# Explain why the Bohr model of the hydrogen atom successfully predicts the wavelengths of spectral lines in the Lyman series but fails to account for the spectra of multi-electron atoms.

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

> The Bohr model treats the hydrogen atom as a single electron orbiting a nucleus in one of a set of allowed circular orbits, each associated with a discrete energy level.

## Mark scheme (4 marks)

1. In the Bohr model, the electron can only occupy orbits where the angular momentum is quantised (an integer multiple of h/2π), leading to discrete energy levels unique to hydrogen.
2. A photon is emitted or absorbed when an electron transitions between two allowed energy levels, and its frequency/wavelength is determined by the energy difference between those levels, correctly matching the Lyman series (transitions to n = 1).
3. In multi-electron atoms, electron–electron repulsion (electrostatic interactions between electrons) alters the energy levels in a way the Bohr model does not account for.
4. The Bohr model also cannot account for the sub-levels (s, p, d…) or the fine structure of spectral lines, since it does not include quantum numbers beyond n (e.g. no orbital angular momentum quantum number or spin), so the predicted single-line spectrum does not match the observed complex spectra of multi-electron atoms.

## Key terms

- [Lyman series](https://www.gradenine.co.uk/glossary/lyman-series)

## Related

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