Atomic energy levels and line spectra
Key idea: H2 Physics lessons on photons, matter waves, wavefunctions, uncertainty and atomic spectra.
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The core idea
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Big question: Why do atoms emit and absorb only particular wavelengths?
Electrons occupy discrete atomic energy levels. A transition emits or absorbs a photon only when hf equals the energy gap. Emission gives bright lines from downward transitions; absorption removes matching wavelengths from a continuous spectrum. Each element's level pattern therefore produces a characteristic spectrum.
Connect spectral lines to energy differences
Atoms have discrete stationary energy levels. An emitted photon carries hf = E_high − E_low when an atom moves down; absorption requires a photon matching an allowed upward energy difference.
A transition's photon energy is a difference between levels, not the energy of either level. Several pairs of levels can produce several spectral lines, and lines from different transitions may coincide if their differences match.
Check your understanding: Can a ground-state atom absorb a photon with less energy than its first allowed gap?
Not as that bound-state transition; the photon energy does not match an allowed difference.
Distinguish absorption and emission
Absorption moves an electron to a higher allowed level when the photon energy matches the gap. Emission occurs when an electron moves to a lower level and a photon carries away that energy difference.
An emission spectrum has bright lines from downward transitions. An absorption spectrum has dark lines when a continuous spectrum passes through cooler atoms. The same level differences underlie corresponding absorption and emission wavelengths, and a return through intermediate levels can produce a cascade of photons.
Check your understanding: Why can an atom excited to a high level emit several photons before returning to ground?
It may fall through intermediate allowed levels in a cascade, emitting one photon for each energy difference.
Key ideas to keep
- Photon energy equals a level difference, not the absolute energy of one level.
- An electron cannot remain between allowed levels.
- One transition can be represented consistently on an energy diagram and in a spectrum.
See the reasoning
Worked example
Turn an energy gap into a spectral line
Question: An atom drops by 4.0 eV. Find emitted wavelength using hc = 1240 eV nm and relate it to a spectrum.
Step 1: Find the transition energy
Why: Photon energy is the difference between levels.
Working: A downward gap of 4.0 eV emits a 4.0 eV photon.
Step 2: Convert energy to wavelength
Why: The supplied hc value is already in eV nm.
Working: λ = hc/ΔE = 1240/4.0 = 310 nm.
Step 3: Connect to the observation
Why: Only allowed energy differences occur.
Working: The atom produces a discrete emission line rather than a continuum.
Answer: λ = 1240/4.0 = 310 nm. Only allowed level differences occur, so isolated atoms produce discrete emission lines rather than a continuum.
Check: A larger energy gap would give a shorter wavelength.
Use a hint if needed
Practise with support
Try this
A photon does not match any upward level difference. State the idealised absorption result.
Hint: Transitions require an allowed energy difference.
Check your answer
It is not absorbed by that isolated atom.
Now work without the hint
Practise independently
Your turn
Distinguish emission and absorption spectra and solve a generic level transition.
Check your answer
Downward transitions emit bright discrete lines; upward absorption removes matching photons from a continuum, producing dark lines. In either direction photon energy magnitude is |ΔE| = hf = hc/λ.
Avoid these traps
Common mistakes
Common mistake
An atom can absorb any photon above a minimum energy.
What is wrong with this reasoning?
Show better thinking
An isolated atom absorbs photons matching allowed upward level differences.
Common mistake
Emission and absorption lines come from unrelated energies.
What is wrong with this reasoning?
Show better thinking
They correspond to the same level differences in opposite transition directions.
Write for the examiner
Exam guidance
Keep energy units consistent and draw the transition arrow in the correct direction before finding wavelength.
Exam-style practice [6 marks]
Levels are −6.0, −4.0 and −1.0 eV. List absorption energies from the ground state and the largest emission energy.
Plan before you answer
- List upward gaps from the ground state.
- Find the largest downward gap.
- Keep absorption and emission directions clear.
Mark your answer and compare the model
Marking points
Tick each point only if your answer states it clearly.
Model answer
Ground-state absorption energies are 2.0 and 5.0 eV. The largest downward difference is 5.0 eV.
Come back in three days
Check what stayed with you
Recall question
Why do absorption lines align with possible emission lines for the same atom?
Check the answer
Both correspond to the same allowed energy-level differences, with opposite transition directions.
Syllabus and review details
This lesson covers the listed H2 Physics 9478 outcomes. Use ΔxΔp ≳ h in the form given in the syllabus. Infinite-square-well results apply to a one-dimensional well with ψ zero at both infinite walls and n = 1, 2, …. Photon and matter-wave evidence supports complementary quantum descriptions. X-ray production, solving the Schrödinger equation, finite barriers, tunnelling and scanning tunnelling microscopy are not required here.
- GCE A-Level H2 PhysicsTopic 19(k) / Topic 19(l) / Topic 19(m) · 2027Checked against the syllabus · partial topic coverageOfficial 9478 syllabus
Course and syllabus information
- Course
- GCE A-Level H2 Physics
- Edition
- GCE A-Level H2 Physics 2027