Half-life | 半衰期 - aleveler.com

📚 Half-life | 半衰期

In radioactive decay, unstable atomic nuclei transform into more stable ones over time. The rate at which this occurs is not constant for a given sample – it is random, yet governed by a clear statistical law. The concept of half-life is central to understanding and quantifying radioactivity, and it appears frequently in IGCSE Edexcel Science examinations. This article explores what half-life means, how it is measured, how to perform calculations, and where it is applied in the real world.

在放射性衰变中，不稳定的原子核会随时间转变为更稳定的核。这种变化的速率对于一个给定的样品并不是恒定的——它是随机的，但遵循着清晰的统计规律。半衰期的概念是理解和量化放射性的核心，常常出现在IGCSE Edexcel科学考试中。本文探讨半衰期的含义、如何测量、怎样进行计算及其在现实世界中的应用。

1. Random Nature of Radioactive Decay | 放射性衰变的随机性

It is impossible to predict when an individual unstable nucleus will decay. The process is entirely random and unaffected by external conditions such as temperature, pressure or chemical bonding. However, with a large number of nuclei, a predictable pattern emerges: a fixed proportion of the remaining nuclei will decay in a given time interval.

我们无法预测一个特定的不稳定原子核何时会发生衰变。整个过程是完全随机的，并且不受温度、压力或化学键等外部条件的影响。然而，当原子核数量很大时，就会出现可预测的规律：在给定的时间间隔内，剩余原子核中会有固定比例的一部分发生衰变。

This random behaviour is similar to tossing thousands of coins at once – you cannot predict one coin, but you can say that approximately half will land heads up. In radioactivity, the ‘tossing interval’ is the half-life.

这种随机行为类似于同时抛掷数千枚硬币——你无法预测某一枚硬币的结果，但你可以说大约一半会正面朝上。在放射性中，“抛掷间隔”就是半衰期。

2. What Is Half-life? | 什么是半衰期？

Half-life is defined as the time taken for half of the radioactive nuclei in a sample to decay, or equivalently, the time taken for the activity of a radioactive source to fall to half its initial value. Activity is the number of decays per second, measured in becquerels (Bq).

半衰期被定义为样品中一半的放射性原子核发生衰变所需的时间，或等价地，放射源的活度下降到其初始值一半所需的时间。活度是每秒衰变的次数，单位为贝克勒尔（Bq）。

Because the number of undecayed nuclei halves each half-life, the quantity of radioactive material never technically reaches zero, but eventually becomes negligible. Half-life is a constant for a given isotope and cannot be altered by physical or chemical means.

由于未衰变原子核的数量每经过一个半衰期就减半，放射性物质的数量在理论上永远不会真正变为零，但最终会变得可以忽略不计。半衰期对于给定的同位素是一个常数，且无法通过物理或化学手段改变。

Number of half-lives elapsed	Fraction of original nuclei remaining	Percentage remaining
0	1	100%
1	1/2	50%
2	1/4	25%
3	1/8	12.5%
4	1/16	6.25%

3. Half-life Graph and Decay Curve | 半衰期图像与衰变曲线

A typical radioactive decay curve plots activity or number of undecayed nuclei against time. The shape is always a decreasing exponential curve. The half-life can be read directly from the graph: find the time taken for the activity to fall from any value to half that value.

典型的放射性衰变曲线将活度或未衰变原子核数量随时间的变化绘制出来。曲线形状总是一条递减的指数曲线。半衰期可以直接从图中读出：找到活度从任一数值下降到该数值一半所需的时间。

To verify that the half-life is constant, you can check whether the time for the activity to halve is the same when measured from 100% to 50%, 50% to 25%, and so on. For any pure isotope, the half-life will be constant regardless of the starting point.

为了验证半衰期是恒定的，你可以检查从100%到50%、从50%到25%等过程所需的时间是否相等。对于任何纯净的同位素，无论起始点如何，半衰期都是恒定不变的。

4. Simple Half-life Calculations | 简单的半衰期计算

For IGCSE Edexcel Science, you are expected to solve problems involving the number of half-lives elapsed. If a sample starts with N₀ nuclei, after n half-lives, the remaining number N is given by: N = N₀ × (½)ⁿ. This formula also works for mass or activity.

在IGCSE Edexcel科学中，你需要解决涉及经过的半衰期个数的问题。如果样品最初有N₀个原子核，经过n个半衰期后，剩余的数目N为：N = N₀ × (½)ⁿ。这个公式同样适用于质量或活度。

N = N₀ × (½)ⁿ

A source has an initial activity of 800 Bq and a half-life of 3 days. After 9 days, 9/3 = 3 half-lives have passed, so the activity becomes 800 × (½)³ = 800 × 1/8 = 100 Bq. Remember to always calculate n = total time ÷ half-life.

一个放射源的初始活度为800 Bq，半衰期为3天。9天后，9/3 = 3个半衰期已经过去，因此活度变为800 × (½)³ = 800 × 1/8 = 100 Bq。请记住始终计算 n = 总时间 ÷ 半衰期。

5. Measuring Half-life in the Laboratory | 实验室中测量半衰期

In the school laboratory, the half-life of a short-lived isotope such as protactinium-234 can be measured using a GM tube and counter. The count rate (corrected for background radiation) is recorded at regular time intervals, and a decay curve is plotted.

在学校实验室里，可以使用盖革-米勒计数管和计数器测量短寿命同位素（如镤-234）的半衰期。定期记录计数率（扣除本底辐射），然后绘制衰变曲线。

Because the count rate is proportional to the activity, the half-life can be found from the graph even if the absolute number of nuclei is unknown. Background radiation must be subtracted from all readings to avoid errors. A correction graph can also be plotted using corrected count rate versus time.

由于计数率与活度成正比，即使不知道原子核的绝对数量，也可以从图中得到半衰期。必须从所有读数中减去本底辐射以避免误差。也可以使用修正后的计数率对时间作图。

6. Half-life and Radioactive Dating | 半衰期与放射性年代测定

Carbon-14 has a half-life of about 5730 years and is used to estimate the age of once-living organic materials. Living organisms constantly exchange carbon with the atmosphere, so the ratio of carbon-14 to carbon-12 remains constant while alive. After death, carbon-14 decays without being replaced.

碳-14的半衰期约为5730年，常用来估算曾经有生命的有机材料的年代。活着的生物体不断与大气交换碳，因此碳-14与碳-12的比例在活着时保持恒定。死后，碳-14不断衰变且无法得到补充。

By measuring the remaining carbon-14 activity in a sample and comparing it to the activity in a living reference, the number of half-lives elapsed can be calculated, giving the age of the specimen. This method is invaluable in archaeology and palaeontology.

通过测量样品中剩余的碳-14活度，并与活体参考值比较，可以计算出经过的半衰期个数，从而得出标本的年龄。这一方法在考古学和古生物学中极为重要。

7. Half-life in Nuclear Medicine | 核医学中的半衰期

Radioisotopes are widely used in medical diagnosis and therapy. For imaging, technetium-99m is a popular choice because its half-life is 6 hours – long enough to complete the examination but short enough to minimise radiation dose to the patient.

放射性同位素广泛用于医疗诊断和治疗。在成像中，锝-99m是一个常见的选择，因为它的半衰期为6小时——足够完成检查，但又足够短以最大程度减少病人的辐射剂量。

For therapeutic purposes, iodine-131 is used to treat thyroid cancer. Its half-life of 8 days provides a balance between delivering a concentrated dose to cancer cells and allowing the body to clear the radioactivity afterwards. The choice of isotope always depends on a suitable half-life for the intended purpose.

在治疗中，碘-131用于治疗甲状腺癌。其8天的半衰期在向癌细胞提供集中剂量与随后让身体清除放射性之间取得了平衡。同位素的选择总是取决于其半衰期是否适合预期用途。

8. Safety and Handling of Radioactive Materials | 放射性材料的安全与处理

A long half-life means a source remains hazardous for thousands or millions of years, creating storage problems for nuclear waste. In contrast, isotopes with very short half-lives may require on-site production because they decay too quickly to be transported.

半衰期长意味着放射源会在数千乃至数百万年内保持危险，给核废料的储存带来难题。相反，半衰期非常短的同位素可能需要就地生产，因为它们衰变得太快而无法运输。

Proper shielding, safe distance and minimising exposure time are the three pillars of radiation protection. When handling sources, students must use tongs and keep them pointed away from the body, while storing them in lead-lined containers when not in use.

恰当的屏蔽、安全距离与最小化暴露时间是辐射防护的三大支柱。学生在操作放射源时，必须使用镊子并使其远离身体，不用时应存放在内衬铅的容器中。

9. Common Misconceptions about Half-life | 关于半衰期的常见误区

Many students think that after two half-lives all radioactive material has decayed. In fact, only 75% has decayed; 25% remains. Another mistake is to assume that half-life changes as the sample gets smaller. The half-life is a fixed property of the isotope and does not depend on the amount present.

许多学生认为经过两个半衰期后，所有放射性物质都已衰变。实际上，只有75%发生了衰变，还有25%剩余。另一个误区是以为半衰期会随着样品变小而改变。半衰期是同位素的固有性质，不依赖于存在的数量。

Also, students sometimes confuse half-life with the total time for all nuclei to decay. Theoretically, the number never reaches zero; the activity simply becomes indistinguishable from background after many half-lives.

此外，学生有时会将半衰期与所有原子核衰变的总时间混淆。理论上，原子核数量永远不会变为零；经过很多个半衰期后，活度只会变得与本底辐射无法区分。

10. Using Half-life to Identify Isotopes | 利用半衰期鉴别同位素

Because each radioactive isotope has a unique half-life, measuring the half-life of an unknown sample can help identify it. For instance, if a sample’s activity halves every 2.5 minutes, it could be aluminium-28, which has a half-life of 2.24 minutes – a close match that would be confirmed with further tests.

由于每种放射性同位素都有独特的半衰期，测量未知样品的半衰期有助于对其进行鉴别。例如，如果一个样品的活度每2.5分钟减半，它可能为铝-28，其半衰期为2.24分钟——这一相近的匹配可通过进一步的测试确认。

This principle is used in forensic science and environmental monitoring to trace sources of contamination or verify the origin of nuclear materials.

这个原理被用于法医学和环境监测中，以追踪污染源或核实核材料的来源。

11. Half-life and Nuclear Waste Management | 半衰期与核废料管理

High-level radioactive waste contains isotopes with half-lives of thousands of years, such as plutonium-239 (half-life 24,100 years). This waste must be stored in geologically stable repositories deep underground to isolate it from the biosphere until its activity falls to safe levels.

高放射性废料含有半衰期长达数千年的同位素，例如钚-239（半衰期24,100年）。这些废料必须储存在地质稳定的深层地下处置库中，以将其与生物圈隔离，直到其活度降至安全水平。

Medium- and low-level wastes with shorter half-lives may be disposed of in engineered near-surface facilities. In all cases, knowledge of half-life is essential for planning storage durations and safety assessments.

半衰期较短的中低放射性废物可以处置在工程化的近地表设施中。无论如何，半衰期的知识对于规划储存期限和安全评估至关重要。

12. Summary and Exam Tips | 总结与应试技巧

Half-life is a fundamental concept linking the random nature of decay to predictable quantitative behaviour. Remember: definition, constant value for a given isotope, the (½)ⁿ formula, ability to read a decay graph, and real-world applications. In Edexcel IGCSE Science papers, examiners often combine graph interpretation with calculations, so practice drawing tangents and reading half-life values from curves.

半衰期是连接衰变随机性与可预测量化行为的基本概念。请牢记：定义、特定同位素的常数、 (½)ⁿ 公式、读衰变图的能力以及实际应用。在Edexcel IGCSE科学考试中，考官常将图像分析与计算结合，因此要多练习从曲线上找半衰期值。

Always show your working, state the number of half-lives clearly, and check that the unit of time matches the half-life unit. If a question asks for the fraction remaining after a non-integer number of half-lives, use the formula with appropriate n.

一定要展示解题步骤，明确写出半衰期的个数，并检查时间单位是否与半衰期单位一致。如果题目要求在非整数个半衰期后剩余的比例，请使用包含适当n的公式。

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Half-life | 半衰期