Quantum Theory and Wave-Particle Duality
Introduced| English | Meaning |
|---|---|
| wave–particle duality/weɪv ˈpɑːtɪkl djuːˈælɪti/ | wave–particle duality |
| photon/ˈfəʊtɒn/ | A quantum of electromagnetic radiation with energy equal to Planck's constant multiplied by its frequency. |
Is light a wave or a particle? Yes.
- Diffraction and interference prove light is a wave. The photoelectric effect proves it's a particle.
- Both are true at once — light is somehow both, depending on how you test it.
- This is wave–particle duality 波粒二象性, the strange heart of quantum physics.
- Even electrons, normally "particles", show wave behaviour too.
Light comes in packets
- Light energy comes in tiny bundles called photons 光子.
- Each photon carries energy $E = hf$ — Planck's constant $h$ times the frequency.
- A brighter beam has more photons, not bigger ones.
- Higher-frequency light means higher-energy photons (blue > red; X-ray > visible).
The energy of a single photon is given by:
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$E = hf$ — Planck's constant times the frequency.
A brighter beam of light of the same colour has:
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Brighter = more photons; each photon's energy depends only on frequency.
When each face shows
- Light shows its wave side in interference, diffraction and refraction.
- It shows its particle side when it hits matter — ejecting electrons, or as photons in a detector.
- Which behaviour you see depends on the experiment, not on the light changing.
- Neither picture alone is complete; you need both.
Light shows its ____ nature in interference and diffraction.
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Interference and diffraction are wave behaviours.
Select all true statements about wave-particle duality.
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Light and matter are both wave and particle; photons have $E = hf$. Brighter means more photons, not more energetic ones.
Matter waves too
- Louis de Broglie proposed that particles also have a wavelength: $\lambda = \dfrac{h}{p}$.
- Electrons fired at a crystal diffract, just like waves — confirming it.
- Big objects have absurdly tiny wavelengths, so we never notice their wave nature.
- Duality is universal; it's just hidden for everyday-sized things.
Wave or particle evidence?
Light shows both natures. Sort each experiment by what it demonstrates.
Particles such as electrons also have a wavelength and can diffract.
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De Broglie's $\lambda = h/p$ was confirmed by electron diffraction.
A brighter light means more photons, not more energetic ones. A single photon's energy is fixed by the frequency ($E = hf$), not the brightness. So dim blue light still has higher-energy photons than bright red light.
Which has higher-energy photons?
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Blue light has a higher frequency, so $E = hf$ gives higher-energy photons.
Which has higher-energy photons: red light or blue light?
- Blue light has a higher frequency, so by $E = hf$ its photons carry more energy.
- Making the red light brighter adds more photons but doesn't raise each photon's energy.
Wave–particle duality: light (and matter) behaves as both a wave and a stream of particles. Light comes in photons of energy $E = hf$ — a brighter beam has more photons, not bigger ones. Even particles have a wavelength ($\lambda = h/p$), usually too tiny to notice.
Write from 15 eV in five photons
- Each photon of a beam carries 3 eV.
- The beam delivers five such photons. Find the total energy, and say what brightness changes.
Each photon in a beam carries 3 eV. Five of those photons arrive at a detector. How much energy arrives in total, and what would making the beam brighter change?
Five photons at 3 eV each carry 15 eV.
How much energy do the five photons deliver?
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Five times 3 eV is 15 eV.