In simple terms
A friendly intro before the formal notes — no formulas yet.
Energy levels in atoms and line spectra
Cambridge 9702 Paper 4 — Energy levels in atoms and line spectra (22.4). Senpai Corner diagram-backed pilot with premium structure and live visuals.
- 1
The ionisation level (a free electron) is defined as 0 eV.
- 2
All bound states have negative energy values.
- 3
The ground state is the level with the most negative energy.
- 4
Downward arrows show photon emission (de-excitation); upward arrows show energy absorption (excitation).
What this topic covers
The official Cambridge syllabus points this lesson works through.
- 22.4.1
Understand that there are discrete electron energy levels in isolated atoms (e.g. atomic hydrogen)
- 22.4.2
Understand the appearance and formation of emission and absorption line spectra
- 22.4.3
Recall and use
Explore the concept
Use the live diagram, PhET or GeoGebra sim, and synced steps — play it, drag controls, or tap a step.
Step-synced diagram — highlights what to look for in the simulation above.
Step 1
The ionisation level (a free electron) is defined as 0 eV.
8 more simulations for this topic — run them in the Simulations section below
Simulations
Every simulation here runs the real model — try the steps on a card, then check what you see against the notes.
8 simulations · 4 to start with
Start herein this order — each one shows a different piece of the topic
- oPhysicsStart here · 19702 22.4 · IB E.1 · IB E.2
Hydrogen Energy Levels
Hydrogen energy-level diagram: pick transitions and see emitted/absorbed photon energies and spectral lines
Why this one: Pick a transition and see the emitted photon's energy equal the gap between the two levels.
Try this
- Pick a transition down to n = 2 and read the photon energy.
- Pick one down to n = 1.
- Pick a transition from n = 3 to n = 2 and compare.
Look for Photon energy equals the difference between the two levels, so transitions to n = 1 give the shortest wavelengths.
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
- 3JCN PhysicsStart here · 29702 22.4 · IB E.1
Atomic Emission Spectra
View emission spectra of elements; relate lines to energy level transitions
Why this one: Compare the emission lines of different elements — each set of levels gives its own fingerprint.
Try this
- View the emission spectrum of hydrogen.
- Switch to another element and compare the line positions.
- Match a line to its energy level transition.
Look for Each line is a photon of energy equal to the difference between two discrete levels, so every element has its own pattern.
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
- 3JCN PhysicsStart here · 39702 22.4 · IB E.1
Franck-Hertz Experiment
Sweep accelerating voltage and see current dips at quantised energies
Why this one: Sweep the accelerating voltage and see current dips where electrons lose exactly one excitation energy.
Try this
- Sweep the accelerating voltage and watch the current.
- Read the voltage spacing between successive dips.
Look for Current dips at equal voltage intervals because electrons lose a fixed quantum of energy to the atoms.
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
- PhETStart here · 4Java · best on a laptop9702 22.4 · IB E.1–E.2
Neon Lights & Other Discharge Lamps
Fire electrons at atoms in a gas tube; watch them excite the atoms and read the emitted lines on the spectrometer.
Why this one: Fire electrons at gas atoms, excite them by collision and read the emitted lines on the spectrometer.
Try this
- Choose hydrogen and raise the voltage until the atoms light up.
- Open the spectrometer — the lines appear at fixed wavelengths.
- Switch to mercury — a different set of lines.
Look for Each element has fixed energy levels, so its emission lines sit at fixed wavelengths: E = hc/λ.
Simulation by PhET Interactive Simulations, University of Colorado Boulder · Licensed to MarkScheme (public licence CC BY-NC 4.0 since 2026-03-30)
More simulations4 more on this topic — core ones first
- SimuPhysicsCore9702 22.3 · 9702 22.4 · IB E.2
Bohr-de Broglie Standing Waves
A de Broglie wave is wrapped around each Bohr orbit; only orbits fitting a whole number of wavelengths survive
Try this
- Wrap the wave round the first orbit.
- Try an orbit between the allowed ones.
- Count the wavelengths in each allowed orbit.
Look for An allowed orbit fits a whole number of de Broglie wavelengths.
Open on SimuPhysicsRuns on their siteSimuPhysics by Mohamed Abdelsalam · Licensed to MarkScheme (site publishes no licence; served with frame-ancestors self)
- SimuPhysicsCore9702 22.4 · IB E.1
Atomic Model & Hydrogen Spectrum Simulation
Excite the atom and watch electrons drop between levels, producing the matching spectral line each time
Try this
- Excite the atom and watch the drop.
- Match each drop to its spectral line.
- Compare a large drop with a small one.
Look for The photon energy equals the difference between the two levels.
Open on SimuPhysicsRuns on their siteSimuPhysics by Mohamed Abdelsalam · Licensed to MarkScheme (site publishes no licence; served with frame-ancestors self)
- 3JCN PhysicsCore9702 22.4 · IB E.1
Atomic Spectra Experiment
Run a spectrometer on a gas discharge tube and read line wavelengths
Try this
- Run the spectrometer on the discharge tube and read a line wavelength.
- Compute the photon energy from the wavelength.
Look for Line wavelengths are discrete, reflecting discrete energy levels in the atom.
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
- 3JCN PhysicsCore9702 22.4 · IB E.1
Energy Levels of Hygrogen
Click between hydrogen energy levels and see the emitted photon wavelength
Try this
- Click from n = 3 to n = 2 and read the photon wavelength.
- Click from n = 2 to n = 1 and compare.
- Try a transition into n = 3.
Look for Photon energy equals the level difference, so transitions into n = 1 give ultraviolet and into n = 2 give visible lines.
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
Key formulas
Tap any symbol to reveal exactly what it means and its units.
Tap a symbol — great for exam definitions
Full topic notes
Formal explanation with the rigour you need for the exam.
The Quantised Atom: Energy Levels
Electrons orbiting an atom's nucleus are not free to possess any amount of energy. Instead, they are restricted to specific, fixed energy states. This fundamental concept is known as energy quantisation. These allowed states are typically visualised using an energy-level diagram, where the lowest and most stable energy state is called the ground state. Higher, less stable states are known as excited states.
Interpreting Energy Level Diagrams
Energy level diagrams are a standard way to visualise quantised energy states. By convention, the energy required to completely remove an electron from the atom (ionisation) is defined as 0 eV. Since energy must be supplied to remove a bound electron, all energy levels within the atom are negative. The ground state is the most negative value, representing the most tightly bound state. Transitions are shown as arrows: an upward arrow for absorption/excitation and a downward arrow for emission/de-excitation. The length of the arrow is proportional to the energy of the photon involved.
The ionisation level (a free electron) is defined as 0 eV.
All bound states have negative energy values.
The ground state is the level with the most negative energy.
Downward arrows show photon emission (de-excitation); upward arrows show energy absorption (excitation).
Electron Transitions
Electrons can move between these discrete energy levels by absorbing or emitting energy. This process is called an electron transition.
1. Excitation: Moving to a Higher Level
An atom can be excited, promoting an electron to a higher energy level, in two primary ways:
- Photon Absorption: The atom absorbs an incident photon. This only occurs if the photon's energy is exactly equal to the energy difference between the electron's initial state and a higher energy level ().
- Collisional Excitation: The atom collides with another particle, typically a fast-moving electron (e.g., in a fluorescent tube). The atomic electron is excited if it receives at least the required energy ($Delta E$) from the kinetic energy of the colliding particle. Any excess kinetic energy is retained by the colliding particle.
Excitation by photon requires an exact energy match.
Excitation by collision requires the colliding particle to have at least the excitation energy.
2. De-excitation: Returning to a Lower Level
An electron in an excited state is unstable and will spontaneously transition to a lower energy level, a process called de-excitation. This transition releases energy in the form of a single photon. The energy of this photon is precisely equal to the energy difference between the initial and final levels. An electron can return to the ground state in a single jump or via a series of smaller jumps, known as a cascade. A cascade results in the emission of multiple photons, each with a different energy (and thus different frequency/wavelength).
Here, is Planck's constant (), is the frequency of the emitted photon, is the higher energy level, and is the lower energy level. Crucially, the energy of the photon is exactly the difference between the initial and final electron energy levels.
De-excitation is the process of an electron moving to a lower energy level.
A photon is emitted with energy equal to the energy difference: .
A cascade is a series of de-excitations, emitting multiple photons.
The Electronvolt (eV): A Convenient Energy Unit
When dealing with atomic energies, Joules (J) are often inconveniently small. Physicists frequently use the electronvolt (eV), a more practical unit. One electronvolt is defined as the kinetic energy gained by a single electron when it is accelerated through an electrical potential difference of one volt.
Electronvolt (eV) is a common unit for atomic energies.
It represents energy gained by an electron accelerating through 1 volt.
Essential to convert between eV and J for calculations using fundamental constants like .
Types of Spectra: A Comparison
There are three main types of spectra:
- Continuous Spectrum: Produced by a hot, dense source (like the filament of an incandescent light bulb). It contains all wavelengths of light, appearing as a continuous rainbow.
- Emission Spectrum: Produced by a hot, low-density gas (like in a neon sign or a star's atmosphere). The gas emits light only at specific wavelengths corresponding to its electron transitions, appearing as a series of bright lines on a dark background.
- Absorption Spectrum: Produced when light from a continuous source passes through a cooler, low-density gas. The gas absorbs light at the specific wavelengths that match its excitation energies, resulting in a continuous spectrum with dark lines superimposed.
Because every element has a unique set of energy levels, the pattern of spectral lines it produces is also unique. This allows an emission or absorption spectrum to be used as an 'atomic fingerprint' to identify the elements present in a substance, such as the atmosphere of a distant star.
Continuous spectrum: All wavelengths, from a hot, dense source.
Emission spectrum: Bright lines, from a hot, low-density gas.
Absorption spectrum: Dark lines, from a cool gas in front of a continuous source.
For a given element, the lines in its emission and absorption spectra occur at the same wavelengths.
Remember to convert electronvolts (eV) to Joules (J) when using Planck's constant in calculations, as Planck's constant is in Joules-seconds (Js). Pay close attention to negative signs when calculating energy differences between levels!
Worked examples
See the formulas applied — reveal one step at a time, like the exam.
An electron in a hydrogen atom de-excites from an energy level of -1.51 eV to a ground state level of -13.6 eV. Calculate the frequency of the emitted photon. (Use and ).
- 1
Find the energy difference (in eV):
Light of wavelength 486 nm is observed in the emission spectrum of hydrogen. This corresponds to a transition to the n=2 energy level, which has an energy of -3.40 eV. Calculate the energy of the initial, higher energy level in eV. (Use , , and ).
- 1
Calculate the energy of the emitted photon in Joules (J):
How it all connects
The big idea sits in the middle — tap a linked idea to explore the link.
Tap a linked idea to see how it connects back to the main topic — that connection is what examiners reward.
Glossary
Key terms for this topic — skim now; the Check step will test them.
- energy quantisation
This fundamental concept is known as energy quantisation. These allowed states are typically visualised using an energy-level diagram, where the lowest and most stable energy state is called the ground state.
- Planck's constant
Here, is Planck's constant (), is the frequency of the emitted photon, is the higher energy level, and is the lower energy level.
- electronvolt (eV)
Physicists frequently use the electronvolt (eV), a more practical unit.
- Planck's constant ()
A fundamental constant linking the energy of a photon to its frequency: .
- De-excitation cascade
When an excited electron returns to a lower state via a series of intermediate energy levels, emitting multiple photons of different energies, rather than in a single jump.
- Wave equation
The wave equation: . This is used to convert between a photon's frequency and wavelength.
Quick check
Write your answer first, then compare it with the model one — the gap is what you would have lost.
Teach it back
If you can explain it simply, you own it — gaps here are marks you’d lose.
Teach it back
Explain this topic as if teaching a friend. We name the gaps an examiner would still dock.
Revision flashcards
Guess first, then flip — retrieval beats re-reading.
Key takeaways
Review these before you close the topic — retrieval beats re-reading.
The ionisation level (a free electron) is defined as 0 eV.
All bound states have negative energy values.
The ground state is the level with the most negative energy.
Downward arrows show photon emission (de-excitation); upward arrows show energy absorption (excitation).
Practice — then mark it
The whole point: a real Cambridge question, marked mark-by-mark.
The lines in Fig. 8.1 correspond to electron transitions down to the energy level -3.40 eV. One of the lines represents emitted radiation of wavelength 488 nm. (i) Calculate the energy of a photon of this radiation.
Determine the energy, in eV, of the energy level from which the electron transition originates to cause the emission of this radiation.
Extra simulations & links
PhET, GeoGebra and other curated tools — open in a new tab.
Frequently asked
Checkpoint
One marked question is worth ten re-reads — close the loop before you move on.
Reading it isn’t knowing it — prove it.
Before you move on: do 9702/42 · Q8(b)(i) on paper, snap a photo, and get examiner-style feedback on exactly where you win and lose marks.
Discuss Energy levels in atoms and line spectra
Ask, share and discuss with other Physics students