Photoelectron Spectroscopy (PES)光电子能谱（PES）

Weighing the electrons in every sublevel

First ionization energy (lesson 2.3.4) only tells us the energy needed to remove the outermost electron. What about the inner ones? In U1.5, Coulomb’s law predicted that 1s electrons are the hardest to remove and valence electrons the easiest. Photoelectron spectroscopy (PES) measures the energy of the electrons in every sublevel directly, turning that prediction into data and giving the most direct evidence for electron configurations.

How PES works

Shine high-energy photons of known energy (ultraviolet light or X-rays) on gaseous atoms, and the photons knock electrons out: the photoelectric effect from lesson 2.2.2. The ejected electrons are called photoelectrons, and the instrument measures their kinetic energy. Part of the photon’s energy overcomes the attraction holding the electron, and the rest becomes the electron’s kinetic energy:

The energy needed to remove an electron from a given sublevel is that sublevel’s binding energy结合能. PES usually reports it in MJ/mol (1 MJ/mol = 1000 kJ/mol); per electron it’s often given in electron volts, and 1 eV corresponds to 0.096485 MJ/mol.

Electrons from every sublevel can be ejected, and the number ejected is proportional to the number of electrons in the sublevel. A plot of “how many electrons” against binding energy is a photoelectron spectrum光电子能谱.

Reading a PES spectrum

• The horizontal axis is binding energy, increasing to the LEFT on AP spectra. The leftmost peak is 1s, and the rightmost is the outermost electrons.
• Each peak is one sublevel. The number of peaks is the number of occupied sublevels.
• Peak height is proportional to the number of electrons. An s peak is at most 2 high and a p peak at most 6, so comparing heights tells you how many electrons each sublevel holds.
• The rightmost peak’s binding energy is the first ionization energy.

Measured data for neon and argon (MJ/mol):

(LBNL X-ray Data Booklet, Table 1-1, converted from eV; the two spin–orbit components of 2p and 3p are combined into one peak, weighted by their electrons.) Reading left to right gives Ne as 1s²2s²2p⁶ and Ar as 1s²2s²2p⁶3s²3p⁶. Neon’s rightmost peak, 2.09 MJ/mol, is almost exactly its first ionization energy of 2081 kJ/mol, and argon’s 1.52 matches its 1521 kJ/mol.

Explaining peak positions with Coulomb’s law

Within one atom: 1s electrons are closest to the nucleus and feel nearly its full charge, so they have the largest binding energy. Electrons farther out are farther away and more shielded, so their binding energies are smaller. Within one shell, 2s lies to the left of 2p: 2p electrons are partly shielded by the 2s electrons and are a little farther out on average. So from left to right the order is always 1s, 2s, 2p, 3s, 3p, 4s.

The same sublevel in different species: when the electrons are in the same shell at about the same distance, more protons mean stronger attraction and a peak farther left. Measured 1s binding energies (MJ/mol):

(The N, O, and F values are for the gaseous molecules $\ce{N2}$, $\ce{O2}$, and $\ce{F2}$; the rest are free atoms; same source.) Isoelectronic species work the same way: $\ce{Ca^2+}$ and Ar both have 18 electrons, so their spectra have the same number of peaks with the same heights, but calcium has 20 protons, so every peak of $\ce{Ca^2+}$ lies to the left of argon’s.

AP accepts only two kinds of reasons: more protons (greater nuclear charge), or an electron in a shell farther from the nucleus. None of these earn credit: “a half-filled p sublevel”, “higher electronegativity”, “a heavier nucleus”, “the electron takes longer to remove”, or anything about isotopes (PES measures sublevels and can’t see isotopes; that’s the mass spectrometry of U1.2).

About the spectra on this page

Every peak of He, Ne, Ar, and Kr is a measured value. Precise free-atom values for the inner peaks of other elements come from a paywalled compilation that you couldn’t check, so this page draws them as schematics. Peak heights still equal electron counts, and the inner peaks show only their left-to-right order (for the same sublevel, more protons means farther left), not their true positions. The rightmost peak is drawn on a real scale: it is the first ionization energy. AP questions always give you the spectrum, and what you need to read is exactly the number of peaks, their heights, and their order.

Look at the complete spectra of Ne, Ar, and Kr first, then the schematics of Na and O. Then count peak heights in “Identify the element”, and overlay two elements in “Compare two”:

Example 1: Identifying an element from its spectrum

The PES of an element has 5 peaks with relative heights 2 : 2 : 6 : 2 : 1 from left to right, and the rightmost peak has a binding energy of 0.578 MJ/mol. What is the element?

Example 2: How do the spectra of Ne and Na differ?

Compare the PES of Ne and Na: how do the number, heights, and positions of the peaks differ, and why?

Common mistakes

Quick check

AP-style free response

Summary

• PES ejects electrons with photons of known energy: binding energy = photon energy − photoelectron kinetic energy, usually in MJ/mol.
• Binding energy increases to the left; each peak is a sublevel, and peak height is the number of electrons. Read the configuration from left to right; the heights add up to the total number of electrons.
• The rightmost peak is the outermost electrons, and its binding energy equals the first ionization energy.
• Within an atom, inner electrons are closer and less shielded, so their peaks are to the left; for the same sublevel in different species, more protons means farther left. Only nuclear charge and distance count as reasons.