Wave-particle duality
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
- Light shows its wave side in interference/diffraction, its particle side in the photoelectric effect.
- This dual behaviour is wave–particle duality.
Practice
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
- 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.
Practice
The de Broglie wavelength of a particle is:
$\lambda = \dfrac{h}{p}$ — wavelength is Planck's constant over momentum.
Practice
A faster particle (more momentum) has a ____ de Broglie wavelength.
$\lambda = \dfrac{h}{p}$, so larger $p$ gives a smaller $\lambda$.
Electron diffraction
- Fire electrons at a thin crystal and they make a ring diffraction pattern — only waves diffract.
- Faster electrons → more momentum → shorter $\lambda$ → rings move closer together.
Practice
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.
Practice
Speeding up the electrons makes the diffraction rings:
Faster electrons → shorter $\lambda$ → less diffraction → the rings close in.
You've got it
Key idea
- 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