Explain why the line emission spectrum of hydrogen provides evidence for the existence of discrete electron energy levels within the atom.

IB DP Physics Standard 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).

When a low-pressure sample of hydrogen gas is excited by an electrical discharge, light is emitted that, when passed through a diffraction grating, produces a series of sharp, coloured lines at specific wavelengths rather than a continuous band of colour.

Model answer (4 marks)

Electrons in an atom can only occupy discrete energy levels, so they can only have specific energies. When an electron falls from a higher to a lower level, the energy difference is released as a photon whose energy is E=hf. Because the energy differences between the allowed levels are fixed, only photons of specific frequencies (or wavelengths) are produced. The observed sharp spectral lines are therefore evidence that electrons exist in discrete energy levels; a continuous spectrum would occur if electrons could have any energy.

Examiner tips

Use the term "quantised" or "discrete" energy levels
Explain the photon emission as a transition between levels
Show the link E=hf to specific wavelengths
Mention that a continuous spectrum would contradict quantisation

Common mistakes

Failing to mention that electrons can only occupy specific energy levels
Confusing the emission process with absorption
Not linking the fixed energy differences to the specific wavelengths of the lines

Mark scheme (4 marks)

Electrons in the atom exist only in discrete (quantised) energy levels, so they can only possess certain specific energies.
When an electron transitions from a higher energy level to a lower energy level, a photon is emitted with energy equal to the difference between the two levels.
Because the energy differences between levels are fixed/specific values, only photons of specific frequencies (or wavelengths) are emitted, since E = hf.
These specific frequencies correspond to the observed sharp spectral lines; a continuous spectrum would result if electrons could possess any energy value, so the line spectrum is direct evidence for quantisation.

Key terms in this question

line emission spectrum