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.
Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).
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.
Model answer (4 marks)
In the Bohr model the electron can only occupy orbits where the angular momentum is quantised, L=nħ, giving discrete energy levels that depend only on the principal quantum number n. When an electron jumps between two allowed levels a photon of energy ΔE=hν is emitted or absorbed, so the wavelength λ=h c/ΔE. For hydrogen the energy levels are E_n=−13.6 eV/n², so transitions to n=1 give the Lyman series, and the calculated wavelengths match the observed lines.
In multi‑electron atoms the electron–electron repulsion shifts the energy of each level. The Bohr model has no term for this interaction, so the predicted energies are wrong. Moreover the model contains only the quantum number n; it has no orbital angular momentum or spin quantum numbers, so it cannot produce the sub‑levels (s, p, d…) or the fine structure that give the complex spectra of heavier atoms. Thus the Bohr model fails for multi‑electron atoms.
In multi‑electron atoms the electron–electron repulsion shifts the energy of each level. The Bohr model has no term for this interaction, so the predicted energies are wrong. Moreover the model contains only the quantum number n; it has no orbital angular momentum or spin quantum numbers, so it cannot produce the sub‑levels (s, p, d…) or the fine structure that give the complex spectra of heavier atoms. Thus the Bohr model fails for multi‑electron atoms.
Examiner tips
- Use the key points: quantised angular momentum → discrete n levels; photon energy ΔE=hν → Lyman series; explain why electron–electron repulsion and missing quantum numbers break the model for multi‑electron atoms.
- Show the energy formula for hydrogen and the transition to n=1 to justify the Lyman series.
- Mention the lack of sub‑levels and fine structure as the reason for failure.
Mark scheme (4 marks)
- 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.
- 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).
- 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.
- 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 in this question
Related
- All IB DP Physics Higher Level (2023 syllabus) revision notes →
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