Topic 1.6 Photoelectron Spectroscopy: interpret a photoelectron spectrum to determine the relative energies of electrons in subshells and the number of electrons in each subshell, and relate it to electron configuration.

What this topic is asking

The College Board (Topic 1.6) wants you to read a photoelectron spectrum (PES). From the position of each peak you read the energy needed to remove electrons from a subshell, and from the height of each peak you read how many electrons are in that subshell. You then link the spectrum to an electron configuration and explain the pattern using the Coulombic model.

What PES measures

Whereas a first-ionization energy measures only the single easiest electron to remove, PES probes every subshell at once, so it is a direct experimental window onto the shell-and-subshell model of Topic 1.5.

Reading a PES spectrum

So a full $s$ subshell (2 electrons) and a full $p$ subshell (6 electrons) at the same vertical scale produce peaks in a $2 : 6$, that is $1 : 3$, height ratio. Reading heights in this way lets you reconstruct the electron configuration peak by peak, and summing the electrons identifies the element.

Why peaks fall where they do

Binding energy is set by Coulomb's law. Electrons closer to the nucleus feel a stronger attraction and are also less shielded by other electrons, so they experience a larger effective nuclear charge and are bound most tightly. That is why:

• The $1s$ electrons (core, closest in) have the highest binding energy and sit at the high-energy end.
• Valence electrons (highest $n$, well shielded) have the lowest binding energy and are easiest to remove.
• Across a period, every peak shifts to higher binding energy because the growing nuclear charge pulls all electrons in more tightly.

This is the same effective-nuclear-charge reasoning that drives periodic trends (Topic 1.7), which is why PES is such a useful bridge: it makes the abstract shell model measurable. A subtle point worth stressing is that within a shell the subshells separate: in a multi-electron atom the $2s$ electrons are bound slightly more tightly than the $2p$ electrons because an $s$ orbital penetrates closer to the nucleus, so a careful spectrum shows distinct $2s$ and $2p$ peaks rather than a single $n = 2$ peak.

Try this

Q1. A PES spectrum has two peaks of equal height at high binding energy and one shorter peak at low binding energy, in the ratio $2 : 2 : 1$. Identify the element. [2 points]

• Cue. Heights 2, 2, 1 give $1s^2\,2s^2\,2p^1$, a total of 5 electrons, which is boron.

Q2. Explain why the $1s$ peak appears at higher binding energy than the $2s$ peak. [1 point]

• Cue. The $1s$ electrons are closer to the nucleus and less shielded, so they feel a greater effective nuclear charge and are held more tightly.