Wave-particle duality
| English | Chinese | Pinyin |
|---|---|---|
| wave–particle duality | 波粒二象性 | bō lì èr xiàng xìng |
| de Broglie wavelength | 德布罗意波长 | dé bù luó yì bō cháng |
| electron diffraction | 电子衍射 | diàn zi yǎn shè |
| momentum | 动量 | dòngliàng |
Both at once
- The photoelectric effect proves light behaves as particles.
- Yet interference and diffraction prove it behaves as waves.
- Light is both — and so, astonishingly, are electrons.
Wave–particle duality 波粒二象性
- Light shows its wave side in interference/diffraction, its particle side in the photoelectric effect.
- This dual behaviour is wave–particle duality.
Electrons fired at graphite form a ring diffraction pattern — only waves diffract, so electrons behave as waves
The de Broglie wavelength
λ = h/p
A particle's wavelength is inversely proportional to its momentum — faster, heavier particles have shorter waves.
Light shows its wave nature in interference, and its particle nature in:
The photoelectric effect needs photons (particles); interference and diffraction need waves.
The de Broglie wavelength 德布罗意波长
- De Broglie proposed that any moving particle has a wavelength $\lambda = \dfrac{h}{p}$.
- For a fast electron this is about an atomic spacing — small, but measurable.
The de Broglie wavelength of a particle is:
$\lambda = \dfrac{h}{p}$ — wavelength is Planck's constant over momentum.
A faster particle (more momentum) has a ____ de Broglie wavelength.
$\lambda = \dfrac{h}{p}$, so larger $p$ gives a smaller $\lambda$.
Electron diffraction 电子衍射
- Fire electrons at a thin crystal and they make a ring diffraction pattern — only waves diffract.
- Faster electrons → more momentum 动量 → shorter $\lambda$ → rings move closer together.
Dark absorption lines in the Sun's spectrum mark the wavelengths absorbed by cooler gas
Electron diffraction shows that electrons can behave as waves.
Only waves diffract, yet a beam of electrons makes a diffraction pattern — so electrons have a wave nature.
Speeding up the electrons makes the diffraction rings:
Faster electrons → shorter $\lambda$ → less diffraction → the rings close in.
You've got it
- wave–particle duality: light (and matter) show both natures
- de Broglie wavelength $\lambda = \dfrac{h}{p}$ — faster particle, shorter wavelength
- electron diffraction is direct proof that particles behave as waves