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How did the Bohr model explain quantised atomic energy levels?

Describe the development of atomic models and explain quantised electron energy levels

A focused answer to the WACE Year 12 Physics Unit 4 content point on atomic models. The Rutherford nuclear model, its instability problem, Bohr's quantised orbits, photon emission and absorption between energy levels, and how de Broglie waves justify quantisation.

Generated by Claude Opus 4.88 min answerUpdated 2026-06-02

Reviewed by: AI editorial process; not yet individually human-reviewed

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What this dot point is asking

WACE wants you to trace how atomic models developed and explain quantised energy levels in terms of photon emission and absorption. This is the bridge between the photon idea and the line spectra of atoms.

From Rutherford to a problem

Rutherford's gold-foil scattering experiment showed that most of an atom is empty space, with nearly all the mass and the positive charge concentrated in a tiny central nucleus. Electrons orbit this nucleus. The trouble is that, by classical electromagnetism, an accelerating (orbiting) charge should continuously radiate energy, lose speed and spiral into the nucleus in a fraction of a second. Real atoms are stable, so the classical picture was incomplete.

Bohr's quantised levels

Bohr postulated that electrons can occupy only certain discrete, stable energy levels (orbits) without radiating, and that radiation occurs only when an electron jumps between levels. Each level has a fixed energy, with the lowest (ground state) most tightly bound and higher levels closer together near the top. The energies are negative, measured relative to a free electron at zero, because the electron is bound to the atom.

Emission and absorption

When an electron falls from a higher level $E_{\text{high}}$ to a lower level $E_{\text{low}}$ , it emits a single photon carrying exactly the energy difference:

hf=E_{\text{high}}-E_{\text{low}}.

To jump up, the atom must absorb a photon of exactly that energy. Because only specific differences exist, atoms emit and absorb only specific frequencies, which is why spectra are discrete lines rather than a continuous band.

Why the levels are quantised

De Broglie's matter waves give a physical reason for Bohr's rule: an electron orbit is stable only when a whole number of electron wavelengths fits around the circumference, forming a standing wave. Orbits that do not fit a whole number of wavelengths interfere destructively and cannot persist, so only certain radii (and hence energies) are allowed.

Photon emitted in an energy-level transition

Wavelength of an emission line

An electron drops from a level at $-1.5\ \text{eV}$ to a level at $-3.4\ \text{eV}$ . Find the wavelength of the emitted photon ( $h=6.63\times10^{-34}\ \text{J s}$ , $1\ \text{eV}=1.6\times10^{-19}\ \text{J}$ ).

Energy of the photon equals the level difference:

E=(-1.5)-(-3.4)=1.9\ \text{eV}=1.9\times1.6\times10^{-19}=3.04\times10^{-19}\ \text{J}.

Wavelength from $E=hc/\lambda$ :

\lambda=\frac{hc}{E}=\frac{(6.63\times10^{-34})(3.0\times10^8)}{3.04\times10^{-19}}=6.5\times10^{-7}\ \text{m}=650\ \text{nm}.

This red line is part of the visible hydrogen spectrum.

The development of the models in order

WACE expects you to be able to outline how the picture of the atom evolved, not just state the final model. Thomson's plum-pudding model treated the atom as positive charge spread through a sphere with electrons embedded in it. Rutherford's gold-foil scattering, in which a few alpha particles bounced almost straight back, showed this was wrong and that the positive charge and nearly all the mass sit in a tiny dense nucleus. Bohr then added quantised energy levels to explain why orbiting electrons do not radiate and why atoms produce discrete line spectra. De Broglie supplied a physical reason for the quantisation through standing matter waves, and the later quantum-mechanical model replaced fixed orbits with probability distributions (orbitals). A short chronological sketch, naming the experiment or idea that forced each change, is a common short-answer question.

Getting the energy difference right

Subtract the lower (more negative) energy from the higher one and take the magnitude; the photon energy is always positive. Convert electronvolts to joules before using $h$ unless you are working in eV throughout. Emission is a downward jump, absorption an upward jump.

Exam-style practice questions

Practice questions written in the style of SCSA exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

WACE 20226 marksA hydrogen atom has energy levels including

E_1=-13.6\ \text{eV}

E_2=-3.40\ \text{eV}

and

E_3=-1.51\ \text{eV}

. (a) Calculate the wavelength of the photon emitted when an electron falls from

E_3

E_2

. (b) Determine the minimum energy, in joules, needed to ionise the atom from its ground state.

Show worked answer →

A 6 mark calculation rewards the transition wavelength and the ionisation energy.

(a) Transition wavelength. Photon energy $E=|E_3-E_2|=|-1.51-(-3.40)|=1.89\ \text{eV}=3.02\times10^{-19}\ \text{J}$ . Then

\lambda=\frac{hc}{E}=\frac{(6.63\times10^{-34})(3.0\times10^{8})}{3.02\times10^{-19}}=6.6\times10^{-7}\ \text{m}.

(b) Ionisation energy. Ionising from the ground state means raising the electron from $-13.6\ \text{eV}$ to $0$ , so $E=13.6\ \text{eV}=13.6\times1.6\times10^{-19}=2.18\times10^{-18}\ \text{J}$ .

Markers reward the level difference of $1.89\ \text{eV}$ , $\lambda=hc/E$ near $6.6\times10^{-7}\ \text{m}$ and the ionisation energy of $2.18\times10^{-18}\ \text{J}$ .

WACE 20215 marksExplain the problem with the Rutherford model of the atom according to classical physics, and explain how Bohr's postulates resolved it.

Show worked answer →

A 5 mark explanation needs the classical instability and Bohr's two key postulates.

The classical problem. In the Rutherford model electrons orbit the nucleus. Classical electromagnetism says an accelerating charge (an orbiting electron is accelerating because its direction changes) must radiate energy continuously. The electron would therefore lose energy, spiral inward and collapse into the nucleus in a tiny fraction of a second, so the atom could not be stable, contradicting observation.

Bohr's resolution. Bohr postulated that electrons occupy only certain discrete, stable energy levels in which they do not radiate, and that radiation occurs only when an electron jumps between levels, emitting or absorbing a photon of energy $hf=E_{\text{high}}-E_{\text{low}}$ . This both kept atoms stable and explained their discrete line spectra.

Markers reward the radiating-accelerating-charge collapse problem and Bohr's stable-levels plus quantised-jump postulates.