# Explain how the de Broglie hypothesis accounts for the discrete energy levels observed in the hydrogen atom.

> IB DP Physics Higher Level (2023 syllabus) — E.2 Quantum physics (HL only) · Explain · 4 marks

> Niels Bohr's model of the hydrogen atom postulated that electrons can only occupy certain allowed orbits without radiating energy. Louis de Broglie later proposed that particles such as electrons possess wave-like properties characterised by a wavelength λ = h/p.

## Mark scheme (4 marks)

1. The electron is associated with a de Broglie wavelength given by λ = h/p (or λ = h/mv).
2. Only orbits in which an integer number of de Broglie wavelengths fit exactly around the circumference are permitted (standing wave condition: nλ = 2πr).
3. If the standing wave condition is not met, destructive interference causes the wave to cancel, so that orbit is not stable/not permitted.
4. Because only certain radii are allowed by the standing wave condition, only certain momenta (and hence kinetic energies) are permitted, giving rise to discrete energy levels.

## Key terms

- [discrete energy levels](https://www.gradenine.co.uk/glossary/discrete-energy-levels)

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