Atomic energy levels and line spectra

Key idea: H2 Physics lessons on photons, matter waves, wavefunctions, uncertainty and atomic spectra.

  • GCE A-Level H2 Physics 2027

Learn the idea

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.

Photon absorption and emission between atomic energy levelsDiscrete atomic energy levels show an upward absorption transition and a downward emission transition, each labelled with photon energy equal to the level difference.EnergyE₁E₂E₃absorptionhf = E₃ − E₁emissionhf = E₃ − E₂
Scroll diagram horizontally to read all labels.
Absorption raises an electron only when the photon energy matches an allowed gap. Emission releases a photon whose energy equals the downward energy-level 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.

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.

  1. 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.

  2. 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.

  3. 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.

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.

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.

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.

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.

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.

Try this next

Use the longer mixed questions to connect the ideas, calculations and diagrams from this topic.

Open Quantum Physics structured practice

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