AP® Chemistry review sheet from Aim for Five (aimforfive.com/chem/units/1/1-6)
Unit 1 · Topic 1.6
1.6 Photoelectron Spectroscopy
Photoelectron spectroscopy (PES) measures how much energy it takes to remove each electron in an atom. Each peak in a spectrum is a subshell: its position shows how tightly those electrons are held, and its height shows how many there are. PES is direct experimental evidence for electron configurations.
Key terms
- photoelectron spectroscopy (PES)
- binding energy
- subshell
- peak height
- ionization energy
How PES works
In PES, a sample is hit with high-energy photons (X-rays or ultraviolet light) that knock electrons out of atoms. The instrument measures the kinetic energy of the ejected electrons. The energy that went into freeing each electron, its binding energy, is the photon's energy minus the electron's kinetic energy.
Electrons that are held tightly (close to the nucleus) have high binding energies. Electrons that are held loosely (outer, shielded electrons) have low binding energies. The binding energy of the outermost electron equals the atom's first ionization energy.
Reading a spectrum
- Each peak is one subshell (1s, 2s, 2p, 3s, …).
- Position: how far the peak is along the binding-energy axis shows how tightly those electrons are held. Units are often MJ/mol or eV.
- Height: a peak's relative height tells you how many electrons are in that subshell, so twice the height means twice the electrons. A full p subshell's peak is three times as tall as a full s subshell's.
- Check the axis direction. Many PES spectra put high binding energy on the left, so 1s is the leftmost peak. Read the labels before you interpret anything.
What PES tells you about structure
Take sodium, 1s² 2s² 2p⁶ 3s¹. Its spectrum has four peaks with relative heights 2 : 2 : 6 : 1. The 1s peak is at a huge binding energy, the 2s and 2p peaks are much lower, and the single 3s electron has the lowest binding energy, about 0.496 MJ/mol, which is sodium's first ionization energy.
The big gaps between groups of peaks show shells: 1s is far from 2s and 2p, which are far from 3s and 3p. The smaller split between 2s and 2p shows that subshells within a shell differ in energy, with s a bit lower (higher binding energy) than p.
Comparing elements: the same subshell has a higher binding energy in an element with more protons. The 1s peak of magnesium (12 protons) is at a higher binding energy than the 1s peak of sodium (11 protons), because the nucleus pulls harder on electrons at about the same distance.
Judging whether a spectrum fits a model
You may be shown a spectrum and asked whether it supports a model of the atom. A model with every electron at the same energy can't explain several peaks. A model with shells but no subshells can't explain why the second shell shows two peaks (2s and 2p) with a 1 : 3 height ratio when full.
Worked examples
Try each one yourself first, then open the solution.
- Example 1
Identify the element
A PES spectrum has five peaks. From highest to lowest binding energy, their relative heights are 2, 2, 6, 2, 1. Identify the element and write its electron configuration.
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- Step 1: Match peaks to subshells in order of decreasing binding energy: 1s, 2s, 2p, 3s, 3p.
- Step 2: Heights give electron counts: 1s² 2s² 2p⁶ 3s² 3p¹.
- Step 3: Total electrons = 2 + 2 + 6 + 2 + 1 = 13. A neutral atom with 13 electrons is aluminum.
Answer: Aluminum: 1s² 2s² 2p⁶ 3s² 3p¹
- Example 2
Comparing two spectra
The PES spectra of sodium and magnesium are compared. Predict how the 1s peaks differ in position and height, and explain.
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- Step 1: Height: both atoms have two 1s electrons, so the 1s peaks have the same height.
- Step 2: Position: magnesium has 12 protons and sodium has 11. The 1s electrons are at about the same distance in both, so by Coulomb's law the greater nuclear charge in Mg holds its 1s electrons more tightly.
- Step 3: So Mg's 1s peak is at a higher binding energy.
Answer: Same height (2 electrons each); Mg's 1s peak is at higher binding energy because its nucleus has one more proton.
- Example 3
Reading peak heights correctly (classic trap)
A student says the tallest peak in an element's PES spectrum must be the one with the highest binding energy, since those electrons are held most tightly. Is the student right?
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- Step 1: Peak height depends only on how many electrons are in the subshell, not on how tightly they're held.
- Step 2: In neon (1s² 2s² 2p⁶), the 2p peak is the tallest (6 electrons), but the 1s peak has by far the highest binding energy.
- Step 3: Position and height carry different information; don't mix them up.
Answer: No. Height shows the number of electrons in a subshell; position shows binding energy.
Common mistakes
- Assuming binding energy increases to the right. Many spectra plot it decreasing to the right; always check the axis.
- Reading peak height as energy. Height is the number of electrons.
- Forgetting that 2s and 2p are separate peaks. Every occupied subshell has its own peak.
- Saying a bigger atom's 1s peak is at lower energy because the atom is bigger. Inner electrons are held more tightly as nuclear charge grows.
On the exam
- Expect spectra to identify an element, to compare two elements, or to explain why one peak is at a higher energy than another. Explanations should mention the number of protons, distance from the nucleus or shielding, tied to Coulomb's law.
- You may be asked to sketch or describe the spectrum of a given atom or ion: get the number of peaks, their relative heights and their order right.
Connected topics
Videos
Check yourself
5 questions on 1.6 Photoelectron Spectroscopy. Pick an answer to see if you got it, and why.
Ca²⁺ ions and Ar atoms both have the electron configuration 1s² 2s² 2p⁶ 3s² 3p⁶. Which of the following best describes how the photoelectron spectrum of Ca²⁺ compares with that of Ar?
| Peak | Binding energy (MJ/mol) | Relative number of electrons |
|---|---|---|
| 1 | 151 | 2 |
| 2 | 12.1 | 2 |
| 3 | 7.19 | 6 |
| 4 | 1.09 | 2 |
| 5 | 0.58 | 1 |
Approximate photoelectron spectroscopy data for the atoms of one element, in its ground state
Which element produced this spectrum?
Peak 3 represents electrons in which subshell?
Compared with peak 5 in this spectrum, the peak with the lowest binding energy in the spectrum of silicon would be
Peak 1 for this element appears at a higher binding energy than the corresponding 1s peak for magnesium. Which of the following best explains this difference?
0 of 5 answered