Lesson 1.5 · Unit 1 · CED topic 1.6
Photoelectron spectroscopy
Electron configurations are not just a bookkeeping device. They can be measured. A technique called photoelectron spectroscopy (PES) fires high-energy light at a sample and records the energy it takes to knock each electron out. The resulting graph is a direct picture of an atom’s shells and subshells: a series of peaks, one for each subshell, with their heights counting the electrons. In this lesson you learn to read these spectra and to use Coulomb’s law to explain where the peaks fall.
Explain the relationship between the photoelectron spectrum of an atom or ion and (i) the ground-state electron configuration of the species and (ii) the interactions between the electrons and the nucleus.
- The energies of the electrons in a given shell can be measured experimentally with photoelectron spectroscopy (PES). The position of each peak in the PES spectrum is related to the energy required to remove an electron from the corresponding subshell, and the relative height of each peak is (ideally) proportional to the number of electrons in that subshell.
How PES works
A beam of photons of known energy strikes a gas-phase sample. A photon with enough energy ejects an electron, and the instrument measures the electron’s kinetic energy. Energy is conserved: \[ E_{\text{photon}} = E_{\text{binding}} + E_{\text{kinetic}} \] so the binding energy (the energy needed to remove the electron from its subshell) is the photon energy minus the measured kinetic energy. Electrons held tightly give up less kinetic energy and show a large binding energy. Each subshell has its own characteristic binding energy, so electrons from the same subshell show up together as one peak.
Reading a PES spectrum
The spectrum plots relative number of electrons (peak height) against binding energy, and by convention the energy axis runs from high on the left to low on the right. Two rules do all the work:
- Position = subshell. Peaks farther left (higher binding energy) belong to subshells closer to the nucleus. The leftmost peak is 1s, then 2s, then 2p, and so on.
- Height = number of electrons. A peak twice as tall as another holds twice as many electrons in that subshell.
The neon spectrum has three peaks, at 870, 48.5 and 21.6 eV, with relative heights 2 : 2 : 6. Match them to subshells from the left: 1s with 2 electrons, 2s with 2, and 2p with 6, which is 1s² 2s² 2p⁶, the configuration of neon (Z = 10). Sodium has the same first three peaks (at much higher energies) and one extra small peak at the far right, at 5.14 eV, a single electron: the 3s electron. Adding it up gives 2 + 2 + 6 + 1 = 11 electrons, so the element has Z = 11, sodium.
The number of peaks equals the number of occupied subshells, and the sum of the relative heights equals the number of electrons. For a neutral atom, that number is the atomic number.
Explaining peak positions with Coulomb’s law
Why does the 1s peak for sodium (1071 eV) sit so far to the left of the 1s peak for neon (870 eV)? Sodium’s nucleus carries a charge of +11 and neon’s +10. The 1s electrons in both atoms are at nearly the same distance and are barely shielded, so by Coulomb’s law the larger nuclear charge holds the 1s electrons more tightly, and more energy is needed to remove them. The same reasoning explains every comparison of the same subshell across elements: more protons, same shielding, higher binding energy.
Within one atom, the peaks fall in order because inner electrons are closer to the nucleus (a smaller \(r\) in Coulomb’s law) and feel more of its charge (less shielding by other electrons). The 1s electrons of sodium need 1071 eV; the outermost 3s electron, far from the nucleus and shielded by ten inner electrons, needs only 5.14 eV. The large jump in binding energy between shells (1071 to 63.5 to 5.14 eV) is the experimental evidence for the shell model.
A PES spectrum of a neutral atom shows peaks with relative heights 2, 2, 3 at binding energies of 410, 25.7 and 14.5 eV. Identify the element.
Step 1. Three peaks means three occupied subshells: 1s, 2s, 2p. The heights give the electrons: 1s² 2s² 2p³.
Step 2. The total is 2 + 2 + 3 = 7 electrons, so Z = 7: nitrogen.
Spectrum A has peaks at 1311, 88.7, 49.5 and 7.65 eV with heights 2, 2, 6, 2. Spectrum B has peaks at 1071, 63.5, 30.6 and 5.14 eV with heights 2, 2, 6, 1. Identify both and explain why the leftmost peak of A is at higher energy.
A is 1s² 2s² 2p⁶ 3s², 12 electrons: magnesium. B is 1s² 2s² 2p⁶ 3s¹, 11 electrons: sodium. The 1s electrons in magnesium (nuclear charge +12) are attracted more strongly than those in sodium (+11) at nearly the same distance, so the 1s peak of magnesium sits at the higher binding energy.
An X-ray photon of 1486.6 eV ejects a sodium 1s electron (binding energy 1071 eV). What is the electron’s kinetic energy?
\(E_{\text{kinetic}} = 1486.6 - 1071 = 415.6\) eV.
Ions in PES
The spectrum of an ion has the same pattern as the matching noble-gas-like configuration. Na+ has 10 electrons, so its spectrum shows three peaks with heights 2 : 2 : 6 and no 3s peak. The peaks of the ion are shifted to somewhat higher energy compared with the atom, because with fewer electrons there is less repulsion and each remaining electron feels a stronger net pull from the nucleus.
- Left means harder to remove. The high-energy end is on the left of the axis.
- Do not read the peak height as energy. Height counts electrons; position gives the energy.
- Use the sum of the heights. Neutral atom: the total is the atomic number. Ion: adjust for the charge.
- A full explanation names Coulomb’s law. State the nuclear charge, the distance or the shielding, and the effect on the attraction.
- Treat heights as electron counts. Real spectra are only roughly proportional, but on the exam the relative heights give the number of electrons in each subshell.
- A neutral atom shows two peaks with relative heights 2 and 1. Identify the element and write its configuration.
Show answer
Two subshells with 2 and 1 electrons: 1s² 2s¹, 3 electrons, so Z = 3: lithium.
- A PES spectrum has peaks of relative height 2, 2, 6, 2, 4 (left to right). Identify the element.
Show answer
1s² 2s² 2p⁶ 3s² 3p⁴: 16 electrons, so Z = 16: sulfur.
- On a PES spectrum, the peak at the far right is tallest in spectrum X and is the same height as the others in spectrum Y. What can you infer about the outermost subshell in each?
Show answer
The tallest peak at the far right means the outermost subshell holds the most electrons in X. A peak the same height as the others in Y means the outermost subshell holds a similar number of electrons as the others. Height always counts electrons, so compare with the subshell capacities (s 2, p 6).
- Explain why the 1s peak of oxygen is at a higher binding energy than the 1s peak of carbon.
Show answer
Oxygen has 8 protons and carbon has 6. The 1s electrons are at about the same distance and are not shielded by other electrons, so by Coulomb’s law the larger nuclear charge of oxygen pulls them harder, and more energy is needed to remove them.
- An electron is ejected from an atom by a photon of 100.0 eV and leaves with a kinetic energy of 63.5 eV. What was its binding energy?
Show answer
\(E_{\text{binding}} = 100.0 - 63.5 = 36.5\) eV.
- Describe how the PES spectrum of Na+ differs from that of Na.
Show answer
Na+ lacks the 3s electron, so its spectrum has only three peaks (1s, 2s, 2p) with heights 2 : 2 : 6 and no peak at the low-energy end near 5 eV. The remaining peaks are slightly shifted to higher energy.