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.

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.

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 $BE = E_{photon} - KE$
3. High-energy photon sources (UV or X-ray) are needed to eject electrons from all subshells
4. Higher binding energy = electron is closer to the nucleus and more tightly held
5. Lower binding energy = electron is farther from the nucleus and easier to remove

In the next part, we will learn how to read and interpret PES spectra — the graphical output of a PES experiment.

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.).

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)

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)

Example: Lithium (Li, Z = 3)

Electron configuration: 1s² 2s¹

A PES spectrum for lithium shows:

• Peak 1 (far left, highest BE): Relative height of 2 → corresponds to 1s² (2 electrons)
• Peak 2 (far right, lowest BE): Relative height of 1 → corresponds to 2s¹ (1 electron)

Check Your Understanding

On a PES spectrum, the x-axis displays binding energy. How is it oriented?

Reading a Spectrum: Nitrogen (Z = 7)

Nitrogen has the electron configuration: 1s² 2s² 2p³

Its PES spectrum shows three peaks:

Peak	Position	Relative Height	Subshell
1	Far left (highest BE)	2	1s²
2	Middle	2	2s²
3	Far right (lowest BE)	3	2p³

Notice:

• The 1s peak has the highest binding energy because those electrons are closest to the nucleus
• The 2s and 2p peaks have lower binding energies
• The 2p peak is taller than the 2s peak because it holds more electrons (3 vs 2)
• The total electron count: 2 + 2 + 3 = 7, which matches nitrogen's atomic number

Practice: Reading Spectra

A PES spectrum shows three peaks with relative heights of 2, 2, and 6 (from left to right, i.e., from highest to lowest binding energy). How many total electrons does this atom have?

Spectrum Analysis

A PES spectrum for an unknown element shows four peaks with the following relative heights (listed from highest to lowest binding energy):

Peak 1: height = 2 Peak 2: height = 2 Peak 3: height = 6 Peak 4: height = 1

Interpreting Peak Heights

Consider a PES spectrum with peaks at relative heights of 2, 2, 6, 2, and 3 (from left to right).

Part 2 Summary

Key points for reading PES spectra:

1. X-axis: Binding energy — high on the left, low on the right
2. Y-axis: Relative number of electrons — peak height tells you how many electrons are in each subshell
3. Each peak = one subshell (1s, 2s, 2p, 3s, 3p, etc.)
4. Left-most peak = highest binding energy = innermost electrons (1s)
5. Right-most peak = lowest binding energy = outermost (valence) electrons
6. Total electrons = sum of all peak heights = atomic number (for neutral atoms)

In the next part, we will connect PES spectra directly to electron configurations.

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.

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

• Peak 1 (height 2) → 1s²
• Peak 2 (height 2) → 2s²
• Peak 3 (height 6) → 2p⁶
• Peak 4 (height 2) → 3s²

Electron configuration: 1s² 2s² 2p⁶ 3s² Total electrons: 2 + 2 + 6 + 2 = 12 → Magnesium (Mg)

Identify the Element

A PES spectrum shows five peaks with relative heights (from highest to lowest binding energy): 2, 2, 6, 2, 5.

What element does this represent?

Relative Binding Energies

The binding energies of subshells follow predictable patterns:

Within the Same Atom:

• 1s has the highest binding energy (closest to nucleus)
• Each successive subshell has a lower binding energy
• Within the same principal energy level, the order is: s > p > d > f

Typical Binding Energy Ranges:

Subshell	Approximate BE Range
1s	Very high (tens to hundreds of MJ/mol)
2s	High
2p	Moderately high
3s	Moderate
3p	Lower
Valence	Lowest (typically < 2 MJ/mol)

Spacing Between Peaks

• There is typically a large gap between peaks from different principal energy levels (e.g., 1s vs 2s)
• There is a smaller gap between subshells within the same principal level (e.g., 2s vs 2p)

Electron Configuration from PES

A PES spectrum for a neutral atom shows peaks with heights 2, 2, 6, 2, 6, 2. What is the electron configuration?

Practice: Element Identification

A PES spectrum shows the following peaks (from highest to lowest BE):

• Peak 1: relative height 2
• Peak 2: relative height 2
• Peak 3: relative height 6
• Peak 4: relative height 2
• Peak 5: relative height 4

Subshell Assignment

An atom has the PES peaks: 2, 2, 6, 2, 6, 2, 1 (from highest to lowest binding energy).

Part 3 Summary

Connecting PES to electron configuration:

1. Each peak in a PES spectrum corresponds to one subshell in the electron configuration
2. Peak height = number of electrons in that subshell
3. Peaks are ordered from highest BE (innermost subshell) to lowest BE (outermost subshell)
4. To identify an element: assign subshells to peaks, sum electrons, find atomic number
5. Binding energy order within an atom: 1s > 2s > 2p > 3s > 3p > 4s > 3d > ...
6. For transition metals, the 3d peak may appear with higher BE than 4s on PES spectra

Next, we will explore the distinction between core and valence electrons in PES spectra.

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	~17 MJ/mol
3	6	2p⁶	Core	~13 MJ/mol
4	2	3s²	Valence	~1.1 MJ/mol
5	2	3p²	Valence	~0.8 MJ/mol

Key observations:

• The core electrons (1s, 2s, 2p) have binding energies ranging from ~13 to ~189 MJ/mol
• The valence electrons (3s, 3p) have binding energies around ~0.8–1.1 MJ/mol
• There is a huge gap between the 2p peak (~13 MJ/mol) and the 3s peak (~1.1 MJ/mol)
• This gap clearly separates core from valence electrons

Core vs Valence

In a PES spectrum, where do valence electrons appear?

Core and Valence Across a Period

As you move across a period (e.g., Na → Ar), the number of core electrons stays the same while the number of valence electrons increases.

For Period 3 elements:

• All have the same core: 1s² 2s² 2p⁶ (10 core electrons)
• Valence electrons increase: Na (1) → Mg (2) → Al (3) → Si (4) → P (5) → S (6) → Cl (7) → Ar (8)

On PES spectra for these elements:

• The core peaks shift slightly to the left (higher BE) as nuclear charge increases
• The valence peaks on the right grow in height as more valence electrons are added
• The gap between core and valence remains prominent

Practice Problem

For an atom with the PES peak heights 2, 2, 6, 2, 6 (from left to right), how many valence electrons does it have?

Identifying Core and Valence

An element has PES peaks with heights: 2, 2, 6, 2, 3 (from highest to lowest binding energy). The first three peaks are clustered at high binding energies and the last two peaks are at much lower binding energies.

Conceptual Understanding

Consider the PES spectrum of oxygen (O, Z = 8) with configuration 1s² 2s² 2p⁴.

Part 4 Summary

Core vs valence electrons in PES:

1. Core electrons appear on the left (high binding energy) — they are inner-shell electrons not involved in bonding
2. Valence electrons appear on the right (low binding energy) — they are outermost electrons that participate in bonding
3. A large gap in binding energy often separates core from valence peaks
4. Across a period, the number of core electrons stays constant while valence electrons increase
5. For Period 2 elements, only 1s electrons are core; for Period 3 elements, 1s² 2s² 2p⁶ are core
6. The number of valence electrons determines the element's chemical properties

Next, we will explore how PES connects to periodic trends, especially effective nuclear charge.

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

$Z_{eff} = Z - S$

Where:

• $Z$ = atomic number (total number of protons)
• $S$ = shielding constant (approximate number of core electrons shielding the valence electrons)
• $Z_{eff}$ = effective nuclear charge felt by a valence electron

As $Z_{eff}$ increases, valence electrons are held more tightly, resulting in higher binding energies on PES spectra.

Binding Energy Across a Period

As you move left to right across a period, the binding energies of ALL electrons increase. This happens because:

1. Each successive element adds one more proton to the nucleus
2. Electrons are added to the same principal energy level (same shell)
3. Electrons in the same shell provide poor shielding for each other
4. Therefore, $Z_{eff}$ increases across the period

Example: Period 2 First Ionization Energies and 1s Binding Energies

Element	Z	1s BE (MJ/mol)	Valence BE (MJ/mol)
Li	3	6.26	0.52
Be	4	11.5	0.90
B	5	19.3	0.80
C	6	28.6	1.09
N	7	39.6	1.40
O	8	52.6	1.31
F	9	67.2	1.68
Ne	10	84.0	2.08

Notice: Both the 1s binding energy and the valence binding energy generally increase across the period.

The slight decreases at B (after Be) and O (after N) are due to subshell effects — B starts filling the 2p subshell, and O begins pairing electrons in 2p.

Trend Check

As you move from left to right across Period 3 (Na to Ar), what happens to the binding energy of the 1s electrons?

Comparing PES Spectra of Adjacent Elements

When comparing PES spectra of adjacent elements in the same period, you should notice:

Sodium (Na, Z = 11): 1s² 2s² 2p⁶ 3s¹

• Five peaks with heights: 2, 2, 6, 1 (but 2s and 2p show as separate peaks)
• Rightmost peak (3s¹): height 1, lowest BE

Magnesium (Mg, Z = 12): 1s² 2s² 2p⁶ 3s²

• Same number of peaks as Na (four peaks)
• Rightmost peak (3s²): height 2, slightly higher BE than Na's 3s peak
• ALL peaks shift slightly left (higher BE) compared to Na

Key Comparisons:

1. Mg's 1s peak has higher BE than Na's 1s peak (more protons pulling on same electrons)
2. Mg's 3s peak is taller (2 vs 1) AND has higher BE
3. The shapes of core electron peaks are similar, but shifted
4. Adding a proton affects all electrons, not just the outermost ones

Comparing Elements

Which of the following correctly compares the PES spectra of fluorine (F, Z = 9) and neon (Ne, Z = 10)?

Effective Nuclear Charge

Calculate the approximate effective nuclear charge ($Z_{eff}$) felt by a valence electron for the following atoms. Use the simple approximation $Z_{eff} = Z - S$ where $S$ equals the number of core electrons.

Applying Periodic Trends to PES

Use your knowledge of periodic trends and effective nuclear charge to answer these questions.

Part 5 Summary

PES and periodic trends:

1. Effective nuclear charge ($Z_{eff} = Z - S$) determines how tightly valence electrons are held
2. Across a period, $Z_{eff}$ increases → all binding energies increase → all PES peaks shift left
3. All electrons are affected by increasing nuclear charge, not just valence electrons
4. Exceptions at B (after Be) and O (after N) arise from subshell transitions and electron pairing
5. Comparing adjacent elements: same peak structure but shifted binding energies
6. Higher $Z_{eff}$ = higher binding energy = harder to remove electrons

In the next part, we will apply all of this knowledge to solve challenging PES problems.

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
2	2	17.4
3	6	13.5
4	2	1.95
5	6	1.01
6	1	0.58

What element is this?

Problem 2: Predicting Spectra

If you were to draw the PES spectrum for aluminum (Al, Z = 13), how many peaks would appear and what would their relative heights be?

Problem 3: Multi-Step Analysis

Two PES spectra are compared. Element X has peaks: 2, 2, 6, 2, 2. Element Y has peaks: 2, 2, 6, 2, 3. Both are neutral atoms.

Problem 4: Reasoning About Spectra

An unknown element has a PES spectrum with peak heights: 2, 2, 6, 2, 6, 2, 6 (from highest to lowest binding energy).

Problem 5: AP-Style Question

A student analyzes the PES spectrum of an unknown gaseous element. The spectrum shows 5 peaks. The first peak (highest BE) has a relative height of 2. The second peak has a relative height of 2. The third peak has a relative height of 6. The fourth and fifth peaks (lowest BE) have relative heights of 2 and 4, respectively.

The student claims the element must be in Period 3 of the periodic table. Is the student correct, and what element is it?

Problem 6: Predicting Peak Heights

Write the expected PES peak heights (from highest to lowest binding energy) for the following element. Separate your answers with commas.

Part 6 Summary

Problem-solving strategies for PES:

1. Systematic approach: List peaks → assign subshells → sum electrons → identify element
2. Check subshell maximums: s ≤ 2, p ≤ 6, d ≤ 10, f ≤ 14
3. Don't forget 3d: For elements beyond Ca (Z > 20), the 3d subshell must appear
4. Compare spectra: Adjacent elements differ by one electron; all BEs shift with Z
5. Predict spectra: Write the electron configuration, then each subshell becomes one peak
6. Verify: Total electrons must equal atomic number for neutral atoms

In the final part, we will review everything and practice AP exam-style questions.

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; peak height = number of electrons
3. X-axis: binding energy (high → low, left → right)
4. Core electrons = high BE (left); valence electrons = low BE (right)
5. Across a period: all binding energies increase due to increasing $Z_{eff}$
6. Element identification: sum peak heights = atomic number

Connecting PES to Ionization Energy

The first ionization energy (IE₁) of an element is directly related to the PES spectrum:

$IE_1 = \text{binding energy of the outermost (valence) electron}$

The rightmost peak on a PES spectrum (lowest binding energy) corresponds to the outermost subshell. The binding energy of this peak equals the first ionization energy.

Example:

• Sodium (Na): The rightmost peak is the 3s¹ peak with BE ≈ 0.50 MJ/mol → IE₁ ≈ 0.50 MJ/mol ≈ 496 kJ/mol
• Chlorine (Cl): The rightmost peak is the 3p⁵ peak with BE ≈ 1.25 MJ/mol → IE₁ ≈ 1.25 MJ/mol ≈ 1251 kJ/mol

Successive Ionization Energies

PES data can also help explain successive ionization energies. The large jump in IE values that occurs when you begin removing core electrons is clearly visible as the gap between valence and core peaks on PES spectra.

AP Review Question 1

The PES spectrum of an element shows the rightmost peak at a binding energy of 1.09 MJ/mol. This value corresponds to which property of the element?

Common Mistakes on the AP Exam

Mistake 1: Confusing the X-Axis Direction

❌ Assuming binding energy increases left to right (like most graphs) ✅ Remember: binding energy is high on the left, low on the right

Mistake 2: Forgetting the 3d Subshell

❌ Writing peaks as 2, 2, 6, 2, 6, 2, 6 for elements with Z > 20 ✅ Include the 3d peak (up to height 10) between 3p and 4s for transition metals

Mistake 3: Confusing Peak Height with Binding Energy

❌ Thinking taller peaks mean higher binding energy ✅ Peak height = number of electrons; peak position (left/right) = binding energy

Mistake 4: Not Matching Total Electrons to Atomic Number

❌ Identifying an element without verifying the total electron count ✅ Always sum all peak heights and confirm it matches the expected atomic number

Mistake 5: Ignoring Subshell Exceptions

❌ Expecting perfectly smooth IE trends across a period ✅ Remember the B/Be and O/N exceptions due to subshell transitions and electron pairing

AP Review Question 2

Two elements, X and Y, are in the same period. Element X has PES peak heights of 2, 2, 6, 2, 3, and Element Y has PES peak heights of 2, 2, 6, 2, 4. Which statement is correct?

AP Review Question 3

A student is given PES data for an unknown element:

• Peak 1: BE = 76.0 MJ/mol, relative height = 2
• Peak 2: BE = 8.8 MJ/mol, relative height = 2
• Peak 3: BE = 6.8 MJ/mol, relative height = 3

The student is asked to identify the element. Which reasoning is correct?

AP Review Question 4

Use the following PES data for an unknown element:

Peak	Binding Energy (MJ/mol)	Relative Height
A	200.2	2
B	23.4	2
C	18.7	6
D	2.45	2
E	1.09	2

Round all answers to 3 significant figures.

AP Review Question 5

Consider the successive ionization energies of magnesium (Mg): IE₁ = 0.74 MJ/mol, IE₂ = 1.45 MJ/mol, IE₃ = 7.73 MJ/mol

There is a large jump between IE₂ and IE₃.

Final Challenge

An element has a PES spectrum with 7 peaks. The peak heights from left to right are: 2, 2, 6, 2, 6, 2, 10. What is this element, and what is special about it?

Complete PES Summary

Congratulations on completing the Photoelectron Spectroscopy unit! Here is everything you need to know for the AP exam:

Essential Equations

• $E_{photon} = BE + KE$ → $BE = E_{photon} - KE$
• $Z_{eff} = Z - S$
• $IE_1$ = binding energy of the rightmost PES peak

Reading Spectra

• X-axis: BE (high left, low right)
• Y-axis: relative number of electrons
• Each peak = one subshell
• Total peak heights = atomic number

Periodic Trends

• Across a period: all BEs increase (higher $Z_{eff}$)
• Exceptions at B/Be and O/N due to subshell effects
• Core vs valence gap visible on spectra

Common AP Tasks

1. Identify elements from PES data
2. Predict PES spectra from electron configurations
3. Connect PES to ionization energies
4. Explain periodic trends using $Z_{eff}$
5. Recognize subshell exceptions