S1.3Structure 1 — Models of the particulate nature of matter

Electron configurations — IB Chemistry SL Revision Notes & Topical Questions

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S1.3 Electron configurations: spectra and energy levels — IB CHEMISTRY SL notes: Distinguish continuous and line spectra and explain emission spectra in terms of electron transitions between energy levels.Wave relationship = c = fλ, with c = 3.00 × 108 m s−1 for all electromagnet…

What the symbols mean
Frequency and wavelength
Photon energy
Order of increasing energy
Visible region
Data booklet

Part 1 of 8The electromagnetic spectrum

The electromagnetic spectrum

Wave relationship

Wave relationship c = fλ, with c = 3.00 × 10⁸ m s⁻¹ for all electromagnetic waves in a vacuum.

What the symbols mean: v = wave speed (m s⁻¹) · f = frequency (Hz) · λ = wavelength (m)

Frequency and wavelength

Frequency and wavelength are inversely related, so higher frequency means shorter wavelength.

Photon energy

E = hf, where h = 6.63 × 10⁻³⁴ J s, and combined E = hc/λ.

Order of increasing energy

Order of increasing energy radio < microwave < infrared < visible < ultraviolet < X-ray < gamma.

Visible region

Visible region red has the longest wavelength (about 700 nm) and lowest energy;
- violet has the shortest (about 400 nm) and highest energy.

Hazard

Hazard gamma rays, X-rays and UV are high frequency and high energy and can damage cells.

Data booklet

Data booklet the relationship c = fλ and the constants are given in the IB Data Booklet.

Part 2 of 8Continuous and line spectra

Continuous spectrum

Continuous spectrum contains all wavelengths over a range with no gaps, such as white light split by a prism or a rainbow.

Line spectrum

Line spectrum shows only discrete lines at particular frequencies, e.g. helium.

Meaning

Meaning emitted light has only certain fixed frequencies, so it is quantised.

Conclusion

Conclusion electrons in atoms can only have certain fixed amounts of energy.

Part 3 of 8Origin of an emission line

A gaseous atom absorbs energy from heat or electricity.

An electron is promoted to a higher energy level (excited state).

The excited electron falls back to a lower energy level.

A photon is emitted with energy equal to the difference between the levels, ΔE = hf.

Only fixed energy gaps exist, so only certain frequencies appear as lines.

Unique spectrum
- each element has its own line spectrum, so spectra and flame tests identify elements.

Part 4 of 8Absorption and emission spectra

Emission spectrum

Emission spectrum bright coloured lines on a dark background, produced as electrons fall to lower levels.

Absorption spectrum

Absorption spectrum dark lines on a continuous background, produced as atoms absorb photons that promote electrons.

Frequencies

Frequencies for a given element the absorption and emission lines occur at the same frequencies.

Analysis

Analysis visible emission is analysed by passing it through a diffraction grating.

Part 5 of 8Hydrogen emission spectrum

Series	Electron falls to	Region	Photon energy
Lyman	n = 1	Ultraviolet	Highest
Balmer	n = 2	Visible	Intermediate
Paschen	n = 3	Infrared	Lowest of the three

Visible light

Visible light emitted when an electron falls from any higher level to n = 2.

Evidence

Evidence the line spectrum shows that electron energy levels are quantised, as Bohr proposed in 1913.

Ionisation energy

Ionisation energy the Lyman series limit is used to find the ionisation energy of hydrogen.

Part 6 of 8Convergence

Convergence

Convergence lines get closer together towards the high-frequency (blue) end of each series.

Cause

Cause energy levels get closer together as n increases, further from the nucleus.

Convergence limit

Convergence limit corresponds to the electron being completely removed from the atom (n = ∞).

Part 7 of 8Energy levels, sublevels and orbitals

Main energy level

Main energy level labelled n = 1, 2, 3, ..., holds a maximum of 2n² electrons (2, 8, 18, 32).

Sublevels

Sublevels level n contains n sublevels: n = 1 has 1s;
- n = 2 has 2s, 2p;
- n = 3 has 3s, 3p, 3d;
- n = 4 has 4s, 4p, 4d, 4f.

Energy order within a level

Energy order within a level s < p < d < f.

Orbitals

Orbitals hold two electrons of opposite spin, with 1, 3, 5 and 7 orbitals in s, p, d and f sublevels.

4s and 3d

4s fills before 3d, but 4s electrons are lost first when transition metal ions form.

Part 8 of 8More from the specification

1Principal quantum shells (n)

Main electron energy levels designated by principal quantum numbers (n = 1, 2, 3...), each subdivided into subshells.

2Subshells and orbitals

Principal shells are divided into specific subshells (s, p, d, f) containing orbitals capable of holding a maximum of two spin-paired electrons.

3Aufbau principle

Fundamental rule stating that electrons fill available atomic subshells of lowest energy before occupying higher energy levels.

4Condensed noble gas shorthand

Shorthand notation representing core inner electrons with a preceding noble gas symbol in brackets followed by outer valence configurations.

5Aufbau principle

Fill the lowest energy subshells first.

6Valence electrons

Electrons in the outer shell.

7Subshell

A set of orbitals of the same type within a shell: s, p, d or f.

8Shell

An energy level around the nucleus that holds a limited number of electrons.

Key terms

Term	Meaning
Continuous spectrum	A spectrum containing all wavelengths in a range with no gaps.
Line spectrum	A spectrum of discrete lines at particular frequencies, showing quantised energy levels.
Emission spectrum	The pattern of frequencies emitted when excited electrons fall to lower energy levels.
Absorption spectrum	Dark lines on a continuous spectrum where atoms absorb specific frequencies.
Convergence limit	The frequency at which the lines of a series merge, corresponding to n = ∞.
Quantised	Restricted to fixed, discrete values.

Avoid these mistakes

Saying lines in an emission spectrum are evenly spaced — they converge at higher frequency.

Thinking electrons can have any energy — only fixed, quantised energies are allowed.

Mixing up emission and absorption — emission is bright lines on dark, absorption is dark lines on a continuum.

Assuming the visible hydrogen lines end on n = 1 — they end on n = 2.

Last updated: 14 October 2026