Photoelectron spectroscopy

Photoelectron spectroscopy fires photons of known energy at a sample and knocks electrons loose. By measuring how much kinetic energy each ejected electron carries away, the instrument works out its binding energy — how tightly that electron was held: binding energy = photon energy − kinetic energy of the ejected electron.

The result is a spectrum of peaks. Each peak is one subshell. A peak's position is the binding energy of the electrons in that subshell, and binding energy tracks Coulombic hold: electrons closer to the nucleus (like 1s) are bound most tightly and show up at the highest binding energy; outer electrons appear at lower binding energy.

A peak's height carries the other half of the story. In the idealized model used at the AP level, a peak's relative height — more precisely its intensity, or area — is proportional to the number of electrons in that subshell. So a subshell with more electrons produces a taller peak. Position tells you which subshell; height tells you how many electrons are in it.

Every PES question is some mix of these reads. Keep the two axes doing different jobs and it stays simple.

1. Count the peaks. One peak per occupied subshell. Three peaks means three subshells hold electrons (for example 1s, 2s, 2p).
2. Read each position as a binding energy. Higher binding energy means more tightly held and closer to the nucleus. The 1s peak sits at the highest binding energy; outer subshells sit lower.
3. Read each height as an electron count. In the idealized model, relative peak height (intensity) is proportional to the number of electrons in that subshell. A height twice as large means twice as many electrons.
4. Add the heights to check the total. For a neutral atom, the electron counts across all peaks sum to the atomic number Z. That sum both identifies the element and confirms you read every peak.

Read together, the spectrum is a picture of the electron configuration: which subshells are filled (positions), and how full each is (heights).

Quick reference card. Keep the two axes — position and height — doing separate jobs.

Question. A photoelectron spectrum of a neutral atom shows three peaks. Going from higher to lower binding energy, their relative heights are 2, 2, and 3. Identify the element and its electron configuration.

Step 1 — three peaks, three subshells. Reading from highest binding energy (innermost) outward, the subshells fill in order 1s, 2s, 2p.

Step 2 — turn heights into electron counts. Height 2 at the 1s peak means 1s²; height 2 at 2s means 2s²; height 3 at 2p means 2p³.

Step 3 — assemble and total. The configuration is 1s² 2s² 2p³, and 2 + 2 + 3 = 7 electrons. A neutral atom with 7 electrons has Z = 7 — nitrogen.

Sanity check. The 2p peak is the tallest, yet it sits at the lowest binding energy. That's exactly right: 2p electrons are outermost and least tightly held, but there are more of them than in 1s or 2s. Height and position are independent readings.