Photoelectron Spectroscopy (PES) - Complete Interactive Lesson

Part 1: Introduction to PES

Introduction to Photoelectron Spectroscopy (PES)

Part 1 of 7 — Introduction to PES

Topics in This Part

Section
🤔 Why PES Matters
How It Works in Practice

🔑 Key Concept: Mastering this material will strengthen your foundation for both the AP Chemistry exam and more advanced chemistry topics.

What You'll Master in Part 1

Understanding the core concepts covered in Part 1
Applying these ideas to solve practice problems
Building toward AP exam readiness for this topic

🔗 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:

$\boxed{E_{photon} = BE + KE}$

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:

$\boxed{BE = E_{photon} - KE}$

🔑 Key Concept: This equation is the foundation of all PES analysis. You control the photon energy, measure the kinetic energy, and calculate the binding energy.

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

A sample of gaseous atoms is bombarded with high-energy photons (usually X-rays or UV light)
Photons eject electrons from all subshells of the atom
The instrument measures the kinetic energy of each ejected electron
The binding energy is calculated for each electron
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.

💡 Tip: If the photon energy is less than the binding energy of a particular electron, that electron . This is a direct consequence of the quantized nature of light — a single photon must provide all the energy needed.

✏️ Practice Problem

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

Problem: 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: What Is PES?

🧪 The Core Equation

$E_{photon} = BE + KE \quad \Rightarrow \quad BE = E_{photon} - KE$

Part 2: Interpreting PES Spectra

Reading PES Spectra

Part 2 of 7 — Interpreting PES Spectra

Topics in This Part

Section
📌 Axes of a PES Spectrum
Peak Position (Left-Right)
Peak Height (Relative)
Example: Lithium (Li, Z = 3)

🔑 Key Concept: Mastering this material will strengthen your foundation for both the AP Chemistry exam and more advanced chemistry topics.

What You'll Master in Part 2

Understanding the core concepts covered in Part 2
Applying these ideas to solve practice problems
Building toward AP exam readiness for this topic

📌 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

Part 3: Binding Energy & Subshells

Connecting PES to Electron Configuration

Part 3 of 7 — Binding Energy & Subshells

Topics in This Part

Section
🔗 The Connection
Example: Four peaks with heights 2, 2, 6, 2
Within the Same Atom:
Typical Binding Energy Ranges:
Spacing Between Peaks

🔑 Key Concept: Mastering this material will strengthen your foundation for both the AP Chemistry exam and more advanced chemistry topics.

What You'll Master in Part 3

Understanding the core concepts covered in Part 3
Applying these ideas to solve practice problems
Building toward AP exam readiness for this topic

📌 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

Part 4: Relative Peak Heights

Core vs Valence Electrons in PES

Part 4 of 7 — Relative Peak Heights

Topics in This Part

Section
📖 Definitions
📌 Visual Signature

🔑 Key Concept: Mastering this material will strengthen your foundation for both the AP Chemistry exam and more advanced chemistry topics.

What You'll Master in Part 4

Understanding the core concepts covered in Part 4
Applying these ideas to solve practice problems
Building toward AP exam readiness for this topic

🧪 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

Part 5: Identifying Elements from PES

PES and Periodic Trends

Part 5 of 7 — Identifying Elements from PES

Topics in This Part

Section
📊 Effective Nuclear Charge
Example: Period 2 First Ionization Energies and 1s Binding Energies
Sodium (Na, Z = 11): 1s² 2s² 2p⁶ 3s¹
Magnesium (Mg, Z = 12): 1s² 2s² 2p⁶ 3s²
Key Comparisons:

🔑 Key Concept: Mastering this material will strengthen your foundation for both the AP Chemistry exam and more advanced chemistry topics.

What You'll Master in Part 5

Understanding the core concepts covered in Part 5
Applying these ideas to solve practice problems
Building toward AP exam readiness for this topic

📌 Binding Energy Across a Period

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

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

Part 6: Problem-Solving Workshop

Problem-Solving Workshop

Part 6 of 7 — Problem-Solving Workshop

Practice Makes Perfect

This workshop features multi-step problems that mirror the AP Chemistry exam format. Each problem requires you to combine concepts from previous parts and show your work clearly.

🔑 Why this matters: The AP Chemistry exam rewards students who can apply concepts to unfamiliar problems — structured practice is the best preparation.

What You'll Master in Part 6

Working through complete multi-step problems from start to finish
Building problem-solving strategies you can apply on the AP exam
Identifying which concepts to apply and in what order

🎯 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.

💡 Tip: Always check that each peak height doesn’t exceed the subshell maximum (s ≤ 2, p ≤ 6, d ≤ 10, f ≤ 14). This catches assignment errors quickly.

Part 7: Synthesis & AP Review

Synthesis & AP Review

Part 7 of 7 — Synthesis & AP Review

Bringing It All Together

This comprehensive review connects every concept from Parts 1–6 with AP-style problems. The questions are designed to mirror what you'll see on the actual exam — multi-step, multi-concept, and requiring clear written explanations.

🔑 Why this matters: AP Chemistry exam questions rarely test one concept in isolation — success requires connecting ideas across topics.

What You'll Master in Part 7

Solving AP-style questions that integrate multiple concepts from this unit
Writing clear, concise explanations using proper chemistry terminology
Identifying and avoiding common AP exam traps and mistakes

🔗 Connecting PES to Ionization Energy

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

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

Concept	Meaning
Binding Energy (BE)	Energy needed to remove an electron from its subshell
Photon Source	High-energy UV or X-ray light ejects electrons
Higher BE	Electron is closer to nucleus, more tightly held
Lower BE	Electron is farther from nucleus, easier to remove

Axis / Feature	What It Shows	Key Detail
X-axis	Binding energy (BE)	High on left, low on right
Y-axis	Relative # of electrons	Peak height = electrons in that subshell
Each peak	One subshell	1s, 2s, 2p, 3s, 3p, etc.
Left-most peak	Innermost electrons (1s)	Highest binding energy
Right-most peak	Valence electrons	Lowest binding energy

Step	Action	Example
1	Assign subshells to each peak (left → right)	1s, 2s, 2p, 3s, 3p
2	Read the peak height for each	2, 2, 6, 2, 5
3	Sum all electrons	2+2+6+2+5 = 17
4	Match to atomic number	Z = 17 → Chlorine

Feature	Core Electrons	Valence Electrons
Position on spectrum	Left (high BE)	Right (low BE)
Role	Not involved in bonding	Participate in bonding & reactions
Across a period	Number stays constant	Number increases

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

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

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)

What Happens	Why	PES Effect
$Z_{eff}$ increases	More protons, same shielding	All peaks shift left (higher BE)
All electrons affected	Nuclear charge pulls entire cloud tighter	Core AND valence BEs increase
IE generally increases	Harder to remove valence e⁻	Rightmost peak moves left

Transition	What Happens	Why
Be → B	IE drops	B removes a 2p e⁻ (higher energy than Be's 2s)
N → O	IE drops	O has a paired 2p e⁻; electron-electron repulsion

Step	Action	Check
1	List all peaks (left → right)	Highest BE to lowest BE
2	Assign subshells	s ≤ 2, p ≤ 6, d ≤ 10, f ≤ 14
3	Sum all electrons	Must equal atomic number
4	Identify the element	Use periodic table

Mistake	Correct Approach
Forgetting 3d for Z > 20	Always include 3d subshell for transition metals
Writing 2, 2, 6, 2, 6, 2, 6 for TMs	Must show 3d peak (up to height 10) between 3p and 4p
Not verifying total	Always sum peak heights = atomic number

Task	Strategy
Compare spectra	Adjacent elements differ by 1 e⁻; all BEs shift with Z
Predict a spectrum	Write e⁻ config → each subshell = one peak
Verify answer	Total e⁻ must = atomic number for neutral atoms

Equation	Used For
$BE = E_{photon} - KE$	Calculate binding energy from PES data
$Z_{eff} = Z - S$	Determine effective nuclear charge
$IE_1$ = BE of rightmost peak	First ionization energy from spectrum

Feature	Interpretation
X-axis	Binding energy (high left, low right)
Y-axis	Relative number of electrons
Each peak	One subshell
Sum of peak heights	Atomic number (for neutral atoms)
Leftmost peak	1s (innermost, highest BE)
Rightmost peak	Valence electrons (lowest BE)

Trend	PES Effect	Exception
Across a period: $Z_{eff}$ ↑	All peaks shift left (higher BE)	IE drops at B and O
Core vs. valence gap	Large BE gap separates them	Boundary depends on period

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

Photoelectron Spectroscopy (PES)