Photoelectron Spectroscopy (PES)

What is PES?

Photoelectron Spectroscopy (PES) is an experimental technique that measures the energy required to remove electrons from an atom or molecule.

Process:

1. High-energy photons strike a sample
2. Photons transfer energy to electrons
3. Electrons are ejected from various orbitals
4. Instrument measures kinetic energy of ejected electrons
5. Data reveals ionization energies for each electron

Key Equation:

$E_{\text{photon}} = IE + KE$

Where:

• $E_{\text{photon}}$ = energy of incoming photon (constant)
• $IE$ = ionization energy (binding energy of electron)
• $KE$ = kinetic energy of ejected electron

Rearranged:

$IE = E_{\text{photon}} - KE$

PES Spectrum Features

X-axis: Binding Energy (Ionization Energy)

• Units: MJ/mol or eV
• Direction: Usually increases left to right
• Higher binding energy = electron held more tightly
• Represents energy needed to remove electron

Y-axis: Relative Number of Electrons

• Also called: Intensity, Signal, or Counts
• Height of peak indicates number of electrons with that binding energy
• Area under peak is proportional to number of electrons

Peaks

Each peak represents electrons from a specific orbital/sublevel:

• Position (x): Binding energy (how tightly held)
• Height (y): Number of electrons in that orbital

Example: A peak at 1.4 MJ/mol with height of 2 means 2 electrons have binding energy of 1.4 MJ/mol

Reading PES Data

General Trends

Binding energy increases with:

1. Closer to nucleus (lower n value)
2. Higher nuclear charge (more protons)
3. Less shielding (inner vs. outer electrons)

Typical order (increasing binding energy):

$\text{Valence orbitals} < \text{Inner orbitals} < \text{Core orbitals}$

For multi-electron atoms:

$ns < np < (n-1)d < (n-1)p < (n-1)s < ... < 1s$

Interpreting Peaks

Example: Nitrogen (N)

Electron configuration: $1s^2 2s^2 2p^3$

Expected PES spectrum:

1. Peak at ~1.4 MJ/mol, height = 3: Three 2p electrons (valence)
2. Peak at ~1.8 MJ/mol, height = 2: Two 2s electrons (valence)
3. Peak at ~10 MJ/mol, height = 2: Two 1s electrons (core)

Three peaks total (three different orbitals)

Information from PES

1. Number of Occupied Orbitals

Number of peaks = Number of occupied sublevels

• 3 peaks → 3 occupied sublevels (e.g., 1s, 2s, 2p)
• 5 peaks → 5 occupied sublevels (e.g., 1s, 2s, 2p, 3s, 3p)

2. Number of Electrons in Each Orbital

Height/area of peak = Number of electrons

• Peak height of 2 → 2 electrons
• Peak height of 6 → 6 electrons

3. Relative Energies

Peak position reveals how tightly electrons are held:

• Rightmost peak (highest binding energy) = 1s (closest to nucleus)
• Leftmost peak (lowest binding energy) = valence electrons (farthest from nucleus)

4. Identifying Elements

Combine information to write electron configuration, then identify element:

Example:

• 4 peaks with heights 2, 2, 6, 2 (left to right)
• Configuration: $1s^2 2s^2 2p^6 3s^2$
• Element: Magnesium (Mg)

Comparing PES Spectra

Same Period (e.g., C, N, O)

Trend: Binding energies increase across period

• More protons → stronger nuclear charge
• Same shielding (same inner electrons)
• Electrons held more tightly

Example:

• 1s electrons: $BE_C < BE_N < BE_O$
• More protons in O pull electrons tighter

Same Group (e.g., Li, Na, K)

Trend: Binding energies decrease down group

• More electron shells → more shielding
• Valence electrons farther from nucleus
• Weaker attraction despite more protons

Example:

• 2s in Li > 3s in Na > 4s in K

Core vs. Valence

Core electrons (inner shells):

• Much higher binding energy
• Closer to nucleus
• Less shielding

Valence electrons (outer shell):

• Lower binding energy
• Farther from nucleus
• More shielding

Large gap between core and valence peaks

Common PES Questions

Type 1: Write electron configuration from spectrum

Given: Peak positions and heights Find: Electron configuration and element

Steps:

1. Count peaks (number of sublevels)
2. Note heights (electrons per sublevel)
3. Assign orbitals from right to left (high to low BE)
4. Write configuration and identify element

Type 2: Predict spectrum from element

Given: Element or electron configuration Find: Number of peaks, relative heights, relative positions

Steps:

1. Write electron configuration
2. Count occupied sublevels (number of peaks)
3. Count electrons per sublevel (peak heights)
4. Order by binding energy (1s highest, valence lowest)

Type 3: Compare spectra

Given: Two elements Find: Differences in binding energies

Steps:

1. Consider nuclear charge (more protons → higher BE)
2. Consider shielding (more shells → lower BE)
3. Compare same orbitals between elements

Example: Sodium (Na)

Electron configuration: $1s^2 2s^2 2p^6 3s^1$

PES spectrum:

• Peak 1: 3s¹ (height = 1, lowest BE ~0.5 MJ/mol) - valence
• Peak 2: 2p⁶ (height = 6, medium BE ~3 MJ/mol) - inner
• Peak 3: 2s² (height = 2, high BE ~6 MJ/mol) - inner
• Peak 4: 1s² (height = 2, highest BE ~100 MJ/mol) - core

Total: 4 peaks

Note: Large gap between 3s and 2p (valence vs. core)

Key Relationships

Binding Energy and Atomic Number

Same orbital, different elements:

Higher atomic number (Z) → Higher binding energy

Example: 1s electrons

• Li (Z=3): ~6 MJ/mol
• C (Z=6): ~11 MJ/mol
• F (Z=9): ~80 MJ/mol

Sublevels in Same Shell

Energy order (increasing BE):

$ns < np < (n-1)d$

Example for n=3: $3s < 3p < 2d$

However, 3d is usually empty or partially filled, and 2d doesn't exist.

More common: $3s < 3p < 2p < 2s < 1s$

Applications

1. Elemental analysis: Identify unknown elements
2. Electron configuration confirmation: Verify predicted configurations
3. Bonding studies: Understand how electrons participate in bonds
4. Material characterization: Analyze surface composition
5. Support for quantum theory: Experimental evidence for orbital model

Tips for AP Exam

1. Right to left: Highest BE (rightmost) is always 1s
2. Count electrons: Sum of peak heights = total electrons = atomic number
3. Valence electrons: Leftmost peak(s) with lowest BE
4. Core electrons: Large gap separates from valence
5. Period = shells: Number of principal energy levels (n values)
6. Peaks ≠ Electrons: Number of peaks is number of sublevels, not total electrons