Emission spectra and photon energy

• Emission spectrum forms when excited electrons fall to lower energy levels and emit photons.

• Continuous spectrum = all wavelengths present; line spectrum = only specific wavelengths present.

• Across the electromagnetic spectrum: longer wavelength leftarrow lower frequency and lower energy; shorter wavelength leftarrow higher frequency and higher energy.

• Key relationships: $c = \lambda f$ and $E = hf$.

• For visible light: red = longer wavelength, lower frequency, lower energy; violet = shorter wavelength, higher frequency, higher energy.

• Each element has a unique line spectrum, so spectra can be used to identify elements.

This image shows the visible hydrogen emission lines as distinct coloured lines rather than a continuous rainbow. It is useful for remembering that hydrogen produces a line spectrum because electrons can only move between discrete energy levels. Source

Hydrogen line spectrum: evidence for discrete energy levels

• The hydrogen emission spectrum proves electrons occupy discrete energy levels, not any energy value.

• Spectral lines converge at higher energies because the energy levels get closer together as $n$ increases.

• You must relate spectral lines to electron transitions to the first, second and third energy levels.

• Transitions to $n=1$ release the highest-energy photons; transitions to $n=2$ release less energy; transitions to $n=3$ release even less.

• Bigger energy drop rightarrow higher frequency, shorter wavelength photon.

• The series names do not need to be memorized.

This diagram shows visible hydrogen transitions ending at the same lower level, with labelled wavelengths such as 656 nm, 486 nm and 433 nm. It helps connect electron transitions to the colours and wavelengths seen in the line spectrum. Source

Main energy levels, sublevels and orbitals

• The main energy level is labelled by the integer $n$.

• Maximum electrons in a main energy level = $2n^2$.

• So the first four levels can hold: $n=1 \rightarrow 2$, $n=2 \rightarrow 8$, $n=3 \rightarrow 18$, $n=4 \rightarrow 32$ electrons.

• A more detailed model divides main energy levels into sublevels: s, p, d, f in order of increasing energy.

• Sublevels contain fixed numbers of orbitals:

  • s has 1 orbital

  • p has 3 orbitals

  • d has 5 orbitals

  • f has 7 orbitals

• Each orbital can hold a maximum of 2 electrons with opposite spin.

• Therefore maximum electrons per sublevel are: s = 2, p = 6, d = 10, f = 14.

• s orbital is spherical. The three p orbitals are oriented at right angles to each other: $p_x$, $p_y$, $p_z$.

This diagram shows the shape of the s orbital and the three p orbitals with different orientations. It is ideal for revising that s is spherical while p orbitals have the same shape but point in different directions. Source

Writing electron configurations

• Use atomic number, $Z$ to find the number of electrons in a neutral atom.

• For ions: cations have lost electrons; anions have gained electrons.

• Electron configurations up to $Z=36$ must be deduced using:

  • Aufbau principle = electrons fill lowest-energy orbitals first

  • Hund’s rule = electrons occupy equal-energy orbitals singly first before pairing

  • Pauli exclusion principle = an orbital holds at most 2 electrons with opposite spin

• Standard filling order up to krypton:

  • 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p

• Both full electron configurations and condensed configurations using a noble gas core are required.

• Example: Cl = 1s² 2s² 2p⁶ 3s² 3p⁵ = [Ne] 3s² 3p⁵.

• Example: Ca = [Ar] 4s².

• Example: Br = [Ar] 4s² 3d¹⁰ 4p⁵.

• For transition-metal ions, electrons are removed from the highest main energy level first (so 4s electrons are removed before 3d).

This diagram shows the Aufbau filling order of orbitals, helping you remember why 4s fills before 3d. It is useful when building both full and noble-gas shorthand electron configurations. Source

Orbital diagrams and key exceptions

• Orbital diagrams (arrow-in-box diagrams) show both filling order and electron spin.

• In a p sublevel, place one electron in each orbital before pairing: ↑ ↑ ↑ then ↑↓ ↑↓ ↑↓.

• Watch the two key exceptions:

  • Cr = [Ar] 4s¹ 3d⁵ (not [Ar] 4s² 3d⁴)

  • Cu = [Ar] 4s¹ 3d¹⁰ (not [Ar] 4s² 3d⁹)

• These exceptions occur because a half-filled or filled d sublevel gives a lower-energy arrangement.

• In exam questions, always check whether the element is Cr or Cu before finalizing the configuration.

This image shows how individual orbitals sit within each sublevel, which is helpful for drawing orbital box diagrams correctly. It reinforces how many orbitals are present in s, p, d, and f sublevels and where electrons pair. Source

This graph shows the overall increase across periods, the decrease down groups, and the small dips/discontinuities that IB loves to test. Use it to spot where changes in sublevel energy and electron pairing explain exceptions to the trend. Source

Exam traps to avoid

• Do not confuse energy levels, sublevels and orbitals.

• Do not say a line spectrum is produced by electrons absorbing energy; for emission, electrons drop down and emit photons.

• Do not forget that each orbital holds only 2 electrons.

• Do not pair electrons in p orbitals too early; apply Hund’s rule first.

• Do not miss the Cr and Cu exceptions.

• Do not remove 3d electrons before 4s when forming many transition-metal ions.

• In HL calculations, do not forget unit conversions, especially nm to m and per atom to per mole.