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 4.77 min answerUpdated 2026-05-29

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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.

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.

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