types and reinforces ideas of ionisation.
α粒子径迹表现为短、粗、直的线条，因为其电离密度大且射程短。β径迹纤细、弯曲且较长，反映了其较小的质量和更强的散射。这一定性实验提供了各辐射类型性质差异的直观证据，并强化了电离概念。
11. Safety Precautions for Radioactive Experiments | 放射性实验的安全预防措施
Working with sealed radioactive sources requires strict adherence to safety protocols. The ALARA principle (As Low As Reasonably Achievable) must be followed: minimise exposure time, maximise distance from the source, and use shielding where appropriate. Sources should never be handled directly; always use forceps or tongs and point the source away from the body. Store sources in labelled lead‑lined containers when not in use.
使用密封放射源必须严格遵守安全规程。应遵循 ALARA 原则（尽可能合理地达到最低水平）：尽量缩短照射时间，增加与源的距离，并适当地使用屏蔽。切勿直接接触源，始终使用镊子或钳子并将源指向远离身体的方向。不使用时，将源存放在贴有标签的铅衬容器中。
The laboratory must have a designated radiation officer, and all usage should be logged. Eating, drinking, and applying cosmetics are forbidden in the work area. Regular contamination checks with a GM monitor should be carried out on bench surfaces and hands. These precautions ensure that the educational benefits of the experiments come with negligible risk.
实验室必须设有专职辐射管理员，所有使用情况都应记录在案。工作区域内禁止饮食和化妆。应使用 GM 监测仪定期检查实验台表面和双手是否受到污染。这些预防措施能确保实验的教育价值在可忽略不计的风险下实现。
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