This AP Chemistry lesson on photoelectron spectroscopy notes gives the key ideas first, then worked examples and diagrams. After that, practise with the worksheet on photoelectron spectroscopy and check yourself with the quiz.
Quick answer: Electrons fill subshells in order of energy, giving each atom a configuration. Photoelectron spectroscopy shows these subshells as peaks: position gives binding energy and height gives the number of electrons. Coulomb’s law, with effective nuclear charge and distance, explains periodic trends in radius and ionisation energy.
Level: AP Chemistry · Curriculum: AP Chem Unit 1
Photoelectron spectroscopy notes: the key ideas
How do electrons fill orbitals?
An electron configuration lists the subshells occupied by an atom’s electrons and how many electrons each holds, for example 1s² 2s² 2p⁶ 3s² for magnesium. Valence electrons are those in the outermost shell.
Three rules decide the order. The aufbau principle fills the lowest-energy subshell first. The Pauli exclusion principle allows two electrons per orbital, with opposite spins. Hund’s rule puts one electron in each orbital of a subshell before pairing any of them.
Chromium and copper break the simple pattern. A half-full or full 3d subshell is slightly more stable, so chromium is [Ar] 4s¹ 3d⁵ and copper is [Ar] 4s¹ 3d¹⁰. When transition metals form cations, the 4s electrons leave before the 3d ones.
Write the configuration of Fe³⁺. Iron has 26 electrons: [Ar] 4s² 3d⁶. Remove the two 4s electrons and then one 3d electron. Fe³⁺ is [Ar] 3d⁵, with five unpaired electrons.
What does a photoelectron spectrum show?
In photoelectron spectroscopy a beam of high-energy photons knocks electrons out of atoms. The kinetic energy of each ejected electron tells us how tightly it was held: binding energy = photon energy − kinetic energy.
Each peak is one subshell. The position gives the binding energy of its electrons. The height is proportional to the number of electrons in it. Core electrons have higher binding energies than valence electrons.
A spectrum has five peaks at about 1560, 118, 73, 11 and 6 eV with relative heights 2 : 2 : 6 : 2 : 1. Matching the heights to subshells gives 1s² 2s² 2p⁶ 3s² 3p¹, which is aluminium.
How does Coulomb’s law explain periodic trends?
F = k q₁q₂/r², where F is the force in newtons, k = 8.99 × 10⁹ N·m²/C², q₁ and q₂ are the charges in coulombs and r is the separation in metres. The attraction grows with charge and falls quickly with distance.
A valence electron feels the nucleus reduced by the inner electrons that shield it. The effective nuclear charge is roughly Zeff ≈ Z − number of core electrons. For magnesium it is 12 − 10 = 2, and for chlorine it is 17 − 10 = 7.
| Trend | Across a period | Down a group | Reason |
|---|---|---|---|
| Atomic radius | decreases | increases | Zeff rises across; more shells down |
| First ionisation energy | generally increases | decreases | stronger pull; electron farther away |
| Electronegativity | increases | decreases | same as ionisation energy |
The distance between a valence electron and the nucleus triples while Zeff doubles. Since F ∝ Zeff/r², the force changes by 2/3² = 2/9 ≈ 0.22 of its old value, so the electron is much easier to remove.
Successive ionisation energies show the shell structure. Magnesium needs 738 and 1451 kJ/mol for its first two electrons, but 7733 kJ/mol for the third. The big jump shows the third electron comes from an inner shell, so magnesium has two valence electrons.
Students say atomic size increases across a period because there are more electrons. The electrons enter the same shell, but the nuclear charge increases, so the radius shrinks.
For any trend question, say three things: which charge, which distance, which shielding. Then connect them with Coulomb’s law.
- Fill order: 1s 2s 2p 3s 3p 4s 3d 4p, two electrons per orbital
- PES: peak position = binding energy, height = number of electrons
- Coulomb’s law: F = k q₁q₂/r²
- Zeff ≈ Z − core electrons
- Radius falls across a period; IE₁ rises across a period
Electron configurations, PES and periodic trends: frequently asked questions
What is the electron configuration of chromium?
It is [Ar] 4s¹ 3d⁵. A half-filled 3d subshell gives extra stability, so one 4s electron moves into 3d.
What do the peaks in a PES spectrum mean?
Each peak is a subshell. Its position shows the binding energy and its height shows how many electrons are in it.
Why does ionisation energy increase across a period?
The nuclear charge rises while the electrons enter the same shell and shield little. The valence electrons are pulled in more strongly and are harder to remove.
Why is there a large jump in successive ionisation energies?
The jump appears when the next electron must come from an inner shell. This shell is closer to the nucleus and less shielded, so it is held far more strongly.
How does Coulomb’s law apply to atoms?
The attraction between nucleus and electron is proportional to the charges and inversely proportional to the distance squared. More charge or less distance means a stronger attraction.
