Explain discrete atomic energy levels and line spectra
Explain why isolated atoms have discrete electron energies and how transitions produce emission and absorption lines.
Section 22 · Quantum physics
A Level; Cambridge International Physics 9702, 2025–2027 syllabus, Topic 22. These original explanations and calculations are study aids; full timed assessment and human subject-teacher review remain outstanding.
Before you begin
- Use wave frequency and wavelength, energy, momentum, SI prefixes, electronvolts and scientific notation.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
Why does an isolated atom produce a line spectrum?
What you will learn
- Describe discrete energy levels in isolated atoms
- Explain emission line formation
- Explain absorption line formation
An isolated atom allows only particular electron energies
Electrons in an isolated atom occupy discrete energy levels rather than any energy in a continuous range. An electron can change between allowed levels by absorbing or emitting a photon whose energy matches the difference between the levels.
For emission, an electron moves from a higher energy level to a lower one and emits a photon. Only particular energy differences are possible, so only particular photon frequencies and wavelengths are emitted. The result is a line spectrum rather than a continuous spectrum.
Absorption selects matching photon energies
For absorption, an electron moves from a lower level to a higher allowed level by absorbing a photon with exactly the required energy difference. Other photon energies do not match that transition and are not absorbed by it in this simple isolated-atom model.
An absorption spectrum can show dark lines at wavelengths removed from a continuous background. The same energy differences give the corresponding emission lines. Each element has its own set of allowed levels, so its line pattern can be characteristic of that element.
Pause and explain
During emission, how does an electron's energy change?
Worked example
Explain why an isolated hydrogen atom emits particular spectral lines rather than every visible wavelength.
Show the worked solution
- Identify the discrete allowed electron energies.
- Relate each emitted photon to one energy-level difference.
- Connect the set of allowed differences to separate frequencies.
Answer Only certain energy-level differences are allowed. Each downward transition emits a photon with one matching energy and frequency, producing separate spectral lines.
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Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
An electron in an atom moves from a higher allowed level to a lower one. Describe what happens to the energy difference.
Give me a hint
Match the transition direction with photon emission.
Compare my reasoning
- The electron loses energy equal to the difference between the levels.
- A photon is emitted with that energy.
- The photon frequency is set by the size of the energy gap.
A photon is emitted with energy equal to the energy-level difference.
Look for these in your work
- Level direction identified
- Energy conservation applied
- Photon relation described
A narrow band of white light passes through a cool gas and a dark line appears in the transmitted spectrum. Explain the line.
Give me a hint
Connect an absorption line to a photon energy that matches an upward transition.
Compare my reasoning
- Atoms in the gas have discrete energy levels.
- Photons with a matching energy are absorbed as electrons move to higher levels.
- The removed wavelength appears as a dark line in the transmitted spectrum.
The gas absorbs selected photon energies that match level gaps, creating a dark absorption line.
Look for these in your work
- Discrete levels stated
- Matching photon absorbed
- Observed line explained
Two elements have different sets of electron energy levels. Why can their emission spectra identify which element is present?
Give me a hint
Relate allowed energy gaps to photon wavelengths and the pattern of lines.
Compare my reasoning
- Each set of levels permits particular transition energy gaps.
- Each gap produces a photon with a particular frequency and wavelength.
- The resulting pattern of lines is characteristic of the element.
Different level spacings produce different characteristic line patterns.
Look for these in your work
- Level structure compared
- Photon frequencies related
- Identification value explained
Common mistakes
- Treating atomic energy levels as continuous
- Saying a photon can have any energy during a particular transition
- Reversing emission and absorption directions
- Confusing an absorption dark line with extra emitted light
What can you explain now?
Why does an isolated atom produce a line spectrum?
Compare with the explanation
Only particular electron energy differences are allowed
Each allowed transition corresponds to a specific photon energy.
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Make it stick
How do discrete atomic levels create matching emission and absorption lines?
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