📚 Radioactive Decay | 放射性衰变
Radioactive decay is a spontaneous process by which an unstable atomic nucleus loses energy by emitting radiation. This phenomenon is random and independent of physical conditions such as temperature and pressure, making it a purely nuclear effect. Understanding the types of decay, the associated conservation laws, and the mathematical description of activity and half‑life is essential for mastering the nuclear physics section of both IB and WJEC physics specifications.
放射性衰变是一种不稳定原子核通过发射辐射而自发损失能量的过程。该现象是随机的，与温度、压力等物理条件无关，因而是一种纯粹的核效应。理解衰变类型、相关的守恒定律以及对活度和半衰期的数学描述，是掌握 IB 和 WJEC 物理大纲中核物理部分的关键。
1. Introduction to Radioactive Decay | 放射性衰变简介
An atomic nucleus contains protons and neutrons bound together by the strong nuclear force. When a nucleus has an imbalance of protons and neutrons, or has excess energy, it becomes unstable and will eventually undergo radioactive decay. This process transforms the original nuclide, called the parent, into a different nuclide, called the daughter, often accompanied by the emission of particles or electromagnetic radiation.
原子核由质子和中子通过强核力结合在一起。当核内质子与中子的数量失衡或核具有过剩能量时，就会变得不稳定，并最终发生放射性衰变。这一过程将初始的核素（母体）转变为另一种核素（子体），通常伴有粒子或电磁辐射的发射。
The key feature of radioactive decay is its spontaneous and random nature. It is impossible to predict exactly when a single nucleus will decay, though the average behaviour of a large number of identical nuclei is extremely predictable. This statistical character is modelled by the decay constant and half‑life.
放射性衰变的关键特征是自发性和随机性。不可能精确预言单个核何时衰变，但大量相同核的平均行为却是高度可预见的。这种统计性质用衰变常数和半衰期加以建模。
2. Types of Radioactive Emissions | 放射性射线的类型
There are four main types of emissions associated with radioactive decay: alpha (α) particles, beta‑minus (β⁻) particles, beta‑plus (β⁺) particles, and gamma (γ) rays. In addition, electron capture competes with β⁺ emission. Each type differs in its nature, penetrating ability, and ionising power.
与放射性衰变相关的发射主要有四种：α粒子、β⁻粒子、β⁺粒子和γ射线。此外，电子俘获与β⁺发射相竞争。每种发射在本质、穿透能力和电离本领上各不相同。
An α particle is a helium nucleus, ⁴₂He; it has a charge of +2e and is highly ionising but poorly penetrating, stopped by a sheet of paper. A β⁻ particle is a fast electron emitted when a neutron converts into a proton. A β⁺ particle is a positron emitted when a proton converts into a neutron. γ radiation is high‑frequency electromagnetic radiation, often emitted after α or β decay when the daughter nucleus is left in an excited state.
α粒子是氦核 ⁴₂He，带有+2e的电荷，电离能力强但穿透力弱，能被一张纸挡住。β⁻粒子是一个快电子，是在中子转变为质子时发射的。β⁺粒子是一个正电子，是在质子转变为中子时发射的。γ辐射是高频电磁辐射，通常在α或β衰变后子核处于激发态时发射。
3. Alpha Decay | α衰变
Alpha decay occurs mostly in heavy nuclei with atomic number Z > 82. In this process, the parent nucleus loses two protons and two neutrons, thereby reducing its mass number by 4 and its atomic number by 2. The general equation is:
α衰变主要发生在原子序数Z > 82的重核。在此过程中，母核失去两个质子和两个中子，因此其质量数减少4，原子序数减少2。一般方程为：
ᴬZX → ᴬ⁻⁴Z₋₂Y + ⁴₂He
A classic example is the decay of uranium‑238 to thorium‑234:
一个经典例子是铀-238衰变为钍-234：
²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He
Alpha particles are emitted with discrete kinetic energies, typically in the range 4–10 MeV. The discrete energies reflect the fact that the energy released in the decay is shared between the α particle and the recoiling daughter nucleus according to conservation of momentum.
α粒子以分立的动能发射，通常处于4–10 MeV范围内。动能的离散反映了衰变释放的能量根据动量守恒在α粒子和反冲子核之间分配的事实。
4. Beta‑Minus Decay | β⁻衰变
Beta‑minus decay occurs in neutron‑rich nuclei. Inside the nucleus, a down quark in a neutron changes into an up quark, converting the neutron into a proton. This process emits an electron (β⁻) and an electron antineutrino:
β⁻衰变发生在中子过剩的核。在核内部，中子里的一个下夸克变成上夸克，使中子转变为质子。这一过程发射一个电子（β⁻）和一个反电子中微子：
n → p + e⁻ + ν̅ₑ
For a nuclide, the decay equation is:
对于核素，衰变方程为：
ᴬZX → ᴬZ₊₁Y + e⁻ + ν̅ₑ
An example is the decay of carbon‑14 to nitrogen‑14:
一个例子是碳-14衰变为氮-14：
¹⁴₆C → ¹⁴₇N + e⁻ + ν̅ₑ
In β⁻ decay, the energy released is shared between the electron and the antineutrino, so the emitted electrons have a continuous energy spectrum up to a maximum endpoint. The antineutrino carries away the missing energy and momentum, postulated by Pauli to satisfy conservation laws.
在β⁻衰变中，释放的能量在电子和反中微子之间分配，因此发射电子的能谱是连续的，直到最大端点能量。反中微子带走了缺失的能量和动量，由泡利提出以满足守恒定律。
5. Beta‑Plus Decay and Electron Capture | β⁺衰变与电子俘获
Beta‑plus decay occurs in proton‑rich nuclei. A proton is converted into a neutron, emitting a positron (β⁺) and an electron neutrino:
β⁺衰变发生在质子过剩的核。一个质子转变为中子，发射一个正电子（β⁺）和一个电子中微子：
p → n + e⁺ + νₑ
The nuclear equation is:
核方程为：
ᴬZX → ᴬZ₋₁Y + e⁺ + νₑ
For example, sodium‑22 decays to neon‑22:
例如，钠-22衰变为氖-22：
²²₁₁Na → ²²₁₀Ne + e⁺ + νₑ
A competing process, electron capture, involves a proton in the nucleus capturing an inner orbital electron, usually from the K‑shell, and combining to form a neutron and a neutrino:
一个与之竞争的过程是电子俘获，核内的一个质子俘获一个内层轨道电子（通常来自K层），结合形成一个中子和一个中微子：
p + e⁻ → n + νₑ
The atomic number decreases by one while the mass number stays the same, just as in β⁺ decay. Electron capture is often followed by the emission of characteristic X‑rays or Auger electrons as outer electrons fill the vacancy left by the captured electron.
如同β⁺衰变一样，原子序数减少1而质量数不变。电子俘获后，外层电子填补被俘获电子留下的空位时，常伴随着特征X射线或俄歇电子的发射。
6. Gamma Decay | γ衰变
Gamma decay is the emission of high‑energy photons from an excited nucleus. After α or β decay, the daughter nucleus may be left in an excited state. It transitions to a lower energy state by emitting one or more γ‑ray photons. Because the photon has no mass or charge, the atomic and mass numbers remain unchanged. A typical representation is:
γ衰变是激发态原子核发射高能光子的过程。在α或β衰变后，子核可能留在激发态。它通过发射一个或多个γ射线光子而跃迁到较低能态。由于光子既无质量也无电荷，原子序数和质量数保持不变。一个典型的表示是：
ᴬZX* → ᴬZX + γ
Gamma rays are electromagnetic waves of very short wavelength, and they are highly penetrating, requiring dense materials such as lead or thick concrete for shielding. They are less ionising than α or β particles because their energy deposition per unit path length is smaller.
γ射线是波长极短的电磁波，穿透力极强，需要铅或厚混凝土等致密材料进行屏蔽。它们的电离能力比α或β粒子弱，因为单位路径长度的能量沉积更小。
Some nuclei can also de‑excite by a process called internal conversion, where the energy is transferred directly to an atomic electron, ejecting it from the atom. However, in most exam specifications the focus is on the emission of a γ photon.
某些核还可以通过一种称为内转换的过程去激发，即能量直接转移给一个原子电子并将它从原子中击出。但在大多数考试大纲中，重点仍是γ光子的发射。
7. Decay Equations and Conservation Laws | 衰变方程与守恒定律
right. The total mass number (A), which counts nucleons, is also conserved. For energy, the total mass‑energy of the products plus their kinetic energies account for the initial mass‑energy of the parent, considering mass‑energy equivalence E = mc².
所有放射性衰变都遵守几条守恒定律。总电荷（Z）守恒：左边原子序数之和等于右边之和。总质量数（A），即核子数，也守恒。在能量方面，根据质能等价E = mc²，产物的总质能及其动能等于母体的初始质能。
In β⁻ and β⁺ decays, the emission of a neutrino or antineutrino is essential to conserve lepton number as well as energy and momentum. In the electron family, the electron and the electron neutrino (νₑ) are assigned lepton number +1, while the positron and the electron antineutrino (ν̅ₑ) have lepton number −1. Thus, in β⁻ decay, a neutron (lepton number 0) effectively turns into a proton, an electron (lepton number +1), and an antineutrino (lepton number −1), keeping the total lepton number zero. This highlights the need for the neutrino hypothesis.
在β⁻和β⁺衰变中，中微子或反中微子的发射对于守恒轻子数以及能量和动量至关重要。在电子家族中，电子和电子中微子（νₑ）的轻子数为+1，而正电子和反电子中微子（ν̅ₑ）的轻子数为−1。因此，在β⁻衰变中，一个中子（轻子数为0）有效地变成一个质子、一个电子（轻子数+1）和一个反中微子（轻子数−1），总轻子数保持为零。这凸显了中微子假说的必要性。
8. Activity and the Decay Constant | 活度与衰变常数
nd. The activity is proportional to the number of undecayed nuclei N present at that time:
放射源的活度A是单位时间内发生的衰变次数。其SI单位是贝克勒尔（Bq），1 Bq = 每秒1次衰变。活度正比于当时存在的未衰变核数目N：
A = λN
The decay constant λ (lambda) is the probability per unit time that a given nucleus will decay. Its unit is s⁻¹. A large λ corresponds to a rapidly decaying source. The decay constant is characteristic of the particular nuclide and is unaffected by chemical or physical conditions.
衰变常数λ是单位时间内单个核发生衰变的概率。其单位是s⁻¹。大的λ对应于快速衰变的源。衰变常数是特定核素的特征，不受化学或物理条件影响。
ndamental differential equation dN/dt = −λN. This gives rise to the exponential decay law.
由于每次衰变使N减少1，N的变化率为−λN，从而得到基本微分方程dN/dt = −λN。由此导出指数衰变规律。
9. Half‑Life | 半衰期
The half‑life T₁/₂ of a radioactive nuclide is the time required for half the original nuclei to decay, or equivalently for the activity to drop to half its initial value. It is related to the decay constant by:
放射性核素的半衰期T₁/₂是原有核衰变掉一半所经历的时间，或者同样地，活度降到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
Since ln 2 is about 0.693, a larger decay constant implies a shorter half‑life. Half‑ the nuclide. For example, ²³⁸U has T₁/₂ ≈ 4.5 × 10⁹ years, while ²¹⁴Po has T₁/₂ ≈ 164 μs.
由于ln 2约为0.693，衰变常数越大，半衰期就越短。半衰期从几分之一秒到数十亿年不等，取决于核素。例如，²³⁸U的半衰期约为4.5×10⁹年，而²¹⁴Po的半衰期约为164微秒。
Experimentally, half‑life can be determined from an activity‑time graph. For a single nuclide, a plot of logarithm of activity versus time yields a straight line of slope −λ. This is a standard laboratory exercise in both IB and WJEC courses.
实验上，可以通过活度–时间图确定半衰期。对于单一核素，活度的对数–时间图将给出斜率为−λ的直线。这是IB和WJEC课程中标准的实验练习。
10. Exponential Decay Law | 指数衰变规律
The number of undecayed nuclei N remaining after a time t is given by:
经过时间t后剩余的未衰变核数目N由下式给出：
N(t) = N₀ e⁻λt
Similarly, the activity and the mass of the parent nuclide follow the same exponential form:
类似地，活度和母核素的质量也遵循同样的指数形式：
A(t) = A₀ e⁻λt
These equations assume that the decay products are stable or are continuously removed, so that the total number of parent nuclei is not replenished. For a mixture of independent nuclides, the total activity is the sum of the individual exponential activities.
这些方程假设衰变产物是稳定的或不断被移除，因而母核总数不得到补充。对于相互独立的核素混合物，总活度是各指数活度之和。
nts are asked to calculate the remaining nuclei, the activity after a given number of half‑ certain fraction. Using the relationship between λ and T₁/₂, one can write N(t) = N₀ (1/2)t / T₁/₂.
在许多问题中，要求学生计算剩余核数、经过若干个半衰期后的活度，或者活度降到某一分数所需的时间。利用λ与T₁/₂的关系，可以写成N(t) = N₀ (1/2)t / T₁/₂。
11. Applications: Radioactive Dating | 应用：放射性定年
n the organism dies, ¹⁴C decays with T₁/₂ = 5730 years and the ratio decreases exponentially, allowing the age of organic remains to be estimated.
放射性衰变最著名的应用之一是放射性碳定年法，利用¹⁴C的β⁻衰变。宇宙射线在高层大气中产生¹⁴C，与稳定的二氧化碳混合并被生物体吸收。生物体活着时，¹⁴C与¹²C之比保持恒定。当生物体死亡后，¹⁴C以5730年的半衰期衰变，该比值按指数下降，从而可估算有机遗骸的年代。
he daughter nuclide relative to the remaining parent gives the age of the rock. Such methods underpin much of our understanding of Earth’s history.
对于古老得多的地质样品，使用如²³⁸U → ²⁰⁶Pb或⁴⁰K → ⁴⁰Ar等衰变链。子核素相对于剩余母核素的积累量给出了岩石的年龄。这些方法构成了我们对地球历史认识的基础。
Medical applications also exploit radioactive decay, for example in PET scans where a β⁺ emitter is introduced and the resulting annihilation photons are detected to map metabolic activity. The short half‑life of the tracer ensures that the activity diminishes rapidly after the procedure.
医疗应用也利用了放射性衰变，例如在PET扫描中，引入β⁺发射体并探测由此产生的湮灭光子，从而绘制代谢活动图。示踪剂的短半衰期确保操作后活度迅速降低。
12. Background Radiation and Safety | 本底辐射与安全
Background radiation is the ionising radiation present in the environment from natural and artificial sources. Natural sources include cosmic rays, radon gas, and radioactive isotopes in rocks and food. Artificial sources may come from medical procedures, nuclear power, and fallout from past weapons testing. In radioactivity experiments, it is essential to measure and subtract the background count rate.
本底辐射是环境中来自天然和人工源的电离辐射。天然源包括宇宙射线、氡气、岩石和食物中的放射性同位素。人工源可能来自医疗程序、核能以及过去武器试验的沉降物。在放射性实验中，必须测量并减去本底计数率。
Safety precautions when handling radioactive sources include using forceps or tongs to maintain distance, minimising exposure time, using shielding appropriate to the radiation type, and never pointing sources at people. The inverse square law for gamma rays also informs safe distances: doubling the distance reduces the intensity to a quarter.
处理放射源时的安全预防措施包括：使用镊子或钳子以保持距离，尽量缩短暴露时间，使用与辐射类型相适应的屏蔽，以及绝不要将源对准他人。γ射线的平方反比定律也提示了安全距离：距离加倍，强度减小到四分之一。
The concept of absorbed dose (gray) and dose equivalent (sievert) may be introduced at higher levels to quantify biological risk, but the fundamental point remains that any unnecessary exposure to ionising radiation should be avoided.
较高层次可引入吸收剂量（戈瑞）和剂量当量（希沃特）的概念以量化生物风险，但根本要点仍是：应避免任何不必要的电离辐射照射。
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