AP Chemistry Photoelectron Spectroscopy

How to read a PES spectrum, in four worked examples with a neon and sodium diagram.

A photoelectron spectrum looks like a short bar chart, and a handful of reading rules turn it into an electron configuration. Questions on it are among the most predictable in Unit 1, which makes it a good place to pick up reliable points. The Unit 1 review introduces the idea in one section; this page is the practice for it, including the one detail that trips many students up: which end of the axis is which.

How to Read a PES Spectrum in Four Steps

In PES, high-energy photons knock electrons out of atoms and the electrons' kinetic energies are measured. Energy conservation gives the binding energy of each electron: photon energy − kinetic energy. Each occupied subshell produces one peak, and three facts decode it:

• Position is the binding energy, the energy needed to remove an electron from that subshell.
• Height is proportional to the number of electrons in the subshell.
• Order: on AP-style graphs binding energy runs from high on the left to low on the right, so the 1s peak is leftmost and the outermost subshell is rightmost.

1. Count the peaks. That is the number of occupied subshells.
2. Order them by binding energy, left to right, which is the order 1s, 2s, 2p, 3s, 3p, and so on.
3. Read the electron counts from the height ratios.
4. Write the configuration and add the electrons to get the atomic number.

Worked Example 1: Finding Binding Energy From Photon and Electron Energies

A neon sample is hit with photons carrying 5.00 MJ/mol. Electrons from one subshell leave with a kinetic energy of 2.90 MJ/mol. Find their binding energy and name the subshell using the neon spectrum below.

Binding energy = photon energy − kinetic energy = 5.00 − 2.90 = 2.10 MJ/mol.
On the neon spectrum below, that is the rightmost, lowest-binding-energy peak, 2p. The 1s peak (about 84 MJ/mol) could not be reached with a 5.00 MJ/mol photon, because the photon does not carry enough energy to eject those electrons. (2s electrons, at about 4.7 MJ/mol, would also be ejected, but with only about 0.3 MJ/mol of kinetic energy.)

Worked Example 2: Reading the Neon Spectrum as an Electron Configuration

Use the neon spectrum above to write the configuration and confirm the element.

Peaks: three, so three occupied subshells.
Order, left to right: 1s, 2s, 2p.
Heights: in the ratio 2 : 2 : 6, so the electron counts are 2, 2, and 6.
Configuration: 1s² 2s² 2p⁶, with 2 + 2 + 6 = 10 electrons. A neutral atom with 10 electrons has 10 protons: neon.

The ratio matters more than the actual height on the page. A subshell holding 6 electrons gives a peak three times as tall as one holding 2, and the full set of configurations behind these counts is in electron configuration.

Worked Example 3: Identifying an Unknown Element From Peak Heights

A neutral atom's PES spectrum has four peaks with relative heights 2 : 2 : 6 : 2, from left to right. Which element is it?

Left to right, the subshells are 1s, 2s, 2p, 3s with 2, 2, 6, and 2 electrons.
Configuration: 1s² 2s² 2p⁶ 3s², a total of 12 electrons.
A neutral atom with 12 electrons has 12 protons: magnesium.

The rightmost peak is the valence subshell. Here it sits in the third shell, so the element is in period 3, and its height of 2 puts it in group 2. Reading valence information straight off the last peak is a quick check on the rest of your work.

Worked Example 4: Comparing Neon and Sodium With Coulomb's Law

Using both spectra, explain (a) why sodium's 1s, 2s, and 2p peaks sit to the left of neon's, and (b) what the extra peak on the right of sodium's spectrum is.

(a) Sodium has 11 protons and neon has 10. The inner subshells are in the same shells with similar shielding, so the stronger nuclear charge pulls on them harder. By Coulomb's law a greater attraction means a higher binding energy, so every inner peak shifts left.
(b) The extra peak is the single 3s electron, with a height of 1. It is far to the right because that electron is in a new shell, farther from the nucleus and shielded by ten core electrons, so its binding energy is low. That value, about 0.50 MJ/mol, equals sodium's first ionization energy.

This is why PES and ionization energy data tell the same story: the large gap between the 3s peak and the 2p peak is the large jump in energy needed to start removing core electrons. The trends are developed in periodic trends.

Five PES Practice Questions With Answers

1. How many peaks does the PES spectrum of oxygen have, and what are their relative heights?
   Show answer

   Three peaks (1s, 2s, 2p) with relative heights 2 : 2 : 4, from the configuration 1s² 2s² 2p⁴.
2. Give the relative heights of the peaks in the PES spectrum of phosphorus.
   Show answer

   1s² 2s² 2p⁶ 3s² 3p³ gives five peaks with heights 2 : 2 : 6 : 2 : 3.
3. Which peak in a spectrum represents the valence electrons?
   Show answer

   The rightmost peak, which has the lowest binding energy and belongs to the outermost occupied subshell.
4. Which has its 1s peak at higher binding energy, lithium or fluorine? Explain.
   Show answer

   Fluorine. It has 9 protons against 3, so the nuclear attraction on a 1s electron is stronger and the electron is held more tightly.
5. A spectrum has peaks in the ratio 2 : 2 : 6 : 1. Name the element and say what the rightmost peak's binding energy equals.
   Show answer

   1s² 2s² 2p⁶ 3s¹, which is sodium. The rightmost peak's binding energy equals sodium's first ionization energy.

Common PES Mistakes

• Reading the axis backwards. On AP-style graphs the 1s peak is on the left, with the highest binding energy.
• Counting peaks as electrons. The number of peaks is the number of subshells; the heights give the electrons.
• Using the absolute height instead of the ratio. Only the relative heights matter.
• Forgetting that the electron total equals the atomic number for a neutral atom.
• Mixing PES up with mass spectrometry. PES shows electrons in subshells; a mass spectrum shows isotopes by mass.

The two techniques are often taught back to back, so if the other one is the weak spot, the mass spectrometry practice problems cover it. And when you want to see how Unit 1 skills like these affect an overall result, the AP Chem Score Calculator lets you try different scenarios.

Related Resources

• AP Chem Score Calculator
• Unit 1 Review: Atomic Structure and Properties
• AP Chemistry Electron Configuration
• AP Chemistry Periodic Trends
• AP Chemistry Ionization Energy
• AP Chemistry Mass Spectrometry Practice Problems
• AP Chemistry Periodic Table
• AP Chemistry Study Guide

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