📚 Particles, Radiation and Radioactivity | 粒子、辐射与放射性
This AQA A-Level Physics topic brings together the structure of matter, the nature of nuclear radiation and the rules that govern particle interactions. You will need to link the behaviour of alpha, beta and gamma radiation to changes inside the nucleus, and then extend those ideas to the fundamental particles and exchange forces of the Standard Model.
本 AQA A-Level 物理主题将物质结构、核辐射的性质以及支配粒子相互作用的规律结合在一起。你需要把 α、β 和 γ 辐射的行为与原子核内部的变化联系起来，并进一步将这些思想延伸到标准模型中的基本粒子和交换力。
1. Inside the Atom | 原子内部
An atom consists of a small, dense nucleus containing protons and neutrons, surrounded by electrons in discrete energy levels. The proton number Z fixes the element, while the nucleon number A gives the total number of protons and neutrons. Isotopes have the same Z but different A.
原子由一个微小而致密的原子核和核外分立能级上的电子组成，原子核内包含质子和中子。质子数 Z 决定了元素种类，核子数 A 表示质子和中子的总数。同位素具有相同的 Z 但不同的 A。
Specific charge is the charge-to-mass ratio of a particle. It is particularly useful for comparing the deflection of ions and subatomic particles in electric and magnetic fields. A particle with a larger specific charge is deflected more easily.
比荷是粒子的电荷与质量之比。它特别适用于比较离子和亚原子粒子在电场和磁场中的偏转情况。比荷越大的粒子越容易发生偏转。
specific charge = charge / mass = Q / m
× 1.60 × 10⁻¹⁹ C. This gives a direct route to calculating the specific charge of an ion.
对于质量数为 A 的原子核，其质量约为 A × 1.66 × 10⁻²⁷ kg，电荷为 Z × 1.60 × 10⁻¹⁹ C。这为计算离子的比荷提供了直接方法。
2. Stable and Unstable Nuclei | 稳定与不稳定原子核
The strong nuclear force holds nucleons together. It is attractive over a range of about 3 fm, but becomes repulsive at very short separations below roughly 0.5 fm. This prevents the nucleus from collapsing and must overcome the electrostatic repulsion between protons.
强核力将核子束缚在一起。它在约 3 fm 的范围内表现为吸引力，但在约 0.5 fm 以下的极短距离内表现为排斥力。这既防止原子核坍缩，又必须克服质子之间的静电斥力。
Heavier stable nuclei need more neutrons than protons because the extra neutrons add strong-force attraction without increasing electrostatic repulsion. If the N/Z ratio is too high or too low, the nucleus becomes unstable and decays.
稳定的轻核通常满足 N ≈ Z。较重的稳定核需要比质子更多的中子，因为额外的中子增加了强核力吸引力，而不会增加静电斥力。如果 N/Z 比值过高或过低，原子核就会不稳定并发生衰变。
Heavy nuclei often decay by alpha emission, which reduces both A and Z. Neutron-rich nuclei tend to undergo beta-minus decay, while proton-rich nuclei may undergo beta-plus decay or electron capture.
重核通常通过 α 衰变减少 A 和 Z。富中子核倾向于发生 β⁻ 衰变，而富质子核可能发生 β⁺ 衰变或电子俘获。
R = R₀ A1/3
The nuclear radius equation shows that nuclear volume is proportional to mass number. It is often tested through data analysis, where ln R is plotted against ln A to find the gradient.
核半径公式表明核体积与质量数成正比。考试中常通过数据分析考查，例如绘制 ln R 对 ln A 的图像并求斜率。
3. Alpha, Beta and Gamma Radiation | α、β 和 γ 辐射
Alpha radiation consists of helium nuclei, beta radiation consists of fast electrons or positrons, and gamma radiation is high-frequency electromagnetic radiation. Their different charge, mass and energy lead to very different ionising and penetrating abilities.
α 辐射由氦核组成，β 辐射由快速电子或正电子组成，γ 辐射是高频电磁辐射。它们的电荷、质量和能量不同，因此电离能力和穿透能力差异很大。
Alpha particles are strongly ionising but only travel a few centimetres in air and can be stopped by paper. Beta particles are less ionising and are stopped by a few millimetres of aluminium. Gamma rays are weakly ionising but very penetrating, requiring thick lead or concrete to reduce their intensity significantly.
α 粒子电离能力很强，但在空气中只能传播几厘米，可被纸张阻挡。β 粒子电离能力较弱，可被几毫米厚的铝片阻挡。γ 射线电离能力很弱，但穿透力极强，需要厚铅板或混凝土才能显著降低其强度。
In electric and magnetic fields, alpha particles are deflected towards the negative plate, beta-minus particles towards the positive plate, and gamma rays are not deflected. The much smaller mass of beta particles means they are deflected more than alpha particles in the same field.
在电场和磁场中，α 粒子向负极板偏转，β⁻ 粒子向正极板偏转，γ 射线不发生偏转。由于 β 粒子质量小得多，在相同场中其偏转比 α 粒子更明显。
4. Radioactive Decay Equations | 放射性衰变方程
Radioactive decay changes the proton number, nucleon number or energy state of a nucleus. Alpha decay reduces Z by 2 and A by 4. Beta-minus decay increases Z by 1 with no change in A, while beta-plus decay decreases Z by 1. Gamma emission leaves both Z and A unchanged.
放射性衰变会改变原子核的质子数、核子数或能态。α 衰变使 Z 减少 2，A 减少 4。β⁻ 衰变使 Z 增加 1，A 不变；β⁺ 衰变使 Z 减少 1。γ 发射不改变 Z 和 A。
²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂α
¹⁴₆C → ¹⁴₇N + ⁰₋₁e + ν̄ₑ
¹⁸₉F → ¹⁸₈O + ⁰₊₁e + νₑ
In beta-minus decay, a down quark in a neutron changes into an up quark, so a neutron becomes a proton and an electron antineutrino is also emitted. In beta-plus decay, an up quark changes into a down quark, converting a proton into a neutron and emitting a positron plus an electron neutrino.
在 β⁻ 衰变中，中子里的一个下夸克变为上夸克，因此中子变成质子，同时发射一个电子反中微子。在 β⁺ 衰变中，一个上夸克变为下夸克，质子变成中子，并发射一个正电子和一个电子中微子。
Gamma decay usually follows alpha or beta decay when the daughter nucleus is left in an excited state. The excited nucleus releases the surplus energy as a high-energy photon.
γ 衰变通常发生在 α 或 β 衰变之后，此时子核处于激发态。激发态原子核以高能光子的形式释放多余能量。
5. Activity and Half-Life | 活度与半衰期
per second. Activity is directly proportional to the number of radioactive nuclei present.
放射源的活度是每秒发生衰变的原子核数量。其单位是贝克勒尔，1 Bq 表示每秒发生 1 次衰变。活度与当前存在的放射性原子核数量成正比。
A = λN
The decay constant λ is the probability of an individual nucleus decaying per second. Radioactive decay is random and spontaneous, so we cannot predict when a particular nucleus will decay, but we can describe the behaviour of a large sample statistically.
衰变常量 λ 是单个原子核每秒发生衰变的概率。放射性衰变是随机且自发的，因此无法预测某个特定原子核何时衰变，但可以对大量原子核的行为进行统计描述。
N = N₀ e−λt
A = A₀ e−λt
tant by the expression T₁/₂ = ln 2 / λ, so a large decay constant means a short half-life.
半衰期 T₁/₂ 是放射性原子核数量或活度减少到原来一半所需的时间。它与衰变常量的关系为 T₁/₂ = ln 2 / λ，因此衰变常量越大，半衰期越短。
T₁/₂ = ln 2 / λ
6. The Inverse Square Law for Gamma Rays | γ 射线的平方反比定律
For a point source of gamma radiation, the intensity I obeys an inverse square law with distance x from the source. This is because the same total energy is spread over the surface of a sphere of radius x, whose area increases as x².
对于 γ 辐射点源，强度 I 与到源的距离 x 遵循平方反比定律。这是因为相同的总能量分布在半径为 x 的球面上，而球面面积随 x² 增大。
I = k / x²
In experiments, a Geiger-Muller tube is placed at different distances from the source and the count rate C is recorded. Since C is proportional to I, a graph of C against 1/x² should give a straight line through the origin, provided background radiation has been subtracted.
实验中，将盖革-米勒计数管放在距源不同距离处，记录计数率 C。由于 C 与 I 成正比，若已扣除本底辐射，则 C 对 1/x² 作图应得到一条过原点的直线。
The inverse square law applies to gamma radiation because gamma rays travel in straight lines and spread out uniformly. It does not apply to alpha or beta radiation over typical laboratory distances because they are rapidly absorbed by air or scattered.
平方反比定律适用于 γ 辐射，因为 γ 射线沿直线传播并均匀扩散。在典型实验距离下，该定律不适用于 α 或 β 辐射，因为它们会被空气迅速吸收或发生散射。
7. Particles and Antiparticles | 粒子与反粒子
Every particle has a corresponding antiparticle with the same rest mass but opposite charge and opposite quantum numbers. For example, the antiparticle of the electron is the positron, which has the same mass but positive charge.
每一种粒子都有对应的反粒子，反粒子具有相同的静止质量，但电荷和量子数相反。例如，电子的反粒子是正电子，其质量相同但带正电。
When a particle and its antiparticle meet, they annihilate. Their rest energy is converted into two photons travelling in opposite directions to conserve momentum. Conversely, a photon with enough energy can create a particle-antiparticle pair in a process called pair production.
当粒子和它的反粒子相遇时，它们会发生湮灭。它们的静止能量转化为两个沿相反方向运动的光子，以保持动量守恒。反之，能量足够高的光子可以通过对产生过程产生一对正反粒子。
E = mc²
E = hf = hc / λ
The rest energy of an electron or positron is 0.511 MeV. Therefore pair production requires a photon energy of at least 1.022 MeV. In annihilation, the total photon energy produced equals the total rest energy plus any kinetic energy of the original particles.
电子或正电子的静止能量为 0.511 MeV。因此对产生要求光子能量至少为 1.022 MeV。在湮灭过程中，产生的光子总能量等于原粒子的总静止能量加上它们原有的动能。
8. Particle Interactions and Exchange Particles | 粒子相互作用与交换粒子
Forces between particles are explained by the exchange of virtual particles. In electromagnetic interactions, the exchange particle is the virtual photon. In the weak interaction, the exchange particles are the W⁺, W⁻ and Z⁰ bosons. The strong force between quarks is carried by gluons.
粒子之间的力通过交换虚粒子来解释。在电磁相互作用中，交换粒子是虚光子。在弱相互作用中，交换粒子是 W⁺、W⁻ 和 Z⁰ 玻色子。夸克之间的强力由胶子传递。
Feynman diagrams represent these interactions. In beta-minus decay, a down quark emits a W⁻ boson and changes into an up quark; the W⁻ then decays into an electron and an electron antineutrino. In beta-plus decay, an up quark emits a W⁺ boson and becomes a down quark, producing a positron and an electron neutrino.
费曼图可以表示这些相互作用。在 β⁻ 衰变中，一个下夸克发射 W⁻ 玻色子并变为上夸克；W⁻ 再衰变为一个电子和一个电子反中微子。在 β⁺ 衰变中，一个上夸克发射 W⁺ 玻色子并变为下夸克，产生一个正电子和一个电子中微子。
The weak interaction is the only fundamental interaction that can change quark flavour. This is why beta decay changes a neutron into a proton or a proton into a neutron. It also involves neutrinos or antineutrinos, which carry away energy and momentum.
弱相互作用是唯一能改变夸克味的基本相互作用。这就是 β 衰变能把中子变为质子或把质子变为中子的原因。该过程还涉及中微子或反中微子，它们带走能量和动量。
9. Classification of Particles | 粒子分类
Particles are divided into hadrons and leptons. Hadrons experience the strong nuclear force; leptons do not. Hadrons are further split into baryons, made of three quarks, and mesons, made of a quark-antiquark pair. Protons and neutrons are baryons, while pions and kaons are mesons.
粒子分为强子和轻子。强子参与强核力作用，轻子不参与。强子又分为由三个夸克组成的重子和由一个夸克-反夸克对组成的介子。质子和中子属于重子，π 介子和 K 介子属于介子。
Leptons are fundamental particles that do not feel the strong force. The electron, muon and their associated neutrinos are leptons. Each charged lepton has a corresponding neutrino. Lepton number is conserved in all particle interactions.
轻子是不参与强力的基本粒子。电子、μ 子以及它们对应的中微子都属于轻子。每种带电轻子都有对应的中微子。在所有粒子相互作用中，轻子数守恒。
Baryon number is also conserved. Baryons have baryon number +1, antibaryons have −1, and all other particles have baryon number 0. This conservation law explains why a proton cannot decay into a positron and a photon: baryon number would change from +1 to 0.
重子数也守恒。重子的重子数为 +1，反重子为 −1，所有其他粒子重子数为 0。这一守恒定律解释了为什么质子不能衰变为正电子和光子：重子数将从 +1 变为 0。
10. Quarks and Conservation Laws | 夸克与守恒定律
The quark model explains the properties of hadrons. Up, down and strange quarks are needed at A-Level. The up quark has charge +2/3, while the down and strange quarks have charge −1/3. Antiquarks have the opposite charges.
夸克模型解释了强子的性质。A-Level 阶段需要掌握上夸克、下夸克和奇异夸克。上夸克带电荷 +2/3，下夸克和奇异夸克带电荷 −1/3。反夸克带相反的电荷。
proton = uud, neutron = udd
The proton consists of two up quarks and one down quark, giving charge +1. The neutron consists of one up quark and two down quarks, giving charge 0. Mesons are made of a quark and an antiquark, such as the π⁺ meson, which is u and anti-d.
质子由两个上夸克和一个下夸克组成，总电荷为 +1。中子由一个上夸克和两个下夸克组成，总电荷为 0。介子由一个夸克和一个反夸克组成，例如 π⁺ 介子由上夸克和反下夸克组成。
rong force but decay by the weak force. At quark level, beta-minus decay is d → u + e⁻ + ν̄ₑ, where the weak interaction changes the quark flavour.
奇异数在强相互作用中守恒，但在弱相互作用中不守恒。这解释了为什么 K 介子等奇异粒子通过强力成对产生，却通过弱力衰变。在夸克层面，β⁻ 衰变可表示为 d → u + e⁻ + ν̄ₑ，其中弱相互作用改变了夸克味。
11. Radiation Safety and Applications | 辐射安全与应用
Ionising radiation can damage living cells and DNA, so safe handling relies on reducing exposure time, increasing distance from the source and using appropriate shielding. Alpha sources are dangerous if ingested because they are strongly ionising inside the body, while gamma sources require heavy shielding even at a distance.
电离辐射会损伤活细胞和 DNA，因此安全操作依赖于缩短照射时间、增大与源的距离以及使用适当的屏蔽。α 源一旦进入体内会非常危险，因为它在体内具有强电离能力；而 γ 源即使在较远处也需要重屏蔽。
Radioactive isotopes are used in smoke detectors, medical tracers, radiotherapy and carbon dating. The chosen isotope must have a suitable half-life: long enough to remain active for its purpose, but short enough not to create long-term contamination.
放射性同位素被用于烟雾探测器、医学示踪、放射治疗和碳年代测定。所选同位素必须具有合适的半衰期：既长到足以在用途期间保持活性，又短到不会造成长期污染。
In medical imaging, a gamma emitter such as technetium-99m is often used because it has a short half-life of about 6 hours and emits gamma rays that can be detected outside the body. In carbon dating, the decay of carbon-14 is used because its long half-life of about 5730 years suits dating archaeological samples.
在医学成像中，常使用锝-99m 等
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