Key Equations

Quantum Physics - OCR A-Level Physics

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.
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