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Bohr Model of The Atom

Key idea: Use the Bohr model as a simple picture for discrete energy levels and photon emission/absorption (ΔE = hf), with clear limitations (A Level Physics).

  • GCE A-Level H2 Physics 2027
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Learning objectives

  • Use photon energy and momentum and analyse the photoelectric effect.
  • Apply de Broglie wavelength and wave-particle evidence.
  • Interpret wavefunctions, probability density and superposition.
  • Apply uncertainty and infinite-square-well energy quantisation.
  • Analyse atomic energy levels and emission or absorption spectra.
Model scope

Use discrete energy levels and |Δ E| = hf for the core syllabus. The Bohr orbit picture is historical support and has important limitations; it is not the final quantum model of the atom.

1. Definitions (Must Know)

A. Bohr model (what it claims)

The Bohr model is a historical model that describes electrons in atoms as occupying discrete stationary states (energy levels).

Electrons emit or absorb photons only when they transition between levels.

B. Transition energy

For a transition between two energy levels:

Δ E = hf = hc/λ

2. Key Ideas (What Earns Marks)

  • Discrete energy levels explain line spectra: only certain Δ E exist.
  • Ground state is the lowest-energy state; excited states are higher-energy states.
  • Photon absorption/emission must match the energy gap exactly:
    • absorption: photon energy equals the gap,
    • emission: photon energy equals the gap.
Scope note

The Bohr model itself is not the main assessment target in 9478. Use it as a simple picture for “discrete energy levels → spectral lines” when helpful.

3. Detailed Explanations

Historical Bohr model and photon transitionA nucleus is surrounded by three labelled circular stationary-state orbits n equals 1, 2 and 3. An electron drops from n equals 3 to n equals 2 and emits a photon with energy h f equal to the energy-level difference. The orbit picture is marked as a historical model.+Zen = 1n = 2n = 3photon: hf = |ΔE|Historical orbit picture—not the final quantum model
Bohr model: a historical picture for discrete stationary states and photon transitions, not the final quantum model of an atom.

A. Why the model was proposed (the problem it tries to solve)

Classical physics struggles to explain:

  • why atoms are stable (why electrons don’t continuously radiate away energy),
  • why atoms have discrete line spectra.

The Bohr model addresses this by saying electrons occupy stable stationary states and only exchange energy in discrete jumps.

B. Emission and absorption in one sentence

If an electron drops from a higher level to a lower level, it emits a photon with: hf = Δ E

If it absorbs a photon, it can only move up if the photon energy matches the gap exactly.

4. Common Mistakes

  • Treating the Bohr orbit picture as a literal modern description (it is a model with limitations).
  • Saying “any photon can be absorbed” (must match a discrete energy gap).

5. Exam Tips

  • For spectra questions, start with: “energy levels are discrete, so only certain photon energies are possible.”
  • Use Δ E = hf to connect the diagram to frequency/wavelength.

6. Worked Examples

Modelled example 1

Photon wavelength from a level change

Core

Problem

An atom emits a photon when it drops through an energy gap of 2.0 eV. Using hc = 1240 eV·nm, find the wavelength and connect it to the line spectrum.
Study the worked solution

  1. Apply energy conservation

    Method

    The emitted photon energy equals the magnitude of the level decrease.

    Reason

    A downward transition releases the discrete energy difference.

    Working

    E_γ = |Δ E| = 2.0 eV

  2. Convert energy to wavelength

    Method

    Use E_γ = hc/λ.

    Reason

    The supplied eV·nm constant keeps the units consistent.

    Working

    λ = 1240/2.0 nm = 620 nm

  3. Interpret

    Method

    This transition contributes a line at 620 nm.

    Reason

    Only discrete atomic energy gaps, hence discrete photon wavelengths, are available.

    Working

    Δ E discrete ⇒ λ discrete

7. Mind Stretchers

Mind stretcher 1: Why do different elements have different spectra?Extension

Explain why hydrogen and neon have different line spectra.

Show Answer

Different atoms have different allowed energy levels (different energy gaps).

So the possible photon energies (and hence frequencies/wavelengths) for transitions are different, producing different line spectra.

8. Optional (Enrichment)

A. Limitations of the Bohr model

The Bohr model works best as a simple picture for hydrogen-like atoms, but it does not fully explain multi-electron atoms and does not match the modern wavefunction description of electrons.

Continue with the next resource in this course.

Course and syllabus information
Course
GCE A-Level H2 Physics
Edition
GCE A-Level H2 Physics 2027