📚 Radioactivity: Decay, Half-Life and Radiation Safety | 放射性：衰变、半衰期与辐射安全
Radioactivity is the spontaneous and random emission of radiation from an unstable atomic nucleus. In the CIE A Level Physics syllabus, this topic links nuclear structure, the properties of alpha, beta and gamma radiation, exponential decay and practical safety. Understanding these ideas is essential for nuclear physics questions involving decay equations, half-life calculations and applications. A secure grasp of the topic also supports later work on mass defect, binding energy and nuclear fission, so it deserves careful revision rather than memorisation of isolated facts.
放射性是不稳定原子核自发、随机地发出辐射的过程。在 CIE A Level 物理大纲中，本主题联系原子核结构、α、β、γ 辐射的性质、指数衰变和实际安全。理解这些概念对于涉及衰变方程、半衰期计算和应用的核物理题目至关重要。牢固掌握本主题也有助于后续学习质量亏损、结合能和核裂变，因此需要认真复习，而不是零散地死记硬背。
1. What Radioactivity Is | 什么是放射性
Radioactivity is the spontaneous and random emission of radiation from an unstable atomic nucleus. The word spontaneous means the decay is not triggered by any external factor such as temperature, pressure, chemical state or electric field; the word random means we cannot predict which nucleus will decay next, nor when a particular nucleus will decay. Every nucleus of a given nuclide has the same probability of decaying in the next second, but the actual moment of decay is unpredictable.
放射性是不稳定原子核自发、随机地发出辐射的过程。"自发"意味着衰变不由温度、压力、化学状态或电场等外部因素触发；"随机"意味着我们无法预测下一个衰变的原子核是哪一个，也无法预测某个特定原子核何时衰变。对于给定核素的每一个原子核，它在下一秒内衰变的概率都相同，但实际衰变的时刻是不可预测的。
Evidence for randomness comes from counting experiments. If you record the number of counts in equal time intervals, the values fluctuate about a mean rather than staying constant. The fluctuations become relatively smaller as the number of counts increases, which is why we quote an average count rate for a large number of nuclei. This statistical behaviour is the basis of the exponential decay law met later in the topic.
随机性的证据来自计数实验。如果你记录相同时间间隔内的计数个数，数值会围绕平均值上下波动，而不是保持不变。计数越多，波动的相对大小越小，因此对于大量原子核我们给出平均计数率。这种统计行为就是本主题后面指数衰变规律的基础。
nt rate recorded by a detector is measured in counts per second and is always smaller than the true activity, because the detector has limited efficiency and only intercepts a fraction of the emitted radiation. In calculations you must always distinguish between the two.
活度以贝克勒尔为单位，1 Bq = 每秒 1 次衰变。探测器记录的计数率以每秒计数（counts per second）为单位，它总是小于真实活度，因为探测器效率有限，只能截获发出的辐射的一部分。在计算中必须始终区分这两个量。
2. Nuclear Structure and Nuclide Notation | 原子核结构与核素符号
gives the total number of protons plus neutrons. A nuclide is represented by its nucleon number A and proton number Z, as in ²³⁵₉₂U for uranium-235. The number of neutrons is therefore N = A − Z, which for uranium-235 gives 235 − 92 = 143 neutrons.
原子核包含质子和中子，统称核子。质子数 Z 决定元素，核子数 A 表示质子加中子的总数。核素用核子数 A 和质子数 Z 表示，例如铀-235 写作 ²³⁵₉₂U。中子数因此为 N = A − Z，对铀-235 即 235 − 92 = 143 个中子。
ar mass is slightly less than the sum of the masses of its separate protons and neutrons; the difference, the mass defect, corresponds to the binding energy that holds the nucleus together.
原子核带 +Ze 的正电荷，其中 e = 1.60 × 10⁻¹⁹ C。其质量约为 A 个原子质量单位，1 u = 1.66 × 10⁻²⁷ kg。原子核的质量略小于其各个质子和中子质量之和；这个差值即质量亏损，对应把原子核结合在一起的结合能。
Nuclear size can be estimated from the relation R = R₀∛ . This is around 10¹⁴ times denser than ordinary solid matter, which shows how concentrated the nucleus is compared with the atom as a whole.
核的大小可用关系式 R = R₀∛A 估算，其中 R₀ ≈ 1.2 × 10⁻¹⁵ m。由于体积与 A 成正比，所有原子核的核物质密度大致相同，约为 2.3 × 10¹⁷ kg m⁻³。这大约是普通固体物质的 10¹⁴ 倍，说明与整个原子相比原子核何等致密。
3. Isotopes and Nuclear Stability | 同位素与核稳定性
Isotopes are atoms of the same element with the same number of protons but different numbers of neutrons. Because chemical properties depend on electron arrangement, isotopes behave identically in chemical reactions, but their nuclear stability can be very different. Carbon-12 and carbon-14, for example, undergo the same chemical reactions, yet carbon-12 is stable while carbon-14 is radioactive with a half-life of about 5730 years.
同位素是质子数相同、中子数不同的同一种元素的原子。由于化学性质取决于电子排布，同位素在化学反应中表现完全相同，但它们的核稳定性可能差别很大。例如碳-12 和碳-14 发生相同的化学反应，但碳-12 稳定，而碳-14 具有放射性，半衰期约为 5730 年。
Nuclei become unstable when the neutron-to-proton ratio is too high or too low, or when the nucleus is simply too large. A nucleus with too many neutrons tends to emit a beta-minus particle, converting a neutron into a proton and so raising Z. A nucleus with too few neutrons tends to emit a beta-plus particle or capture an electron, lowering Z. Very heavy nuclei with Z greater than about 82 are generally alpha emitters.
当中子与质子的比例过高或过低，或者原子核本身太大时，核就会变得不稳定。中子过多的原子核倾向于发射 β⁻ 粒子，把一个中子变成质子从而提高 Z；中子过少的原子核倾向于发射 β⁺ 粒子或俘获电子，从而降低 Z。Z 大于约 82 的重核通常是 α 放射体。
Radioactive decay therefore always moves a nucleus towards a more stable configuration, usually towards the band of stability on a graph of neutron number against proton number. This is why a single unstable nuclide may decay through a chain of steps before reaching a stable end product, as in the uranium series that ends at lead-206.
因此放射性衰变总是使原子核趋向更稳定的组态，通常趋近于"中子数对质子数"图上的稳定带。这就是为什么一种不稳定核素可能经过一连串衰变步骤才到达稳定的最终产物，例如最终变为铅-206 的铀系。
4. Alpha Radiation | α 辐射
An alpha particle is a helium nucleus, ⁴₂He, consisting of two protons and two neutrons. It carries a charge of +2e and has a mass of about 4 u. Alpha emission therefore reduces the nucleon number by 4 and the proton number by 2, so both A and Z of the parent nuclide change. Alpha decay is typical of heavy nuclei such as uranium-238 and radium-226.
α 粒子是氦原子核 ⁴₂He，由两个质子和两个中子组成。它带 +2e 的电荷，质量约为 4 u。因此 α 发射使核子数减少 4、质子数减少 2，母核的 A 和 Z 都发生变化。α 衰变是铀-238、镭-226 等重核的典型衰变方式。
A typical alpha decay equation is:
²²⁶₈₈Ra → ²²²₈₆Rn + ⁴₂He
该过程的典型衰变方程为：
²²⁶₈₈Ra → ²²²₈₆Rn + ⁴₂He
Alpha particles are strongly ionising because of their large charge and relatively slow speed: they produce about 10⁴ ion pairs per millimetre of air. As a result they lose energy quickly and have a range of only a few centimetres in air, and are stopped by a sheet of paper or a few centimetres of air. In an electric or magnetic field they are deflected towards the negative plate or in the direction given by Fleming's left-hand rule, but the deflection is small because of their large mass.
α 粒子因电荷大、速度相对较慢而电离能力很强：在空气中每毫米约产生 10⁴ 对离子。因此它们很快就损失能量，在空气中的射程只有几厘米，一张纸或几厘米空气就能将其挡住。在电场或磁场中它们偏向负极板，或按左手定则给出的方向偏转，但由于质量大，偏转很小。
The alpha particles emitted by a given nuclide have discrete kinetic energies, typically 4-6 MeV. This is because the energy released in the decay is shared between the alpha particle and the recoiling daughter nucleus in a fixed way, so the alpha spectrum consists of sharp lines rather than a continuous distribution.
给定核素发出的 α 粒子具有分立的动能，通常为 4-6 MeV。这是因为衰变释放的能量按固定方式在 α 粒子和反冲子核之间分配，所以 α 能谱由尖锐的谱线组成，而不是连续分布。
5. Beta Radiation | β 辐射
Beta-minus decay occurs in neutron-rich nuclei. Inside the nucleus a neutron changes into a proton, and an electron together with an electron antineutrino is emitted. The nucleon number A stays the same while the proton number Z increases by 1. The emitted electron is not one of the orbiting electrons; it is created in the nucleus at the moment of decay.
β⁻ 衰变发生在中子过多的原子核中。核内一个中子转变为质子，同时发出一个电子和一个反中微子。核子数 A 不变，质子数 Z 增加 1。发出的电子不是绕核电子，而是在衰变瞬间由核内产生的。
Beta-plus decay occurs in proton-rich nuclei. A proton changes into a neutron, and a positron together with an electron neutrino is emitted, so Z decreases by 1 while A is unchanged. A competing process is electron capture, in which the nucleus absorbs an orbiting electron and emits a neutrino only.
β⁺ 衰变发生在质子过多的原子核中。一个质子转变为中子，同时发出一个正电子和一个中微子，因此 Z 减少 1，A 不变。与之竞争的过程是电子俘获，即原子核吸收一个绕核电子，只发出一个中微子。
Typical equations for these processes are:
¹⁴₆C → ¹⁴₇N + ⁰₋₁e + antineutrino
²²₁₁Na → ²²₁₀Ne + ⁰₊₁e + neutrino
这些过程的典型方程为：
¹⁴₆C → ¹⁴₇N + ⁰₋₁e + 反中微子
²²₁₁Na → ²²₁₀Ne + ⁰₊₁e + 中微子
Beta particles are less ionising than alpha particles but far more penetrating. They produce roughly 100 ion pairs per millimetre of air, have a range of a few metres in air and are stopped by a few millimetres of aluminium. Unlike alpha particles, beta particles are emitted with a continuous range of kinetic energies because the available energy is shared randomly between the electron, the antineutrino and the daughter nucleus. The existence of this continuous spectrum was the original evidence for the neutrino.
β 粒子的电离能力弱于 α 粒子，但穿透力强得多。它们在空气中每毫米大约产生 100 对离子，射程在空气中可达几米，几毫米厚的铝即可将其挡住。与 α 粒子不同，β 粒子的动能是连续分布的，因为可用的能量在电子、反中微子和子核之间随机分配。这种连续能谱的存在正是中微子最初被提出的实验依据。
6. Gamma Radiation | γ 辐射
Gamma radiation is electromagnetic radiation of very short wavelength, emitted as photons from a nucleus that is left in an excited state after alpha or beta decay. A gamma photon has no charge and no rest mass, so gamma emission changes neither the nucleon number A nor the proton number Z of the nuclide.
γ 辐射是波长极短的电磁辐射，由 α 或 β 衰变后处于激发态的原子核以光子形式发出。γ 光子不带电、没有静质量，因此 γ 发射既不改变核素核子数 A，也不改变质子数 Z。
Because gamma emission involves only a loss of energy, it is often written with an asterisk to show the excited state, for example:
⁹⁹ᵐ₄₃Tc → ⁹⁹₄₃Tc + ⁰₀γ
由于 γ 发射只涉及能量损失，常以星号表示激发态，例如：
⁹⁹ᵐ₄₃Tc → ⁹⁹₄₃Tc + ⁰₀γ
Gamma rays are the least ionising of the three radiations but the most penetrating, since they have no charge and interact only weakly with matter. They can pass through several centimetres of lead, and their intensity is reduced exponentially as they pass through an absorber rather than being stopped at a definite range.
γ 射线是三种辐射中电离能力最弱的，但穿透力最强，因为它不带电，与
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图