📚 IB Physics: Nuclear Physics & Quantum Foundations | IB 物理：核物理与量子基础精讲
The transition from classical to modern physics is one of the most fascinating steps in the IB Physics syllabus. Quantum physics explains the behaviour of light and matter at the atomic scale, while nuclear physics explores the structure of the nucleus and the huge energies locked inside. These two topics are closely linked: both are quantum in nature, and both require you to move beyond “common sense” intuition. This guide condenses the essential definitions, equations, and exam strategies you need for top marks.
从经典物理到现代物理的跨越，是 IB 物理课程中最引人入胜的部分之一。量子物理研究光与物质在原子尺度上的行为，而核物理探索原子核的结构以及其中蕴含的巨大能量。这两个主题紧密相连：它们在本质上都遵循量子规律，都需要你超越“常识”直觉。本指南浓缩了冲刺高分的必备定义、方程式与考试策略。
1. The Photoelectric Effect | 量子基础：光电效应
The photoelectric effect provided the first decisive evidence that light is quantised. When light shines on a metal surface, electrons can be emitted, but only if the photon energy hf exceeds the metal’s work function φ. Einstein’s equation is:
hf = φ + Kmax
where Kmax is the maximum kinetic energy of the emitted electrons. Since Kmax can be measured via the stopping potential Vs, we also write Kmax = eVs. This immediately explains why a low-intensity but high-frequency beam can emit electrons while a high-intensity low-frequency beam cannot: the frequency, not the intensity, fixes the photon energy.
其中 Kmax 是发射电子的最大动能。由于 Kmax 可通过遏止电压 Vs 测量，我们写作 Kmax = eVs。这立刻解释了为什么低强度高频光束能发射电子，而高强度低频光束却不能：决定光子能量的是频率而非强度。
- No time delay: photoelectrons appear instantly, because energy is absorbed as a single photon event. 无时间延迟：光电子瞬间出现，因为能量以单个光子事件被吸收。
- Threshold frequency: f₀ = φ/h; below it no emission occurs. 截止频率：f₀ = φ/h；低于该频率不发生发射。
- Intensity controls photocurrent: more photons per second → more electrons per second (for f > f₀). 强度控制光电流：每秒光子数更多 → 每秒电子数更多（当 f > f₀）。
2. Wave-Particle Duality & de Broglie Wavelength | 波粒二象性与德布罗意波长
In 1924, de Broglie proposed that all matter has a wavelength, given by:
λ = h/p = h/(mv)
where p is momentum, m is mass and v is speed. For electrons, this wavelength is observable: electron diffraction experiments produce interference patterns identical to X-ray diffraction, showing that particles also behave as waves. In IB, you should be able to calculate the de Broglie wavelength of a particle and explain why macroscopic objects have undetectably small wavelengths.
其中 p 是动量，m 是质量，v 是速度。对于电子，这个波长可被观测：电子衍射实验产生与 X 射线衍射完全相同的干涉图样，表明粒子也表现出波动性。在 IB 考试中，你需要能够计算粒子的德布罗意波长，并解释为什么宏观物体的波长小到无法探测。
Notice that if you know the kinetic energy K of a particle, the momentum can be written as p = √(2mK). This is useful in problems where an electron is accelerated through a known potential difference, because the electric potential energy eΔV is converted into kinetic energy.
请注意，若已知粒子的动能 K，动量可写为 p = √(2mK)。这在电子经已知电势差加速的问题中非常有用，因为电势能 eΔV 会转化为动能。
3. Atomic Energy Levels and Photon Transitions | 原子能级与光子跃迁
Electrons in atoms occupy discrete energy levels. When an electron makes a transition from a higher state Ei to a lower state Ef, the energy difference is emitted as a photon:
ΔE = Ei − Ef = hf = hc/λ
Absorption occurs when a photon supplies exactly the energy needed to jump to a higher level. For the hydrogen atom, the allowed electron energies are given by En = −13.6/n² eV, where n is the principal quantum number. The Lyman series (final level n = 1), Balmer series (n = 2) and Paschen series (n = 3) lie in the ultraviolet, visible and infrared regions respectively.
吸收则发生在光子恰好提供跃迁到更高能级所需能量的时候。对于氢原子，电子的允许能量由 En = −13.6/n² eV 给出，其中 n 是主量子数。莱曼系（末态 n = 1）、巴耳末系（n = 2）和帕申系（n = 3）分别位于紫外、可见光和红外区域。
Remember that the ground state energy is −13.6 eV, so the ionisation energy needed to free the electron completely is 13.6 eV. This value can also be obtained from the Lyman limit (λ = 91 nm).
请记住，基态能量为 −13.6 eV，因此使电子完全脱离原子的电离能为 13.6 eV。这个数值也可以从莱曼系限（λ = 91 nm）得到。
4. Heisenberg’s Uncertainty Principle | 海森堡不确定性原理
A purely quantum system cannot have perfectly defined position and momentum simultaneously. The standard statement is:
Δx Δp ≥ ħ/2
where ħ = h/2π. There is also a time-energy form:
ΔE Δt ≥ ħ/2
which explains why short-lived excited states produce broad spectral lines: a very small Δt forces a large uncertainty in energy, so the emitted photon frequency is not perfectly sharp. You should understand that this is not a measurement limitation but a fundamental property of nature.
其中 ħ = h/2π。还存在时间-能量形式：ΔE Δt ≥ ħ/2。这解释了为什么短寿命激发态会产生较宽的光谱线：极小的 Δt 迫使能量有较大的不确定性，因此发射光子频率并非完全锐利。你应该理解，这并非测量限制，而是自然的基本属性。
In numerical problems, take care to use consistent units: if Δx is in metres, Δp should be in kg·m/s. Often questions give values in eV/c or MeV/c; convert using 1 eV = 1.6 × 10⁻¹⁹ J.
在数值问题中，请注意单位一致：若 Δx 用米，单位 Δp 应为 kg·m/s。题目常给出 eV/c 或 MeV/c 的值；请利用 1 eV = 1.6 × 10⁻¹⁹ J 进行换算。
5. Wave Functions and Probability | 波函数与概率
Quantum particles are described by a wave function Ψ(x,t). The square of its absolute value, |Ψ|², gives the probability density of finding the particle at a given point. This makes quantum physics intrinsically probabilistic: we can predict distributions but not individual outcomes.
量子粒子由波函数 Ψ(x,t) 描述。其绝对值平方 |Ψ|² 给出在某一位置找到粒子的概率密度。这使量子物理本质上是概率性的：我们可以预测量子的分布，却无法预言单个结果。
For an infinite square well,
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