📚 Atomic Nucleus Structure and Nuclear Forces | 原子核结构与核力
In IB Physics, the atomic nucleus is the dense core of the atom, containing protons and neutrons. Understanding its structure and the forces that hold it together is essential for explaining nuclear stability, radioactivity, and energy release in nuclear reactions.
在IB物理中，原子核是原子的致密核心，由质子和中子组成。理解其结构以及将它们维系在一起的力，对于解释核稳定性、放射性和核反应中的能量释放至关重要。
1. The Nucleus: Protons and Neutrons | 原子核：质子与中子
The nucleus consists of nucleons — protons (positive charge) and neutrons (neutral). The number of protons is the atomic number Z, which defines the element. The total number of nucleons is the mass number A = Z + N, where N is the neutron number.
原子核由核子组成——质子（带正电）和中子（电中性）。质子数即为原子序数 Z，它决定了元素的种类。核子总数称为质量数 A = Z + N，其中 N 是中子数。
2 nucleus has Z = 6 and N = 6, so A = 12. The nuclear radius is roughly proportional to A¹ᐟ³, meaning more nucleons create a larger, but still extremely compact, sphere.
例如，碳-12原子核有 Z = 6、N = 6，因此 A = 12。核半径大致正比于 A¹ᐟ³，这意味着核子越多，原子核越大，但依然极其致密。
2. Isotopes and Nuclides | 同位素与核素
Isotopes are nuclei of the same element with the same number of protons but different numbers of neutrons. They share chemical properties but differ in mass and nuclear stability.
同位素是指同一种元素中质子数相同而中子数不同的原子核。它们具有相同的化学性质，但质量与核稳定性不同。
For instance, hydrogen-1 (¹H), hydrogen-2 (²H, deuterium), and hydrogen-3 (³H, tritium) are isotopes of hydrogen. The notation AZN is often used, e.g. 235U143 for uranium-235.
例如，氢-1（¹H）、氢-2（²H，氘）和氢-3（³H，氚）都是氢的同位素。常用记号 AZN 表示，如铀-235写作 235U143。
3. Nuclear Size and Density | 核尺寸与密度
The nuclear radius R can be estimated using the empirical formula R = R₀ A1/3, where R e number of nucleons, giving a nearly constant nuclear density of about 2.3 × 10¹⁷ kg·m⁻³.
核半径 R 可由经验公式 R = R₀ A1/3 估算，其中 R₀ ≈ 1.2 × 10⁻¹⁵ m（1.2 飞米）。这意味着核体积正比于核子数，因此核密度近似恒定，约为 2.3 × 10¹⁷ kg·m⁻³。
R = R₀ A¹ᐟ³ , R₀ ≈ 1.2 fm
If the entire atom were scaled up to a football stadium, the nucleus would be the size of a pea at the centre. The nucleus contains more than 99.9% of the atom's mass but occupies almost none of its volume.
如果将整个原子放大到一座体育场那么大，原子核就像场地中央的一粒豌豆。原子核拥有原子超过99.9%的质量，却几乎不占任何体积。
4. Strong Nuclear Force: Main Properties | 强核力：主要性质
The strong nuclear force (strong interaction) is the fundamental force that binds protons and neutrons together. It operates at very short ranges — roughly up to 3 fm — and is essentially zero beyond about 10 fm.
强核力（强相互作用）是将质子和中子束缚在一起的基本力。它的作用距离极短——大约不超过3飞米——在约10飞米以外几乎消失。
Key properties of the strong force:
强核力的关键性质：
- Attractive at typical nucleon separation: It holds nucleons together against electrostatic repulsion.
- Short range: It falls off very rapidly with distance, unlike gravity or electromagnetism.
- Charge independence: The force between two protons, two neutrons, or a proton and a neutron is approximately the same (ignoring electromagnetic effects).
- Saturation: A nucleon interacts strongly only with its nearest neighbours, leading to nuclear density being constant.
- 在典型核子间距下表现为吸引力：它克服质子间的静电排斥力，将核子束缚在一起。
- 短程性：它随距离增大而急剧减弱，不像引力或电磁力那样是长程力。
- 电荷无关性：质子—质子、中子—中子、质子—中子之间的强核力强度近似相同（忽略电磁效应）。
- 饱和性：一个核子只与其最近邻的少数核子发生强相互作用，因此核密度保持恒定。
5. Why the Nucleus Does Not Fly Apart | 为什么原子核不会飞散
Protons repel each other via the electric force, which is long-range and acts between every pair of protons. If only electromagnetism existed, a nucleus would instantly disintegrate.
质子之间通过电力相互排斥，该力是长程力，作用于每一对质子之间。如果只有电磁力存在，原子核会瞬间分裂。
The strong force overcomes this repulsion. At separations around 1–2 fm, the strong attraction is much larger than the Coulomb repulsion. However, because the strong force is short-ranged, a nucleus with too many protons relative to neutrons can become unstable due to Coulomb repulsion.
强核力克服了这种排斥。在间距约为1–2飞米时，强吸引力远大于库仑排斥力。然而，由于强核力是短程力，如果核内质子数相对于中子数过多，库仑排斥会导致原子核不稳定。
6. Neutrons as “Nuclear Glue” | 中子作为“核胶水”
Neutrons contribute to the strong force but carry no electric charge, so they add attraction without adding Coulomb repulsion. This is why heavier stable nuclei tend to have more neutrons than protons.
中子参与强核力但不带电，因此它们增加吸引力却不会增加库仑排斥。这就是为什么质量较大的稳定原子核往往中子数多于质子数。
For light nuclei like helium-4, the neutron-to-proton ratio is about 1:1. For uranium-238, the ratio is about 1.6:1. The extra neutrons help dilute the proton–proton repulsion and hold the nucleus together.
对于像氦-4这样的轻核，中子数与质子数之比约为1:1。对于铀-238，这一比例约为1.6:1。额外中子有助于稀释质子—质子排斥力，从而维持原子核的稳定。
7. Mass Defect and Binding Energy | 质量亏损与结合能
The mass of a nucleus is always less than the sum of the masses of its individual nucleons. This difference is called the mass defect Δm.
原子核的质量总是小于其所有独立核子质量之和。这个差值称为质量亏损 Δm。
Δm = Z·mₚ + N·mₙ − m_nucleus
According to Einstein's mass–energy relation, this lost mass is converted into the binding energy that holds the nucleus together.
根据爱因斯坦的质能关系，这部分损失的质量转化为将原子核结合在一起的结合能。
Eb = Δm·c²
For example, the helium-4 nucleus has a binding energy of about 28.3 MeV, which corresponds to roughly 7.1 MeV per nucleon — a very high value that explains helium's exceptional stability.
例如，氦-4原子核的结合能约为28.3 MeV，对应平均每个核子约7.1 MeV——这是非常高的数值，解释了氦核非凡的稳定性。
8. Binding Energy per Nucleon Curve | 平均结合能曲线
The graph of binding energy per nucleon against mass number A is central to nuclear physics. It rises sharply for light nuclei, reaches a maximum around A ≈ 56 (iron-56), and then slowly decreases for heavier nuclei.
平均结合能随质量数 A 变化的曲线是核物理的核心内容。它对于轻核迅速上升，在 A ≈ 56（铁-56）附近达到峰值，然后对于重核缓慢下降。
The peak at iron-56 indicates that this nucleus is the most stable. This curve explains two energy-releasing processes:
铁-56处的峰值表明该原子核最稳定。这条曲线可以解释两种释放能量的过程：
- Nuclear fusion: combining very light nuclei into heavier ones (e.g. hydrogen into helium) moves up the curve toward the peak.
- Nuclear fission: splitting very heavy nuclei (e.g. uranium-235) into lighter fragments also moves up the curve toward the peak.
- 核聚变：将极轻的原子核结合成更重的核（例如氢聚变为氦）使系统沿曲线上行，趋向峰值。
- 核裂变：将极重的原子核（如铀-235）分裂为较轻的碎片也使系统沿曲线上行，趋向峰值。
9. The Liquid-Drop Model | 液滴模型
The nucleus behaves like a drop of incompressible liquid. The liquid-drop model treats nucleons as molecules in a drop, with short-range attractive forces and a constant density. It successfully explains nuclear fission, binding energy trends, and why the nucleus is spherical.
原子核的行为类似于不可压缩的液滴。液滴模型将核子看作液滴中的分子，具有短程引力和恒定密度。它成功地解释了核裂变、结合能变化趋势以及原子核为何近似球形。
However, the liquid-drop model cannot explain shell structure or magic numbers. For those, the nuclear shell model is needed, where nucleons occupy discrete energy levels like electrons in an atom.
然而，液滴模型无法解释壳层结构和幻数。为此需要核壳层模型，其中核子占据分立的能级，就像电子在原子中占据能级一样。
10. Nuclear Stability and the Band of Stability | 核稳定性与稳定带
The stability of a nucleus depends on its neutron-to-proton ratio. On a graph of N versus Z, stable nuclei lie within a narrow diagonal region called the “band of stability.”
原子核的稳定性取决于其中子—质子比。在 N—Z 图上，稳定原子核位于一条狭窄的对角线区域内，称为“稳定带”。
Light stable nuclei have approximately equal numbers of protons and neutrons. As Z increases, the stable neutron-to-proton ratio rises above 1.5, because more neutrons are needed to overcome the growing Coulomb repulsion.
轻的稳定核中质子数和中子数近似相等。随着 Z 增大，稳定的中子—质子比会升至1.5以上，因为需要更多中子来克服不断增大的库仑排斥力。
Nuclei outside the band of stability undergo radioactive decay: those with too many neutrons undergo β⁻ decay, while those with too many protons may undergo β⁺ decay or electron capture.
位于稳定带之外的原子核会发生放射性衰变：中子过多时发生 β⁻ 衰变，质子过多时可能发生 β⁺ 衰变或电子俘获。
11. Nuclear Reactions: Conservation Rules | 核反应中的守恒定律
In any nuclear reaction, several quantities are conserved: total energy (including rest energy), total momentum, total charge, and the total number of nucleons (baryon number).
在任何核反应中，以下物理量守恒：总能量（包括静能量）、总动量、总电荷，以及核子总数（重子数）。
For example, in the fission of uranium-235 by a neutron:
例如，铀-235在中子轰击下发生裂变：
n + ²³⁵U → ¹⁴¹Ba + ⁹²Kr + 3n + energy
+ 3. The released energy comes from the mass defect between the initial and final nuclei.
电荷和核子数都守恒：0 + 92 = 56 + 36，1 + 235 = 141 + 92 + 3。释放的能量来源于反应前后原子核的质量亏损。
12. Key Formulas for IB Exams | IB考试中的关键公式
You must be able to apply several formulas quickly:
你需要能够快速应用以下公式：
- Nuclear radius: R = R₀A¹ᐟ³
- Mass defect: Δm = Z·mₚ + N·mₙ − m_nucleus
- Binding energy: E = Δm·c²
- Binding energy per nucleon: E/A
- 核半径：R = R₀A¹ᐟ³
- 质量亏损：Δm = Z·mₚ + N·mₙ − m_nucleus
- 结合能：E = Δm·c²
- 平均结合能：E/A
eful with units when converting to MeV. In IB exams, 1 u ≈ 931.5 MeV/c² is often provided.
始终注意质量用原子质量单位（u）或kg表示，并在转换为MeV时小心单位。在IB考试中，通常给出 1 u ≈ 931.5 MeV/c²。
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