📚 Radioactive Decay | 放射性衰变
Radioactive decay is a spontaneous and random process by which an unstable atomic nucleus loses energy by emitting radiation. For OCR A-Level Physics, this topic demands a clear understanding of decay types, exponential decay law, half-life, activity, and applications such as carbon dating. Mastery of these concepts lays the foundation for nuclear physics and practical data analysis.
放射性衰变是一个自发的、随机的过程，不稳定的原子核通过发射辐射来释放能量。对于 OCR A-Level 物理考试，该主题要求清晰地理解衰变类型、指数衰变规律、半衰期、活度以及碳定年等应用。掌握这些概念将为核物理和实验数据分析打下坚实基础。
1. The Nature of Radioactive Decay | 放射性衰变的本质
An unstable nucleus will eventually decay into a more stable configuration. The process is independent of external conditions such as temperature or pressure. Radioactivity is a random process at the level of a single nucleus, meaning it is impossible to predict exactly when a particular nucleus will decay. However, for a large number of nuclei, the overall behaviour follows a predictable statistical pattern.
不稳定的原子核最终会衰变成更稳定的结构。该过程不受温度、压力等外部条件的影响。对于单个原子核而言，放射性是一个随机过程，意味着无法准确预测某个特定原子核何时会衰变。但对于大量原子核，整体行为遵循可预测的统计规律。
2. Alpha (α) Decay | α 衰变
In alpha decay, a parent nucleus emits an alpha particle, which consists of two protons and two neutrons (a helium-4 nucleus, ⁴₂He). The mass number A decreases by 4 and the atomic number Z decreases by 2. A general equation is: ᴬₓX → ᴬ⁻⁴₂₋₂Y + ⁴₂He. Alpha particles have a high ionising ability but low penetration — they can be stopped by a sheet of paper or a few centimetres of air.
在 α 衰变中，母核发射一个由两个质子和两个中子组成的 α 粒子（即氦-4 核，⁴₂He）。质量数 A 减少 4，原子序数 Z 减少 2。通用方程为：ᴬₓX → ᴬ⁻⁴₂₋₂Y + ⁴₂He。α 粒子具有很强的电离能力，但穿透力弱——一张纸或几厘米空气即可阻挡。
3. Beta-minus (β⁻) Decay | β⁻ 衰变
Beta-minus decay occurs in neutron-rich nuclei. A neutron is converted into a proton, emitting an electron (β⁻ particle) and an electron antineutrino. The atomic number Z increases by 1 while the mass number A remains unchanged. The general equation is: ᴬₓX → ᴬ₂₊₁Y + ⁰₋₁e + ν̄ₑ. Due to the antineutrino, the energy spectrum of emitted electrons is continuous.
β⁻ 衰变发生在中子过剩的原子核中。一个中子转化为质子，同时发射一个电子（β⁻ 粒子）和一个反电子中微子。原子序数 Z 增加 1，质量数 A 保持不变。通用方程为：ᴬₓX → ᴬ₂₊₁Y + ⁰₋₁e + ν̄ₑ。由于反中微子的存在，所发射电子的能谱是连续的。
4. Beta-plus (β⁺) Decay | β⁺ 衰变
Beta-plus decay happens in proton-rich nuclei. A proton is converted into a neutron, emitting a positron (β⁺ particle) and an electron neutrino. The atomic number Z decreases by 1, while the mass number A stays the same. The general equation is: ᴬₓX → ᴬ₂₋₁Y + ⁰₊₁e + νₑ. Positrons quickly annihilate with electrons, producing gamma photons.
β⁺ 衰变发生在质子过剩的原子核中。一个质子转化为中子，发射一个正电子（β⁺ 粒子）和一个电子中微子。原子序数 Z 减少 1，质量数 A 不变。通用方程为：ᴬₓX → ᴬ₂₋₁Y + ⁰₊₁e + νₑ。正电子会迅速与电子湮灭，产生 γ 光子。
5. Gamma (γ) Decay | γ 衰变
Gamma decay usually accompanies alpha or beta decay. After emitting an alpha or beta particle, the daughter nucleus may be left in an excited state. It loses excess energy by emitting a high-energy photon — a gamma ray. There is no change in mass number or atomic number. Gamma radiation is highly penetrating and requires thick lead or concrete to absorb.
γ 衰变通常伴随 α 或 β 衰变发生。在发射 α 或 β 粒子后，子核可能处于激发态。它会通过发射一个高能光子——γ 射线来释放多余能量。质量数和原子序数均不变化。γ 辐射穿透力极强，需要厚铅板或混凝土来吸收。
6. Decay Constant and Activity | 衰变常数与活度
The probability per unit time that a given nucleus will decay is called the decay constant λ (unit: s⁻¹). The activity A of a sample is the number of decays per unit time and is proportional to the number of undecayed nuclei N: A = λN. Activity is measured in becquerels (Bq), where 1 Bq = 1 decay per second. As nuclei decay, both N and A decrease exponentially with time.
单位时间内单个原子核发生衰变的概率称为衰变常数 λ（单位：s⁻¹）。样品的活度 A 是单位时间内发生衰变的次数，与未衰变原子核数目 N 成正比：A = λN。活度以贝克勒尔（Bq）为单位，1 Bq = 每秒 1 次衰变。随着原子核衰变，N 和 A 都随时间指数衰减。
7. Exponential Decay Law | 指数衰变规律
Radioactive decay follows an exponential law: N = N₀ e⁻λt, where N₀ is the initial number of nuclei at time t = 0. The same relationship holds for activity: A = A₀ e⁻λt and for mass (m) of the radioactive isotope. This mathematical form arises because the rate of decay is proportional to the number of nuclei present.
放射性衰变遵循指数规律：N = N₀ e⁻λt，其中 N₀ 是 t = 0 时刻的初始原子核数。同样的关系适用于活度：A = A₀ e⁻λt 和放射性同位素的质量 m。这一数学形式源于衰变率与当前原子核数目成正比。
8. Half-life | 半衰期
The half-life T₁/₂ is the time taken for the number of undecayed nuclei (or the activity) to fall to half its initial value. It is related to the decay constant by: T₁/₂ = ln 2 / λ = 0.693 / λ. Half-life is particularly useful because it is constant and independent of the amount of material. For OCR problems, you may be asked to determine half-life from a graph of N against t or A against t.
半衰期 T₁/₂ 是未衰变原子核数目（或活度）降至初始值一半所需的时间。它与衰变常数的关系为：T₁/₂ = ln 2 / λ = 0.693 / λ。半衰期非常有用，因为它是常数，与样品的量无关。在 OCR 题目中，可能会要求从 N–t 图或 A–t 图确定半衰期。
9. Using the Exponential Decay Equation | 指数衰变方程的应用
Practical calculations often involve finding the remaining fraction of a sample after a certain time. Use N/N₀ = e⁻λt or, when dealing with integer numbers of half-lives, use the simpler form N = N₀ (½)ⁿ, where n = t / T₁/₂. Remember to convert all time units consistently. Examiners expect you to take natural logarithms to linearise the relationship: ln N = ln N₀ – λt.
实际计算中常涉及求经过某一时间后样品的剩余分数。使用 N/N₀ = e⁻λt，或者当时间包含整数个半衰期时，用更简单的 N = N₀ (½)ⁿ，其中 n = t / T₁/₂。注意保持一致的时间单位。考官期望你会使用自然对数将关系线性化：ln N = ln N₀ – λt。
10. Radioactive Dating: Carbon-14 | 放射性定年：碳-14
Carbon-14 dating is a classic application of exponential decay. Living organisms maintain a constant ratio of carbon-14 (radioactive, T₁/₂ ≈ 5730 years) to carbon-12. Upon death, the intake of carbon-14 stops, and the existing ¹⁴C decays. By measuring the remaining activity or the ratio R, the time since death can be estimated using t = –(T₁/₂ / ln 2) ln (R / R₀). This method is reliable for samples up to about 50 000 years old.
碳-14 定年是指数衰变的经典应用。活体生物保持着碳-14（放射性，半衰期约 5730 年）与碳-12 的恒定比例。生物死亡后，碳-14 的摄入停止，原有的 ¹⁴C 开始衰变。通过测量剩余活度或比例 R，可利用 t = –(T₁/₂ / ln 2) ln (R / R₀) 估算死亡时间。该方法对大约 50 000 年以内的样品较为可靠。
11. Background Radiation and Corrected Count Rate | 背景辐射与修正计数率
When measuring activity in the lab, a Geiger-Müller tube will record counts from the source as well as from background radiation. The true count rate from the source is obtained by subtracting the background count rate from the measured count rate. Background radiation comes from cosmic rays, rocks, and even building materials, and must be measured separately with the source removed.
在实验室测量活度时，盖革-米勒管会记录来自放射源和背景辐射的计数。源的真正计数率由实测计数率减去背景计数率得到。背景辐射来自宇宙射线、岩石甚至建筑材料，必须在移走放射源的情况下单独测量。
12. Graphical Analysis and Required Practical | 图像分析与必做实验
The OCR specification often requires students to determine half-life from experimental data. Plotting corrected count rate against time yields an exponential decay curve. Using a logarithmic plot (ln count rate vs time) produces a straight line whose gradient is –λ. From λ, T₁/₂ can be found. Always discuss uncertainties in count readings (due to random nature of decay) and suggest taking repeated readings and longer counting intervals for more accurate results.
OCR 考纲经常要求学生通过实验数据确定半衰期。将修正计数率对时间作图，得到指数衰变曲线。采用对数坐标（ln 计数率 对 时间）可产生一条直线，其斜率为 –λ。由 λ 可求出 T₁/₂。务必要讨论计数读数的随机误差（源于衰变的随机性），并建议重复测量、延长计数时间以获得更精确的结果。
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