E.2.1 Wave–particle duality (HL only)

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: 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: 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: Electrons are emitted immediately after light strikes the surface, with no delay.
4. Intensity Affects Quantity, Not Energy: 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.
3. A time delay would occur as electrons accumulate energy from low-intensity light, but emission is instantaneous.

Einstein’s Explanation: Light as Photons

1. Albert Einstein resolved this dilemma by proposing that light consists of discrete packets of energy called photons.
2. The energy ($E$) of a photon is proportional to the frequency ($f$) of the light: $E = hf$, where $h$ is Planck’s constant ($6.63 \times 10^{-34} \, \text{J s}$).
3. When a photon strikes the metal surface, its energy is transferred to a single electron.
4. The electron uses some of this energy to overcome the attractive forces holding it in the metal.
5. This minimum energy is called the work function ($\phi$) of the metal.
6. Any remaining energy becomes the electron’s kinetic energy ($E_{\text{max}}$): $$E_{\text{max}} = hf - \phi$$

Stopping Voltage and Maximum Kinetic Energy

The maximum kinetic energy of the emitted electrons can be measured using the stopping voltage ($V_s$).

The relationship is:

$$eV_s = E_{\text{max}}$$

Threshold Frequency and Work Function

At this frequency, the photon’s energy equals the work function ($hf_{\text{c}} = \phi$), and the electrons have zero kinetic energy:

$$f_{\text{c}} = \frac{\phi}{h}$$

Wave–Particle Duality: Light Behaves as Both

1. Interference and diffraction show light behaving as a wave.
2. The photoelectric effect shows the same light behaving as a stream of particles (photons).
3. Neither model alone is complete, so light has a dual wave–particle nature.

If light can be both wave and particle, can matter also behave as a wave? That is the question answered by the de Broglie hypothesis.