E.2 Quantum physics (HL only)

By the late 19th century, classical physics seemed complete , Maxwell's equations described electromagnetic waves beautifully. Yet a series of experiments involving light and matter produced results that classical wave theory simply could not explain. The resolution required an entirely new framework: quantum physics.

The key crisis came from the photoelectric effect: when ultraviolet light hit a metal surface, electrons were ejected instantly. But bright red light , no matter how intense , ejected nothing. Classical wave theory predicted that any frequency of light, given enough intensity and time, should eventually eject electrons. Experiment flatly contradicted this.

This subtopic covers three interconnected pillars of quantum physics at HL:

1. The photoelectric effect , evidence for the particle nature of light
2. Wave-particle duality and the de Broglie hypothesis , evidence for the wave nature of matter
3. Compton scattering , further evidence for the particle nature of light

Together, these phenomena reveal that both light and matter possess a dual nature , sometimes behaving as waves, sometimes as particles, depending on what we measure.

Photoelectric Effect: The emission of electrons from a metal surface when electromagnetic radiation of sufficiently high frequency is incident upon it.

Photoelectron: An electron emitted from a metal surface as a result of the photoelectric effect.

When light shines on a clean metal surface, careful experiment reveals four crucial observations:

1. Threshold frequency exists: Electrons are only emitted if the light's frequency exceeds a minimum value, the threshold frequency $f_c$. Below this frequency, no electrons are emitted regardless of intensity.
2. Instantaneous emission: Once the frequency threshold is met, electrons are emitted with essentially zero time delay , even at very low intensities.
3. Intensity controls number, not energy: Increasing the intensity of light (above threshold) increases the number of emitted electrons, but not their maximum kinetic energy.
4. Frequency controls kinetic energy: Increasing the frequency of the incident light increases the maximum kinetic energy of emitted electrons.

These four observations are completely incompatible with classical wave theory, which predicted:

• Higher intensity → more energetic electrons
• Any frequency would eventually work if bright enough
• There should be a measurable time delay for electrons to absorb sufficient energy

All three classical predictions are wrong.