Quantum Physics Foundations (AP Physics 2, Unit 7)

Photon

A single quantum (discrete packet) of electromagnetic radiation; used to model light’s energy transfer as occurring in chunks rather than continuously.

Quantization (of light energy)

The idea that light exchanges energy with matter in discrete amounts (photons), not as a continuously divisible wave.

Photon energy equation (E = hf)

Gives the energy of one photon as Planck’s constant times frequency; higher frequency means higher energy per photon.

Planck’s constant (h)

Fundamental constant linking photon energy to frequency; approximately 6.63 × 10^-34 J·s.

Speed of light relation (c = λf)

Connects wave speed c, wavelength λ, and frequency f for light; implies frequency and wavelength are inversely related.

Photon energy–wavelength form (E = hc/λ)

Expression for photon energy using wavelength; shorter wavelength (higher frequency) means higher photon energy.

Light intensity (photon model)

Primarily corresponds to photon flux (number of photons arriving per second per area), not the energy per photon.

Photoelectric effect

Emission of electrons from a metal surface when light shines on it; evidence that light can behave like particles (photons).

Photoelectrons

Electrons emitted from a metal surface due to the photoelectric effect.

Threshold frequency (f₀)

Minimum light frequency required to eject electrons from a given metal; below f₀ there is no emission regardless of intensity.

Work function (φ)

Minimum energy required to free an electron from a metal surface; depends on the material.

Einstein’s photoelectric equation (K_max = hf − φ)

Energy conservation for the photoelectric effect: photon energy minus work function equals the maximum kinetic energy of emitted electrons.

Maximum kinetic energy (K_max)

The greatest kinetic energy among emitted photoelectrons; increases with frequency above threshold, not with intensity.

Immediate emission (photoelectric observation)

When f > f₀, electrons are emitted essentially without time delay even at low intensity, supporting the photon model.

Stopping potential (V_s)

Reverse voltage needed to stop the fastest photoelectrons from reaching the collector in a photoelectric setup.

Stopping potential relation (eVs = Kmax)

At the stopping potential, an electron’s electric potential energy change equals the maximum kinetic energy of emitted electrons.

Elementary charge magnitude (e)

Magnitude of the charge of an electron/proton; approximately 1.60 × 10^-19 C (used in eV and eV↔J conversions).

Linear V_s vs f graph

Plot of stopping potential versus frequency is linear with slope h/e and an intercept that relates to the metal’s work function.

Threshold wavelength (λ₀)

Longest wavelength (lowest frequency) that can still eject electrons; defined by φ = hc/λ₀.

Electronvolt (eV)

Energy unit equal to 1.60 × 10^-19 J; also equals the energy gained by a charge e moving through 1 V.

Wave-particle duality

Principle that light and matter show both wave-like behavior (interference/diffraction) and particle-like behavior (localized, quantized interactions), depending on the experiment.

Photon momentum (p = h/λ)

Momentum carried by a photon in terms of wavelength; shows light can transfer momentum despite zero rest mass.

Photon momentum–energy form (p = E/c)

Photon momentum expressed using energy; derived from E = hf and c = λf, giving p = E/c.

de Broglie wavelength (λ = h/p)

Wavelength associated with a moving particle; quantifies matter’s wave-like behavior and explains phenomena like electron diffraction.

Electron accelerated through a potential difference (K = eV)

For an electron starting from rest, kinetic energy gained equals eV; commonly used to find momentum and de Broglie wavelength in electron-beam problems.