A-Level Physics May/June 2025 Q9(b)(i): Explain, with reference to photons, why V_S depends on the frequency of the incident el…

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  The stopping potential, $V_S$, is the potential difference required to stop the most energetic photoelectrons from reaching the collector plate. The work done by this potential on an electron is $eV_S$, which must be equal to the maximum kinetic energy ($E_{k,max}$) of the emitted electron. Therefore, $eV_S = E_{k,max}$.

  The incident electromagnetic radiation consists of discrete packets of energy called photons. The energy of a single photon, $E$, is directly proportional to the frequency, $f$, of the radiation, as given by the equation $E = hf$.

  According to the photoelectric equation, $hf = \Phi + E_{k,max}$, where $\Phi$ is the work function of the metal. This shows that the maximum kinetic energy of an emitted electron depends on the energy of the incident photon. A higher frequency results in a higher photon energy, which in turn leads to a greater maximum kinetic energy for the photoelectrons. Since a larger $E_{k,max}$ requires a larger stopping potential to overcome it, $V_S$ depends on the frequency.

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  How the marks are awarded

  • B1 — The first mark is for explaining that the stopping potential is related to the maximum kinetic energy of the emitted electrons, e.g., by stating that the work done $eV_S$ equals $E_{k,max}$.
  • B1 — The second mark is for stating that the energy of a photon is dependent on its frequency, often by quoting the equation $E = hf$.
  • B1 — The third mark is for linking the photon energy to the electron's maximum kinetic energy, explaining that a higher photon energy leads to a higher maximum kinetic energy for the electron.

  Common mistakes

  • Confusing the roles of intensity and frequency, incorrectly stating that higher intensity increases the stopping potential.
  • Providing a vague explanation, such as 'more frequency means more energy', without specifying that it is the photon's energy that determines the electron's maximum kinetic energy.
  • Omitting the role of photons entirely and attempting to explain the phenomenon using a wave model of light.
  • Failing to link the maximum kinetic energy of the electron back to the stopping potential required to stop it.

  Examiner tip: For 'explain' questions in quantum physics, clearly state the chain of cause and effect, linking the properties of the photon to the resulting properties of the electron.

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