Wave-particle duality is the idea that quantum objects such as photons and electrons can show both wave-like and particle-like behavior. Light can spread out, diffract, and interfere like a wave, but it also arrives in separate packets of energy called photons. Electrons are particles with mass and charge, yet they can also form interference patterns.
This concept matters because it is one of the central clues that the microscopic world follows quantum rules, not everyday intuition.
The double-slit experiment shows the duality clearly. When single photons or electrons pass through two slits one at a time, each one is detected as a single dot on the screen, like a particle. After many particles arrive, the dots build up into bright and dark bands, which is the pattern expected from wave interference.
If a detector measures which slit each particle goes through, the interference pattern disappears, showing that measurement changes the behavior we observe.
Key Facts
- Photon energy is E = hf, where h is Planck's constant and f is frequency.
- Photon momentum is p = h / λ, where λ is wavelength.
- The de Broglie wavelength of matter is λ = h / p.
- Double-slit fringe spacing is Δy = λL / d for small angles, where L is screen distance and d is slit separation.
- Single particles hit the screen at localized points, but many hits can build an interference pattern.
- Measuring which slit a particle passes through destroys the interference pattern.
Vocabulary
- Wave-particle duality
- The quantum principle that objects such as light and electrons can show wave behavior or particle behavior depending on the experiment.
- Photon
- A photon is a quantum packet of electromagnetic radiation with energy E = hf.
- De Broglie wavelength
- The de Broglie wavelength is the wavelength associated with a moving particle, given by λ = h / p.
- Interference
- Interference is the combining of waves so that they reinforce in some places and cancel in others.
- Which-path information
- Which-path information is knowledge of which slit or path a quantum object took during an experiment.
Common Mistakes to Avoid
- Thinking the particle literally splits in half at the slits. Quantum theory predicts a probability wave through the setup, while each detection still appears as one localized hit.
- Assuming interference requires many particles traveling at the same time. The pattern can build up even when particles are sent one at a time, because each particle is described by a wave-like probability distribution.
- Using λ = v / f for electrons in the same way as for light. Matter waves use the de Broglie relation λ = h / p, and the particle speed must be handled through momentum.
- Believing that observation means a human must look at the experiment. In physics, measurement means any interaction that records which-path information, even if no person watches it directly.
Practice Questions
- 1 A photon has frequency 6.00 x 10^14 Hz. Using h = 6.63 x 10^-34 J s, calculate its energy.
- 2 Electrons pass through a double slit with slit separation 2.0 x 10^-6 m. Their de Broglie wavelength is 5.0 x 10^-10 m, and the screen is 1.5 m away. Use Δy = λL / d to find the spacing between adjacent bright fringes.
- 3 In a double-slit experiment with single electrons, explain why the screen shows individual dots at first but an interference pattern after many electrons have arrived.