📚 A Simple Model of the Atom | 原子的简单模型
At GCSE level the atom is often pictured as a tiny solar system: a dense central nucleus surrounded by orbiting electrons. In A-Level physics, this simple nuclear model is developed quantitatively. Understanding how the model was established, what evidence supports it, and what its limitations are provides the foundation for particle physics, quantum phenomena and nuclear decay.
在 GCSE 阶段，原子常被画成微小的太阳系：致密的中心原子核被绕行的电子包围。在 A-Level 物理中，这个简单核式模型得到定量发展。理解该模型是如何建立的、有哪些实验证据以及其局限性，是粒子物理、量子现象和核衰变的基础。
1. From Indivisible Spheres to a Nuclear Atom | 从不可分球体到核式原子
Early atomic theory from Democritus and Dalton treated atoms as indivisible solid spheres. The discovery of the electron by J. J. Thomson in 1897 showed that atoms contain smaller negative particles. Thomson's "plum pudding" model therefore proposed that negative electrons were embedded in a sphere of positive charge, like fruit in a pudding.
早期原子理论从德谟克利特和道尔顿开始，将原子视为不可分的实心球体。1897 年汤姆孙发现电子，表明原子含有更小的负电粒子。因此汤姆孙的葡萄干布丁模型提出，负电子嵌在正电荷球体中，就像布丁中的果粒。
2. The Alpha-Particle Scattering Experiment | α粒子散射实验
In 1909, Geiger and Marsden, under Rutherford's direction, fired alpha particles at a very thin gold foil. A zinc sulfide screen detected scattered alpha particles. They observed that most alpha particles passed through with little or no deflection, some were deflected through small angles, and about 1 in 8000 bounced back at angles greater than 90°.
1909 年，盖革和马斯登在卢瑟福指导下，用 α 粒子轰击极薄的金箔。硫化锌屏用于探测散射的 α 粒子。他们观察到大多数 α 粒子几乎无偏转地穿过，一些发生小角度偏转，大约每 8000 个中有 1 个以大于 90° 的角度反弹回来。
3. Evidence for a Small Charged Nucleus | 小尺度带电核的证据
The fact that most alpha particles passed straight through showed the atom is mostly empty space. Small deflections were caused by electrostatic repulsion from a positive charge. Large-angle scattering could not be explained by Thomson's model, because a diffuse positive charge would exert only weak forces. The back-scattered particles required a very small, dense, positively charged nucleus containing almost all the mass.
大多数 α 粒子直线穿过，表明原子内部绝大部分是空的。小角度偏转由正电荷的静电排斥引起。大角度散射无法用汤姆孙模型解释，因为弥散正电荷只能施加微弱作用力。反弹粒子要求存在一个非常小、致密、带正电且几乎包含全部质量的原子核。
4. Key Features of the Nuclear Model | 核式模型的关键特征
The nuclear atom has a central nucleus of radius about 10⁻¹⁵ m to 10⁻¹⁴ m, while the atom has radius about 10⁻¹⁰ m. The nucleus contains positive protons and neutral neutrons. Electrons orbit at comparatively large distances. The atom is electrically neutral because the number of electrons equals the number of protons.
核式原子中心原子核半径约为 10⁻¹⁵ m 至 10⁻¹⁴ m，而原子半径约为 10⁻¹⁰ m。原子核包含带正电的质子和不带电的中子。电子在相对较大的距离上绕行。原子整体呈电中性，因为电子数等于质子数。
5. Protons, Neutrons and Electrons | 质子、中子与电子
An electron has charge -1.60 × 10⁻¹⁹ C and mass 9.11 × 10⁻³¹ kg, about 1/1836 of a proton's mass.
质子和中子统称为核子。质子带电荷 +1.60 × 10⁻¹⁹ C，质量 1.67 × 10⁻²⁷ kg。中子不带电，质量略大。电子带电荷 -1.60 × 10⁻¹⁹ C，质量 9.11 × 10⁻³¹ kg，约为质子质量的 1/1836。
| Particle 粒子 | Charge 电荷 | Mass 质量 |
|---|---|---|
| Proton 质子 | +1.60 × 10⁻¹⁹ C | 1.67 × 10⁻²⁷ kg |
| Neutron 中子 | 0 | 1.67 × 10⁻²⁷ kg |
| Electron 电子 | -1.60 × 10⁻¹⁹ C | 9.11 × 10⁻³¹ kg |
6. Nuclide Notation and Isotopes | 核素符号与同位素
A nuclide is written with mass number A (protons + neutrons) at top left and proton number Z at bottom left, for example ²³⁵₉₂U. The relationship between A, Z and neutron number N is:
核素写作左上角质量数 A（质子数 + 中子数）和左下角质子数 Z，例如 ²³⁵₉₂U。A、Z 与中子数 N 的关系为：
A = Z + N
Isotopes are atoms of the same element with the same Z but different A. They have the same chemical properties because they have the same number of electrons, but different physical properties such as mass and nuclear stability.
同位素是同一元素中 Z 相同而 A 不同的原子。由于电子数相同，它们化学性质相同，但质量、核稳定性等物理性质不同。
7. Specific Charge of the Electron and Nucleus | 电子和原子核的比荷
Specific charge is charge divided by mass. For the electron it is:
比荷是电荷除以质量。电子的比荷为：
e/mₑ = 1.60 × 10⁻¹⁹ C / 9.11 × 10⁻³¹ kg ≈ 1.76 × 10¹¹ C kg⁻¹
For a nucleus of proton number Z and mass number A, the specific charge is approximately:
对于质子数为 Z、质量数为 A 的原子核，比荷近似为：
specific charge ≈ Ze / (A × 1.66 × 10⁻²⁷ kg)
8. Scale and Empty Space | 原子中的尺度与空旷空间
If the nucleus were enlarged to the size of a marble, the atom would be about 100 metres across. This illustrates that an atom is mostly empty space. The nuclear density is around 10¹⁷ kg m⁻³, enormously greater than ordinary matter.
如果把原子核放大到弹珠大小，原子直径约为 100 米。这说明原子内部绝大部分是空的空间。核密度约为 10¹⁷ kg m⁻³，远大于普通物质。
9. Forces Within the Nucleus | 原子核内的力
Electrons are held by electrostatic attraction to the positive nucleus. Between protons there is strong electrostatic repulsion, so the nucleus must contain another force. The strong nuclear force between nucleons is attractive at separations of about 1–3 fm and repulsive at very short range, preventing the nucleus from collapsing.
电子依靠与正电荷原子核之间的静电引力束缚。质子之间存在强静电排斥，因此原子核内必然存在另一种力。核子之间的强核力在约 1–3 fm 的间距内表现为吸引，在极短距离表现为排斥，从而防止原子核塌缩。
10. Limitations of the Simple Model | 简单模型的局限性
Rutherford's model could not explain why atoms emit discrete line spectra or why electrons do not spiral into the nucleus. According to classical electromagnetic theory, an accelerating electron should radiate energy continuously. Bohr later added quantised orbits, and full quantum mechanics replaced the planetary picture.
卢瑟福模型无法解释原子为何发射分立线状光谱，也无法解释电子为何不会旋入原子核。根据经典电磁理论，加速电子应连续辐射能量。玻尔后来引入量子化轨道，完整的量子力学则取代了行星式图像。
Published by TutorHao | Physics Revision Series | aleveler.com
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