Key Equations

The Photoelectric Effect — AQA A-Level Physics

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Einstein's photoelectric equation
$$hf = \phi + E_{k(\max)}$$
  • Where:
    • $h$ = Planck's constant (J s)
    • $f$ = frequency of incident radiation (Hz)
    • $φ$ = work function (J)
    • $E_k(max)$ = maximum kinetic energy of photoelectrons (J)
All terms must be in the same units. At the threshold: hf₀ = φ and E_k(max) = 0.
Electronvolt conversion
$$1 \text{ eV} = 1.60 \times 10^{-19} \text{ J}$$
  • Where:
    • $eV$ = electronvolt
    • $J$ = joule
eV → J: multiply. J → eV: divide.
Kinetic energy from potential difference
$$eV = \frac{1}{2}mv^2$$
  • Where:
    • $e$ = charge of electron (C)
    • $V$ = potential difference (V)
    • $m$ = mass of electron (kg)
    • $v$ = velocity (m s⁻¹)
For an electron accelerated from rest through p.d. V.
Work function from threshold frequency
$$\phi = hf_0$$
  • Where:
    • $φ$ = work function (J)
    • $h$ = Planck's constant (J s)
    • $f_0$ = threshold frequency (Hz)
Follows from the photoelectric equation when E_k(max) = 0.
Maximum kinetic energy from stopping potential
$$E_{k(\max)} = eV_s$$
  • Where:
    • $E_k(max)$ = maximum kinetic energy (J)
    • $e$ = electron charge (C)
    • $V_s$ = stopping potential (V)
Use magnitude of V_s. Stopping potential is independent of intensity.
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