Photoelectron Spectroscopy (PES)

Introduction to Photoelectron Spectroscopy (PES)

Photoelectron Spectroscopy (PES) is a powerful analytical technique that allows chemists to directly measure the binding energies of electrons in atoms and molecules.

Every electron in an atom is held in place by the attractive force of the nucleus. The binding energy (BE) is the amount of energy required to completely remove that electron from the atom. PES gives us experimental data about these binding energies, confirming and extending what we know about electron configurations.

🤔 Why PES Matters

• It provides direct experimental evidence for the shell and subshell model of the atom
• It reveals that electrons in different subshells have different binding energies
• It shows the relative number of electrons in each subshell
• It connects atomic structure to measurable, physical quantities

🔗 The Photoelectric Effect Connection

PES is based on the photoelectric effect, discovered by Einstein in 1905. When a photon of sufficient energy strikes an atom, it can eject an electron. The fundamental equation is:

$E_{photon} = BE + KE$

Where:

• $E_{photon}$ = energy of the incoming photon (known and controlled)
• $BE$ = binding energy of the ejected electron (what we want to measure)
• $KE$ = kinetic energy of the ejected electron (measured by the instrument)

By rearranging: $BE = E_{photon} - KE$

Since we know the photon energy and can measure the kinetic energy of the ejected electron, we can calculate the binding energy.

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How It Works in Practice

1. A sample of gaseous atoms is bombarded with high-energy photons (usually X-rays or UV light)
2. Photons eject electrons from all subshells of the atom
3. The instrument measures the kinetic energy of each ejected electron
4. The binding energy is calculated for each electron
5. The results are displayed as a PES spectrum

Check Your Understanding

In PES, what does the binding energy of an electron represent?

📌 The Photon Source

For PES to work, the incoming photon must have enough energy to eject electrons from every subshell. This is why high-energy photon sources are used:

• UV light (ultraviolet photoelectron spectroscopy, UPS): Used to study valence electrons with lower binding energies
• X-rays (X-ray photoelectron spectroscopy, XPS): Used to study core electrons with higher binding energies

The photon energy must satisfy: $E_{photon} > BE$ for any electron we wish to eject.

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Key Point

If the photon energy is less than the binding energy of a particular electron, that electron cannot be ejected. This is a direct consequence of the quantized nature of light — the energy comes in discrete packets (photons), and a single photon must provide all the energy needed.

Practice Problem

A PES experiment uses photons with an energy of 1200 eV. An ejected electron is measured to have a kinetic energy of 450 eV. What is the binding energy of that electron?

Calculation Practice

A PES experiment uses photons with energy 2000 eV. An electron is ejected with a kinetic energy of 1130 eV.

Conceptual Check

Consider two electrons: Electron A has a binding energy of 200 eV and Electron B has a binding energy of 2500 eV.

📋 Part 1 Summary

Key takeaways from this introduction to PES:

1. PES measures binding energies — the energy needed to remove electrons from atoms
2. Based on the photoelectric effect: $E_{photon} = BE + KE$, so $BE=$

Reading PES Spectra

Now that you understand how PES works, let's learn how to read and interpret the spectra it produces. A PES spectrum is a graph that displays all the information about the binding energies and number of electrons in an atom.

📌 Axes of a PES Spectrum

• X-axis: Binding Energy — Measured in megajoules per mole (MJ/mol) or electron volts (eV). The x-axis runs from high binding energy on the left to low binding energy on the right.
• Y-axis: Relative Number of Electrons — The height of each peak indicates the number of electrons in that subshell.

⚠️ Important: The x-axis is reversed compared to most graphs — high values are on the LEFT. This is a common source of confusion!

📌 Understanding Peaks

Each peak in a PES spectrum corresponds to a subshell (1s, 2s, 2p, 3s, etc.).

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Peak Position (Left-Right)

• Peaks on the far left = highest binding energy = electrons closest to the nucleus (core electrons)
• Peaks on the far right = lowest binding energy = electrons farthest from the nucleus (valence electrons)

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Peak Height (Relative)

• The height of a peak is proportional to the number of electrons in that subshell
• A peak that is 3 times taller than another contains 3 times as many electrons
• For example, a 2p subshell (6 electrons) produces a peak 3 times taller than a 2s subshell (2 electrons)

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Connecting PES to Electron Configuration

One of the most powerful aspects of PES is that it provides direct experimental evidence for the electron configuration model. Each peak in a PES spectrum corresponds exactly to a subshell in the electron configuration.

🔗 The Connection

Electron Configuration	PES Peaks (left to right)
1s²	One peak, height 2
1s² 2s²	Two peaks, heights 2, 2
1s² 2s² 2p⁴	Three peaks, heights 2, 2, 4
1s² 2s² 2p⁶ 3s¹	Four peaks, heights 2, 2, 6, 1

The peaks appear in order from highest binding energy (innermost subshell) to lowest binding energy (outermost subshell), matching the order of subshells from the nucleus outward.

📌 Mapping Peaks to Subshells

To identify an element from its PES spectrum:

Step 1: Count the number of peaks — this tells you how many occupied subshells there are.

Step 2: Read the relative height of each peak — this tells you how many electrons are in each subshell.

Step 3: Assign subshells in order (1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, ...).

Step 4: Write the electron configuration.

Step 5: Sum the electrons to find the atomic number and identify the element.

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Example: Four peaks with heights 2, 2, 6, 2

Core vs Valence Electrons in PES

PES spectra make the distinction between core electrons and valence electrons visually obvious. Understanding this distinction is critical for predicting chemical behavior and interpreting spectra.

📖 Definitions

• Core electrons: Inner-shell electrons that are NOT involved in chemical bonding. They have high binding energies and appear on the left side of PES spectra.
• Valence electrons: Outermost electrons that participate in chemical bonding. They have low binding energies and appear on the right side of PES spectra.

📌 Visual Signature

On a PES spectrum, you will typically see a large gap in binding energy between the core electrons and the valence electrons. This gap makes it easy to visually separate the two groups.

🧪 Example: Silicon (Si, Z = 14)

Electron configuration: 1s² 2s² 2p⁶ 3s² 3p²

PES spectrum (left to right):

Peak	Height	Subshell	Type	Binding Energy
1	2	1s²	Core	~189 MJ/mol
2	2	2s²	Core

PES and Periodic Trends

PES spectra don't just tell us about individual atoms — they reveal periodic trends that help explain the behavior of elements across the periodic table. The key concept connecting PES to periodic trends is effective nuclear charge ($Z_{eff}$).

📊 Effective Nuclear Charge

$Z_{eff} = Z - S$

Problem-Solving Workshop

Now it is time to put your PES knowledge to work. This section features multi-step problems that require you to integrate everything you have learned:

• Reading PES spectra (axes, peaks, heights)
• Connecting peaks to electron configurations
• Identifying elements from PES data
• Predicting PES spectra from known configurations
• Applying periodic trends

These problems mirror the style and difficulty of AP Chemistry exam questions.

🎯 Strategy: Identifying Unknown Elements

When given PES data and asked to identify an element, follow this systematic approach:

Step 1: List the peak heights from left to right (highest to lowest BE).

Step 2: Assign subshells in order: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, ...

Step 3: Check that each peak height does not exceed the maximum for that subshell:

• s subshells: max 2
• p subshells: max 6
• d subshells: max 10
• f subshells: max 14

Step 4: Sum all electrons to get the atomic number.

Step 5: Look up the element.

Step 6: Verify your answer makes chemical sense.

Problem 1: Mystery Element

A PES spectrum shows six peaks with the following data:

Peak	Relative Height	Binding Energy (MJ/mol)
1	2	151

Synthesis & AP Review

This final part brings together everything about Photoelectron Spectroscopy. We will review the key concepts, connect PES to ionization energy, address common mistakes, and practice AP exam-style questions.

🔄 Key Concepts Review

1. PES measures binding energies of electrons using $BE = E_{photon} - KE$
2. Each peak = one subshell; = number of electrons