\[E = h\nu = \frac{hc}{\lambda} = hc\tilde\nu,\qquad E/\mathrm{eV} \approx \frac{1239.84}{\lambda/\mathrm{nm}}\]
光子动量photon momentum
\[p = \frac{h}{\lambda} = \frac Ec\]含义Meaning
光以能量为 hν 的量子（光子）形式被吸收和发射。普朗克（1900）为解释黑体辐射引入能量量子，爱因斯坦（1905）推广到光本身。
Light is absorbed and emitted in quanta of energy hν. Planck (1900) introduced quanta to explain black-body radiation; Einstein (1905) extended them to light itself.
符号说明Symbols
| 符号Symbol | 含义 Meaning | 单位 Unit |
|---|---|---|
| \(h\) | 普朗克常数 6.626×10⁻³⁴ J·sPlanck constant | J·s |
| \(E\) | 光子能量photon energy | J, eV |
推导Derivation
普朗克假设振子能量只能是 hν 的整数倍，导出与实验吻合的黑体辐射公式，避免“紫外灾难”。
Planck assumed oscillator energies come in multiples of hν, fitting black-body spectra and avoiding the ultraviolet catastrophe.
用 c = λν 改写；每摩尔光子能量 \(E_m = N_Ahc/\lambda\)：500 nm 光子约 239 kJ/mol，可与化学键能比较。
Per mole \(E_m = N_Ahc/\lambda\): 500 nm ≈ 239 kJ/mol, comparable to bond energies.
适用条件与局限Assumptions & limitations
单光子关系；强激光下可发生多光子吸收。
Single-photon relation; intense lasers allow multiphoton absorption.