IGCSE Physics: Radiation Types & Half-Life Calculations | IGCSE物理：辐射类型与半衰期计算

📚 IGCSE Physics: Radiation Types & Half-Life Calculations | IGCSE物理：辐射类型与半衰期计算

Radioactivity is a core topic in IGCSE Physics, and understanding the three main types of radiation together with half-life calculations is essential for exam success. This guide covers the properties of alpha, beta and gamma radiation, their penetrating and ionising abilities, and step-by-step methods for solving half-life problems.

放射性是 IGCSE 物理的核心主题，理解三种主要辐射类型以及半衰期计算对考试成功至关重要。本指南涵盖 α、β 和 γ 辐射的性质、贯穿能力和电离能力，以及解决半衰期问题的分步方法。

1. What is Radioactivity? | 什么是放射性？

Radioactivity is the spontaneous decay of an unstable nucleus, emitting radiation in the process. This process is random and cannot be influenced by external factors such as temperature or pressure.

放射性是不稳定原子核的自发衰变，在此过程中释放辐射。这个过程是随机的，不受温度或压力等外部因素的影响。

There are three main types of radiation emitted during radioactive decay: alpha (α) particles, beta (β) particles and gamma (γ) rays. Each type has distinct physical properties that determine how it interacts with matter.

放射性衰变过程中发射三种主要辐射类型：α 粒子、β 粒子和 γ 射线。每种类型都有独特的物理性质，决定其与物质的相互作用方式。

2. Alpha Particles (α) | α 粒子

An alpha particle is identical to a helium nucleus, consisting of two protons and two neutrons. It has a relative charge of +2 and a relative mass of 4.

α 粒子与氦原子核相同，由两个质子和两个中子组成。其相对电荷为 +2，相对质量为 4。

Because alpha particles have a relatively large mass and charge, they are strongly ionising. They collide with atoms and knock electrons off, creating ions along their path.

由于 α 粒子的质量和电荷相对较大，它们具有很强的电离能力。它们与原子碰撞并撞击出电子，沿路径产生离子。

ₐ⁴X → ₐ₋₂⁴Y + α (₂⁴He)

An alpha decay equation shows that the parent nucleus loses 2 protons and 2 neutrons, decreasing the atomic number by 2 and the mass number by 4.

α 衰变方程表明母核失去 2 个质子和 2 个中子，原子序数减少 2，质量数减少 4。

3. Beta Particles (β) | β 粒子

A beta particle is a fast-moving electron emitted from the nucleus when a neutron converts into a proton. It has a relative charge of −1 and a negligible mass.

β 粒子是从原子核中发射出的高速电子，当中子转化为质子时产生。其相对电荷为 −1，相对质量几乎为零。

Beta particles are less ionising than alpha particles because they are smaller and faster, but they can still ionise atoms as they pass through matter. They are more penetrating than alpha particles.

β 粒子的电离能力比 α 粒子弱，因为它们更小且速度更快，但它们在穿越物质时仍能电离原子。它们比 α 粒子具有更强的贯穿能力。

ₐⁿX → ₐ₊₁ⁿY + β (−₁⁰e)

In beta decay, the atomic number increases by 1 while the mass number remains unchanged, as a neutron becomes a proton.

在 β 衰变中，原子序数增加 1，而质量数保持不变，因为中子变成了质子。

4. Gamma Rays (γ) | γ 射线

Gamma rays are electromagnetic waves with very high frequency and energy, similar to X-rays but even more energetic. They have no mass and no charge.

γ 射线是频率极高、能量极高的电磁波，类似于 X 射线但能量更高。它们没有质量也没有电荷。

Gamma rays are the most penetrating form of radiation. They are weakly ionising because they rarely interact with atoms, but when they do, they can eject electrons from atoms.

γ 射线是贯穿能力最强的辐射形式。它们的电离能力很弱，因为很少与原子相互作用，但一旦相互作用，就能从原子中撞击出电子。

Gamma emission often accompanies alpha or beta decay, as the nucleus releases excess energy after undergoing a transformation.

γ 发射通常伴随 α 或 β 衰变，因为原子核在发生转变后会释放多余能量。

5. Comparison of Properties | 性质对比

The following table summarises the key differences between the three types of radiation. You should memorise this for the IGCSE exam.

下表总结了三种辐射类型之间的关键差异。你应该为 IGCSE 考试记住这些内容。

Property	Alpha (α)	Beta (β)	Gamma (γ)
Nature	Helium nucleus	Electron	EM wave
Relative mass	4	~0	0
Relative charge	+2	−1	0
Ionising power	Strong	Moderate	Weak
Penetrating power	Weak (stopped by paper)	Moderate (stopped by aluminium)	Strong (needs lead or concrete)

In air, alpha particles travel only a few centimetres, beta particles can travel a few metres, and gamma rays can travel hundreds of metres.

在空气中，α 粒子只能传播几厘米，β 粒子可以传播几米，而 γ 射线可以传播数百米。

6. What is Half-Life? | 什么是半衰期？

Half-life (t½) is the time taken for half of the unstable nuclei in a radioactive sample to decay. It is a constant for a given isotope and does not depend on the initial amount or external conditions.

半衰期（t½）是指放射性样品中一半的不稳定原子核发生衰变所需的时间。对于给定的同位素，它是一个常量，不取决于初始数量或外部条件。

After one half-life, the activity or count rate falls to half its original value. After two half-lives, it falls to one quarter, after three half-lives to one eighth, and so on.

经过一个半衰期后，放射性活度或计数率降至原始值的一半。经过两个半衰期后降至四分之一，经过三个半衰期后降至八分之一，依此类推。

N = N₀ × (½)ⁿ

Where N is the remaining amount, N₀ is the initial amount, and n is the number of half-lives elapsed.

其中 N 是剩余量，N₀ 是初始量，n 是经过的半衰期次数。

7. Using Half-Life in Calculations | 半衰期计算的应用

To calculate the remaining mass or activity after a given time, first determine how many half-lives fit into that time period. Then apply the half-life formula.

要计算给定时间后的剩余质量或活度，首先确定该时间段包含多少个半衰期。然后应用半衰期公式。

Example 1: A sample has an initial activity of 800 Bq and a half-life of 3 hours. What is the activity after 9 hours?

例 1：一个样品的初始活度为 800 Bq，半衰期为 3 小时。9 小时后的活度是多少？

Number of half-lives = 9 ÷ 3 = 3. After each half-life, activity halves: 800 → 400 → 200 → 100 Bq.

半衰期次数 = 9 ÷ 3 = 3。每个半衰期后活度减半：800 → 400 → 200 → 100 Bq。

800 × (½)³ = 800 × ⅛ = 100 Bq

Example 2: A radioactive isotope has a half-life of 6 days. How many days are needed for the count rate to fall from 960 counts per minute to 15 counts per minute?

例 2：一种放射性同位素的半衰期为 6 天。计数率从每分钟 960 次降至每分钟 15 次需要多少天？

Find the number of half-lives: 960 → 480 → 240 → 120 → 60 → 30 → 15. That is 6 half-lives.

求半衰期次数：960 → 480 → 240 → 120 → 60 → 30 → 15。一共是 6 个半衰期。

Time = 6 × 6 = 36 days.

时间 = 6 × 6 = 36 天。

8. Reading Half-Life from a Graph | 从图表读取半衰期

A decay curve shows the count rate or remaining mass over time. To find the half-life from a graph, locate the initial value on the vertical axis, then find the time at which the value halves.

衰变曲线显示计数率或剩余质量随时间的变化。要从图表中求半衰期，先找到纵轴上的初始值，然后找到该值减半所对应的时间。

Check your answer by repeating the process: start from the half-value and see if it halves again over the same time interval. If it does, you have correctly identified the half-life.

通过重复该过程来验证答案：从半值开始，看是否在同一时间间隔内再次减半。如果确实如此，说明你正确找到了半衰期。

Exam tip: Always draw a horizontal line from the half-value on the y-axis to the curve, then drop a vertical line to the x-axis. The x-coordinate gives the half-life.

考试提示：务必从纵轴上的半值画一条水平线与曲线相交，然后向横轴做垂线。横坐标即为半衰期。

Half-life = time for activity to drop from A₀ to A₀/2

If the initial activity is 120 Bq and it drops to 60 Bq in 4 minutes, then t½ = 4 minutes. It should then drop from 60 Bq to 30 Bq in another 4 minutes.

如果初始活度为 120 Bq，在 4 分钟内降至 60 Bq，则 t½ = 4 分钟。它应该再经过 4 分钟从 60 Bq 降至 30 Bq。

9. Uses of Radiation | 辐射的应用

Different types of radiation are used in different fields depending on their properties.

不同类型的辐射根据其性质被应用于不同领域。

Alpha particles: Used in smoke detectors. The alpha source ionises the air between two plates, creating a small current. Smoke particles absorb the alpha particles, reducing the current and triggering the alarm.
α 粒子：用于烟雾探测器。α 放射源使两板之间的空气电离，产生微小电流。烟雾颗粒吸收 α 粒子，降低电流并触发警报。
Beta particles: Used in thickness control of paper and aluminium foil. If the material becomes too thick, fewer beta particles pass through, and the rollers adjust automatically.
β 粒子：用于纸张和铝箔的厚度控制。如果材料变得过厚，穿过的 β 粒子减少，滚筒会自动调整。
Gamma rays: Used to sterilise medical equipment because they can kill bacteria. They are also used in radiotherapy to destroy cancerous tumours, and for tracing leaks in underground pipes.
γ 射线：用于医疗设备消毒，因为它们能杀死细菌。它们也用于放射治疗以摧毁癌性肿瘤，以及追踪地下管道的泄漏。

10. Background Radiation | 背景辐射

Background radiation is the low-level radiation that is always present around us. It comes from natural sources such as cosmic rays, rocks and soil containing uranium and radon gas, as well as man-made sources like medical X-rays and nuclear power.

背景辐射是指我们周围始终存在的低水平辐射。它来自天然来源，如宇宙射线、含铀和氡气的岩石和土壤，以及人造来源，如医疗 X 射线和核能。

When measuring the activity of a radioactive source, you must first measure the background count rate and subtract it from the total count rate. This ensures that your measurements reflect only the source’s activity.

在测量放射源的活度时，必须先测量背景计数率，并从总计数率中减去它。这样可以确保你的测量值仅反映放射源本身的活度。

Corrected count rate = Total count rate − Background count rate

Example: The total count rate is 250 counts per minute, and the background count rate is 50 counts per minute. The corrected count rate is 200 counts per minute.

例如：总计数率为每分钟 250 次，背景计数率为每分钟 50 次。则校正后的计数率为每分钟 200 次。

11. Radiation Safety | 辐射安全

Radiation can damage living cells and cause mutations or cancer. Therefore, appropriate safety measures are needed when handling radioactive sources.

辐射会损伤活细胞并导致突变或癌症。因此，在处理放射源时需要采取适当的安全措施。

Use tongs or remote handling tools to keep a safe distance from the source.
使用钳子或远程操作工具，与放射源保持安全距离。
Limit the time of exposure to reduce the total dose received.
限制暴露时间以减少受到的总剂量。
Store sources in lead-lined containers when not in use.
不使用时将放射源存放在衬铅容器中。
Never point a radioactive source at yourself or others.
切勿将放射源指向自己或他人。
Wear gloves and wash hands after handling sources to avoid contamination.
操作放射源后戴手套并洗手，避免污染。

Remember the three principles of radiation protection: time, distance and shielding.

记住辐射防护的三项原则：时间、距离和屏蔽。

12. Exam Tips & Common Mistakes | 考试技巧与常见错误

Students often make avoidable errors in half-life calculations. Here are the most common ones and how to avoid them.

学生在半衰期计算中常犯一些可以避免的错误。以下是最常见的错误以及如何避免。

Forgetting to subtract background radiation before calculating half-life. Always use the corrected count rate.
忘记在计算半衰期前扣除背景辐射。务必使用校正后的计数率。
Confusing the number of half-lives with the total time. Remember: total time = number of half-lives × half-life.
将半衰期次数与总时间混淆。记住：总时间 = 半衰期次数 × 半衰期。
Stopping after one half-life when the question asks for a greater reduction. Continue halving until you reach the target value.
当问题要求更大的衰减量时，只计算一个半衰期就停止。继续减半直到达到目标值。

When reading a decay graph, use a ruler to draw accurate guide lines, and clearly show your method on the graph if the question asks for the half-life to be determined graphically.

在读取衰变图时，用直尺画精确的辅助线，如果问题要求在图上确定半衰期，请在图上清晰展示你的方法。

13. Worked Example: Mixed Calculation | 综合例题

A sample of a radioactive isotope has a mass of 32 g and a half-life of 12 days. Calculate the mass remaining after 48 days.

一种放射性同位素样品质量为 32 g，半衰期为 12 天。计算 48 天后剩余的质量。

Number of half-lives = 48 ÷ 12 = 4.

半衰期次数 = 48 ÷ 12 = 4。

Remaining mass = 32 × (½)⁴ = 32 × 1/16 = 2 g.

剩余质量 = 32 × (½)⁴ = 32 × 1/16 = 2 g。

32 g → 16 g → 8 g → 4 g → 2 g

Notice how the mass halves four times, giving a final answer of 2 g. Always show your halving steps in the exam so that you can earn partial credit even if you make a calculation error.

注意质量连续四次减半，最终答案是 2 g。在考试中务必写出逐步减半的过程，这样即使计算有误，也能获得部分分数。

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IGCSE Physics: Radiation Types & Half-Life Calculations | IGCSE物理：辐射类型与半衰期计算