📚 Nuclear Physics | 核物理
Nuclear physics is the branch of physics that studies the structure, properties, and behaviour of atomic nuclei. It explains radioactive decay, nuclear energy release, and the fundamental interactions that hold the nucleus together. Understanding these concepts underpins applications from carbon dating to nuclear power and medical imaging.
核物理是研究原子核的结构、性质与行为的分支学科。它解释了放射性衰变、核能的释放以及将原子核束缚在一起的基本相互作用。对这些概念的理解支撑着从碳定年到核能发电和医学成像等广泛应用。
1. Rutherford Scattering and the Nuclear Atom | 卢瑟福散射与核式原子
In the Geiger–Marsden experiment, alpha particles were directed at a thin gold foil. Most particles passed straight through, but a small fraction were deflected through large angles, and about 1 in 8000 rebounded backwards. This could not be explained by Thomson's 'plum pudding' model.
在盖革–马斯登实验中，α粒子被射向一片薄金箔。大部分粒子径直穿过，但有一小部分以较大角度偏转，大约每8000个中就有1个被反弹回来。这无法用汤姆孙的“葡萄干布丁”模型解释。
Rutherford proposed that the atom has a tiny, dense, positively charged nucleus at its centre, containing most of the mass. The electrons orbit this nucleus at relatively large distances, leaving the atom mostly empty space. The occasional large-angle scattering occurs when an alpha particle comes close to the heavy nucleus and experiences a strong Coulomb repulsion.
卢瑟福提出，原子中心有一个极小的、致密的带正电的原子核，其中集中了原子的绝大部分质量。电子在距核较远的地方绕核运动，使得原子内部绝大部分是空的空间。偶尔出现的大角度散射是由于α粒子靠近重核并受到强烈的库仑排斥力所致。
2. Nuclear Composition and Notation | 原子核的组成与符号
The nucleus consists of protons and neutrons, collectively called nucleons. The atomic number Z is the number of protons, which determines the element's identity. The mass number A is the total number of nucleons (protons + neutrons). The neutron number N is given by A – Z.
原子核由质子和中子组成，统称为核子。原子序数 Z 是质子数，它决定了元素的种类。质量数 A 是核子的总数（质子加中子）。中子数 N 由 A – Z 给出。
A nuclide is represented by the notation AZX, where X is the chemical symbol. For example, the uranium-238 nucleus is written as 23892U. A proton can be written as 11p and a neutron as 10n.
一种核素用符号 AZX 表示，其中 X 为元素符号。例如，铀-238 的原子核写作 23892U。一个质子可写作 11p，一个中子写作 10n。
3. Isotopes | 同位素
Isotopes are nuclei of the same element that have the same number of protons (same Z) but different numbers of neutrons (different A). They share identical chemical properties because the electron configuration is the same, but their masses differ. Common examples include 12C, 13C and 14C (carbon isotopes) and 235U and 238U (uranium isotopes).
同位素是指同一种元素中质子数相同（Z 相同）而中子数不同（A 不同）的原子核。它们的电子排布相同，因此化学性质完全一样，但质量不同。常见的例子有碳同位素 12C、13C 和 14C，以及铀同位素 235U 和 238U。
Radioactive isotopes, such as 14C, are unstable and decay over time, making them useful for radiometric dating and medical tracers. The existence of isotopes provided evidence that the nucleus contains neutrons, which contribute to mass but not to the nuclear charge.
放射性同位素（例如 14C）不稳定，会随时间衰变，这使它们可用于放射性测年和医学示踪。同位素的存在证明了原子核内存在中子，中子贡献质量但不贡献核电荷。
4. The Strong Nuclear Force | 强核力
The strong nuclear force is the fundamental interaction that binds nucleons together in the nucleus. It is an attractive force that acts between all nucleons (proton-proton, neutron-neutron, and proton-neutron) and is independent of electric charge. It is much stronger than the electrostatic repulsion between protons at very short distances.
强核力是将核子束缚在原子核内的基本相互作用。它是一种作用于所有核子之间（质子与质子、中子与中子、质子与中子）的吸引力，与电荷无关。在极短的距离内，它比质子间的静电斥力大得多。
The force has a very short range, approximately 1–3 femtometres (fm). Beyond this distance, it drops rapidly to zero. This short-range nature leads to saturation: a given nucleon only interacts strongly with its nearest neighbours. The strong force is repulsive at even shorter distances (<0.5 fm), preventing the nucleons from collapsing into each other.
该力力程极短，约为 1–3 飞米（fm）。超出此范围，力迅速降为零。这种短程特性导致了饱和性：一个给定的核子只与其最近邻的核子发生强相互作用。在更短的距离（<0.5 fm）下，强核力表现为排斥力，从而阻止核子坍缩到一起。
5. Mass Defect and Binding Energy | 质量亏损与结合能
The mass of a stable nucleus is always less than the sum of the masses of its individual protons and neutrons. This difference is called the mass defect, Δm. According to Einstein's mass–energy equivalence, this missing mass is equivalent to the energy released when the nucleus is formed. The binding energy of a nucleus is the energy required to separate it into its constituent nucleons.
稳定原子核的质量总是小于其各个质子与中子的质量之和。这个差值称为质量亏损 Δm。根据爱因斯坦的质能方程，这部分“消失”的质量等效于核形成时所释放的能量。原子核的结合能就是将其拆散成单个核子所需的能量。
Binding energy = Δm c² = [(Z mp + N mn) – Mnucleus] c²
In calculations, atomic mass units (u) are often used. 1 u has a mass of 1.66054 × 10–27 kg and is equivalent to an energy of 931.5 MeV via E = mc². Therefore, a mass defect of 1 u corresponds to a binding energy of 931.5 MeV.
计算中常使用原子质量单位（u）。1 u 的质量为 1.66054 × 10–27 kg，通过 E = mc² 相当于 931.5 MeV 的能量。因此，1 u 的质量亏损对应 931.5 MeV 的结合能。
6. Binding Energy per Nucleon and Stability | 平均结合能与核稳定性
A more useful quantity is the binding energy per nucleon, found by dividing the total binding energy by the mass number A. A graph of binding energy per nucleon against mass number reveals a broad peak around A le nucleus. The average binding energy per nucleon rises sharply for light nuclei, reaches a maximum at iron, and then gradually decreases for heavier nuclei.
一个更有用的量是平均结合能（比结合能），即将总结合能除以质量数 A。比结合能随质量数的变化曲线显示在 A ≈ 56 （铁-56）附近有一个宽峰，铁-56 是最稳定的核。轻核的比结合能迅速上升，在铁附近达到最大，之后对于重核又逐渐下降。
This shape explains why energy can be released either by fusing light nuclei (fusion) or by splitting heavy nuclei (fission). Both processes move the resulting nuclei towards the maximum binding energy per nucleon, releasing the energy difference.
这一曲线形状解释了为何既可以通过轻核的聚变释放能量，也可以通过重核的裂变释放能量。这两种过程都使产物核的比结合能向最大值移动，同时释放出能量差。
7. Radioactive Decay: Alpha, Beta, Gamma | 放射性衰变：α、β、γ
Alpha decay occurs in heavy, neutron-rich nuclei. The nucleus emits an alpha particle (42He), consisting of two protons and two neutrons. The mass number decreases by 4 and the atomic number decreases by 2. A typical example is the decay of uranium-238: 23892U → 23490Th + 42He. Alpha particles have low penetration (stopped by paper or skin) but cause strong ionisation.
α衰变发生在较重的富中子核中。原子核发射出一个由两个质子和两个中子组成的α粒子（42He）。质量数减少4，原子序数减少2。典型例子是铀-238的衰变：23892U → 23490Th + 42He。α粒子穿透力弱（能被纸或皮肤阻挡），但电离能力强。
Beta-minus (β⁻) decay on is converted into a proton, emitting an electron (β⁻) and an antineutrino: n → p + e⁻ + νe. The atomic number increases by 1, while the mass number remains unchanged. For example, 146C → 147N + e⁻ + νe.
β⁻衰变发生在中子过多的核中。一个中子转变为一个质子，并发射出一个电子（β⁻）和一个反中微子：n → p + e⁻ + νe。原子序数增加1，质量数保持不变。例如：146C → 147N + e⁻ + νe。
Beta-plus (β⁺) decay on is transformed into a neutron, releasing a positron (e⁺) and a neutrino: p → n + e⁺ + νe. The atomic number decreases by 1, and A stays constant. Gamma decay involves the emission of a high-energy photon from an excited nucleus. In gamma emission, neither A nor Z changes; the nucleus simply loses excess energy.
β⁺衰变发生在质子过多的核中。一个质子转变为一个中子，放出正电子（e⁺）和一个中微子：p → n + e⁺ + νe。原子序数减少1，质量数不变。γ衰变则是由处于激发态的核发射高能光子。γ辐射中A和Z均不改变，原子核仅失去多余的能量。
8. Decay Constant, Half-life and Activity | 衰变常数、半衰期与活度
The activity A of a radioactive sample is the rate at which nuclei decay. It is proportional to the number of undecayed nuclei N:
放射性样品的活度 A 是指核衰变的速率。它与尚未衰变的核数目 N 成正比：
A = – dN/dt = λN
y. Activity is measured in becquerels (Bq), where 1 Bq = 1 decay per second. The half-life T1/2 is the time taken for half of the radioactive nuclei in a sample to decay, and it is related to the decay constant by:
衰变常数 λ（单位 s⁻¹）表示单个核在单位时间内发生衰变的概率。活度的单位是贝克勒尔（Bq），1 Bq 相当于每秒衰变1次。半衰期 T1/2 是样品中放射性核衰变掉一半所需的时间，它与衰变常数的关系为：
T1/2 = ln 2 / λ
Different isotopes have extremely different half-lives, ranging from fractions of a second to billions of years. For instance, 14C has a half-life of about 5730 years, whereas 238U has a half-life of 4.5 × 10⁹ years.
不同同位素的半衰期差异极大，从不到一秒到数十亿年不等。例如，14C 的半衰期约 5730 年，而 238U 的半衰期则为 4.5 × 10⁹ 年。
9. Exponential Decay Law | 指数衰变定律
The number of undecayed nuclei decreases exponentially with time, following the law:
尚未衰变的核数目随时间按指数规律减少，遵循如下定律：
N = N₀ e–λt
Similarly, the activity decays exponentially:
同样，活度也按指数衰减：
A = A₀ e–λt
A graph of N against time is a smooth exponential decay curve. After one half-life, N = N₀/2; after two half-lives, N = N₀/4, and so on. Because the decay is random and spontaneous, we can never predict when a particular nucleus will decay, but the statistical behaviour of a large number of nuclei is highly predictable.
N 随时间变化的曲线是一条平滑的指数衰减曲线。经过一个半衰期，N = N₀/2；经过两个半衰期，N = N₀/4，依此类推。由于衰变是随机且自发的，我们无法预言某个特定的核将在何时衰变，但大量核的统计行为却是高度可预测的。
These exponential relationships are exploited in radiometric dating (e.g. carbon‑14 dating) and in medical applications where the activity of a tracer can be monitored over time.
这些指数关系
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