Quantum Physics

Photon model, photoelectric effect, wave-particle duality, energy levels and line spectra.

Spec Points Covered
  • I can describe the photonA quantum (discrete packet) of electromagnetic radiation. Its energy is proportional to its frequency. model and use $E = hf$ and $E = hc/\lambda$ to calculate photonA quantum (discrete packet) of electromagnetic radiation. Its energy is proportional to its frequency. energyThe capacity to do work. Measured in joules (J)..
  • I can convert between joules and electronvolts.
  • I can describe the photoelectric effectThe emission of electrons from a metal surface when electromagnetic radiation of sufficiently high frequencyThe number of complete oscillations passing a point per unit time. Measured in hertz (Hz). is incident on it. and explain the observations that cannot be explained by the wave model.
  • I can apply Einstein's photoelectric equation $hf = \phi + KE_{\max}$ to solve problems.
  • I can explain the terms threshold frequencyThe number of complete oscillations passing a point per unit time. Measured in hertz (Hz).The minimum frequencyThe number of complete oscillations passing a point per unit time. Measured in hertz (Hz). of incident radiation required to cause photoelectric emission from a particular metal surface., work functionThe minimum energyThe capacity to do work. Measured in joules (J). required to liberate an electron from the surface of a metal., and stopping potentialThe minimum potential difference required to stop the most energetic photoelectrons emitted in the photoelectric effect..
  • I can describe wave-particle dualityThe concept that all matter and radiation exhibit both wave-like and particle-like properties. Particles have a de Broglie wavelengthThe minimum distance between two points on a wave that are in phase (e.g. crest to crest). Measured in metres (m).; photons exhibit particle behaviour in the photoelectric effectThe emission of electrons from a metal surface when electromagnetic radiation of sufficiently high frequency is incident on it.. and use the de Broglie equation $\lambda = h/p = h/mv$.
  • I can explain atomic energyThe capacity to do work. Measured in joules (J). levels and how transitions between them produce emission and absorption line spectra.
  • I can use $hf = E_{1} - E_{2}$ to calculate the frequency or wavelengthThe minimum distance between two points on a wave that are in phase (e.g. crest to crest). Measured in metres (m). of emitted or absorbed photons.
Notes
01 Photon Photon → 02 Electronvolt (eV) Electronvolt (eV) → 03 Photoelectric effect Photoelectric effect → 04 This is a statement of conservation of energy $hf = \phi + KE_{max}$ → 05 Wave-particle duality $\lambda = \frac{h}{p} = \frac{h}{mv}$ → 06 Electrons in atoms exist in discrete energy levels (quantised states). They cannot have $hf = E_{1} - E_{2}$ → 07 The photoelectric effect cannot be explained by the wave model of light. Three key pieces of → 08 Electron diffraction provides direct evidence that particles have wave-like properties →
Σ Key Equations Full Reference →
On Data Sheet
Not on Data Sheet
Photon energy (frequency)
$$E = hf$$
  • Where:
    • $E$ = J
    • $h$ = J s
    • $f$ = Hz
Fundamental equation for photon energy. h = 6.63 × 10⁻³⁴ J s (on data sheet).
Photon energy (wavelength)
$$E = \frac{hc}{\lambda}$$
  • Where:
    • $E$ = J
    • $\lambda$ = m
Alternative form using wavelength. Always convert wavelength to metres before substituting.
Einstein's photoelectric equation
$$hf = \phi + KE_{max}$$
  • Where:
    • $hf$ = J
    • $\phi$ = J
    • $KE_{max}$ = J
Conservation of energy for the photoelectric effect. At the threshold frequency, KE_max = 0 and hf₀ = φ.
De Broglie wavelength (momentum)
$$\lambda = \frac{h}{p}$$
  • Where:
    • $\lambda$ = m
    • $h$ = J s
    • $p$ = kg m \(s^{-1}\)
Applies to all moving particles. p = mv for non-relativistic particles.
De Broglie wavelength (mass and velocity)
$$\lambda = \frac{h}{mv}$$
  • Where:
    • $\lambda$ = m
    • $m$ = kg
    • $v$ = m \(s^{-1}\)
Equivalent to λ = h/p with p = mv. Wavelength is only detectable for particles with very small mass.
Photon energy from energy level transition
$$hf = E_{1} - E_{2}$$
  • Where:
    • $hf$ = J
    • $E_1$ = J
    • $E_2$ = J
E₁ is the higher energy level, E₂ is the lower. Both are negative for bound electrons. The photon energy is always positive.
Electronvolt conversion
$$1 \text{ eV} = 1.6 \times 10^{-19} \text{ J}$$
  • Where:
    • $eV$ = J
Must be memorised. NOT on the OCR data sheet. Required for almost every quantum physics calculation.
Stopping potential
$$eV_s = KE_{max}$$
  • Where:
    • $e$ = C
    • $V_s$ = V
    • $KE_{max}$ = J
The stopping potential is the p.d. needed to reduce the photocurrent to zero. Combines with Einstein's equation: eV_s = hf − φ.