Photoelectron Spectroscopy

How PES works

In PES, a sample of gas-phase atoms is hit with high-energy photons (UV or X-ray) of a known energy. A photon knocks an electron out of an atom. The electron flies away with some kinetic energy, and the instrument measures it.

Energy is conserved, so the photon energy is split between the energy needed to remove the electron and the kinetic energy it carries away:

BE is the binding energy: how much energy it takes to pull that electron out of the atom. Since $E_{\text{photon}}$ is known and KE is measured, you get $\text{BE} = E_{\text{photon}} - \text{KE}$.

Notice how the axis is drawn: PES graphs conventionally have binding energy increasing to the left. The 1s electrons, held most tightly, sit at the far left. The spectrum above is a simplified sketch with the peaks spaced for readability, not to scale.

Reading a spectrum: configuration and element

Each peak is a subshell. Count the peaks, read their heights, and you have the electron configuration.

• Peaks go in order from the highest binding energy (1s) to the lowest.

• A height of 2 is an s subshell (full), 6 is a p subshell (full), and 10 would be d.

• A height of 1, 3, 4, or 5 is a partly filled subshell.

• Add up all heights to get the total number of electrons. For a neutral atom, that number is the atomic number $Z$.

You can predict the number of peaks directly from the configuration. Hydrogen and helium each have just one peak (1s). Hydrogen's has height 1 and helium's has height 2. Lithium has two peaks (1s with height 2 and 2s with height 1).

Why peaks sit where they do

The position of a peak comes from Coulomb's law: the attraction between the nucleus and an electron grows with the charges and weakens with distance.

Two things control how tightly an electron is held:

1. Nuclear charge. More protons pull harder. This shifts all peaks of an atom to higher binding energy as $Z$ increases. The 1s peak moves dramatically: carbon's is near 29 MJ/mol and neon's is near 84 MJ/mol, because neon's nucleus has 10 protons versus 6.

2. Distance and shielding. Electrons in a lower shell (smaller $n$) are closer to the nucleus. Inner electrons also shield outer electrons from the full nuclear charge, so outer electrons feel a smaller effective nuclear charge.

That is why, in any one atom, the order of binding energy is 1s > 2s > 2p > 3s > 3p. Within the same shell, 2s is held a bit more tightly than 2p because 2s electrons spend more time close to the nucleus.

Moving down a group works the other way. The outermost electrons of potassium are in the 4th shell, farther away and shielded by more inner electrons than sodium's 3s electron, so potassium's outer peak is at lower binding energy. Yet potassium's 1s peak is at much higher binding energy than sodium's, because the 1s electrons feel a nucleus with 19 protons instead of 11, with nothing between them and the nucleus.

Writing a full explanation

On the AP® exam you must justify claims, not just state them. A strong PES explanation has three parts:

1. Claim: which peak or element is higher or lower.

2. Evidence: the relevant numbers or heights.

3. Reasoning: Coulomb's law with nuclear charge, distance, and shielding.

Successive ionization energies

PES peaks show how many valence electrons an atom has: the lowest-binding-energy peaks belong to the valence shell. The same idea shows up in successive ionization energies, the energies needed to remove the 1st, 2nd, 3rd electron, and so on, from one atom.

There is a big jump after the last valence electron is removed, because the next electron comes from an inner shell that is closer to the nucleus and less shielded. For example, if the 3rd ionization energy of an element is much larger than its 2nd, the atom has 2 valence electrons, which matches a PES with two electrons in the outermost peak.

Summary

Back to the start: the spectrum is a fingerprint because every element has its own set of peak positions and heights, which you can now read as an electron configuration.