Explain how the Franck–Hertz experiment provides evidence for the existence of discrete energy levels in atoms.

IB DP Physics Higher Level (2023 syllabus) — E.1 Structure of the atom · Explain · 4 marks · View as Markdown

Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).

In the Franck–Hertz experiment, electrons are accelerated through mercury vapour. The current collected at the anode is observed to drop sharply at regular intervals of approximately 4.9 eV as the accelerating voltage is increased.

Model answer (4 marks)

Electrons accelerated through mercury vapour collide with mercury atoms. If the electron energy is below the 4.9 eV gap between the ground and first excited state, the collisions are elastic – the electrons keep their kinetic energy and reach the anode, so the current rises smoothly. When the accelerating voltage reaches 4.9 eV (or a multiple thereof) the electrons have just enough energy to excite the atom; the collision becomes inelastic and the electron loses almost all of its kinetic energy. It can no longer overcome the small retarding potential at the anode, so the current drops sharply. The fact that the current drops at regular, equal voltage intervals of about 4.9 eV shows that electrons can transfer only specific, discrete amounts of energy to the atoms, providing evidence that atoms possess quantised energy levels.

Examiner tips

  • Use the term ‘elastic’ and ‘inelastic’ collisions to show understanding of energy transfer.
  • Explain the role of the retarding potential in turning the current off.
  • Mention the 4.9 eV energy gap and its repetition as evidence of discrete levels.
  • Keep the answer concise – 4 marks only.

Common mistakes

  • Confusing the 4.9 eV value with the total accelerating voltage; students sometimes say ‘4.9 V’ instead of ‘4.9 eV’.
  • Failing to explain why the current drops (i.e. the electron cannot reach the anode after losing energy).
  • Not linking the regular voltage intervals to the concept of quantised energy levels.

Mark scheme (4 marks)

  1. Electrons collide with mercury atoms and can only transfer energy when they possess at least 4.9 eV (the energy difference between the ground state and first excited state).
  2. Below 4.9 eV, collisions between electrons and mercury atoms are elastic, so electrons retain their kinetic energy and reach the anode, giving a steady (or rising) current.
  3. At multiples of 4.9 eV, electrons undergo inelastic collisions, losing (almost) all their kinetic energy to the mercury atoms, and can no longer overcome the small retarding potential at the anode, causing the current to drop sharply.
  4. The regular, repeating pattern of current drops at equal voltage intervals shows that only specific, discrete amounts of energy can be absorbed by the atom, which is consistent with quantised (discrete) energy levels.

Key terms in this question

discrete energy levels

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