E.2.1 Wave–particle duality (HL only) Notes

The Photoelectric Effect and Wave-Particle Duality

1. Consider you’re holding a metal plate in a brightly lit room.
2. As light shines on the plate, something extraordinary happens: electrons are ejected from its surface.
3. But here’s the twist, this only occurs if the light’s frequency is above a certain threshold, no matter how intense the light is.
4. Why doesn’t brighter light always eject electrons?

Evidence for Light’s Particle Nature: The Photoelectric Effect

When light strikes the metal, electrons are ejected and travel to the collecting plate, completing an electric circuit and generating a measurable current.

Key Observations of the Photoelectric Effect:

1. Threshold Frequency:
   1. Electrons are emitted only if the light’s frequency exceeds a minimum value, called the threshold frequency ($f_{\text{c}}$).
2. Frequency Determines Kinetic Energy:
   1. The kinetic energy ($E_{\text{max}}$) of the emitted electrons increases with the frequency of the light but is unaffected by its intensity.
3. Instantaneous Emission:
   1. Electrons are emitted immediately after light strikes the surface, with no delay.
4. Intensity Affects Quantity, Not Energy:
   1. Increasing the light’s intensity increases the number of emitted electrons (current) but does not affect their kinetic energy.

Why Light as a Wave Fails to Explain These Observations

If light were purely a wave:

1. Increasing intensity (wave amplitude) would increase the energy of emitted electrons, but this is not observed.
2. Electrons would eventually absorb enough energy to escape, even at low frequencies, contradicting the threshold frequency requirement.