AP Chemistry: Photoelectron Spectroscopy (PES)

AP Chemistry – Photoelectron Spectroscopy (PES)

AP Chemistry: Photoelectron Spectroscopy (PES) – Exam-Ready Study Guide

What This Is

Photoelectron Spectroscopy (PES) is a lab technique that measures the ionization energies of electrons in an atom or molecule by blasting them with high-energy light (usually X-rays or UV rays) and detecting the speed of the ejected electrons. This reveals the electron configuration and relative energies of orbitals, helping chemists understand bonding, reactivity, and atomic structure. On the AP exam, PES is tested in multiple-choice questions and free-response questions (FRQs)—often as a graph you must interpret to identify elements or compare orbital energies.

Real-world example: PES was used to confirm the electron configuration of superheavy elements (like element 118, Oganesson) when they were first synthesized. It also helps in materials science to study surfaces of catalysts or semiconductors.

Key Terms & Concepts

• Photoelectric Effect: When light of sufficient energy (frequency) hits a material, it ejects electrons. The energy of the ejected electrons depends on the frequency of the light and the binding energy of the electron.

• Equation: E = hν = KE + BE

  
  
  • E = energy of the photon (J)
  • h = Planck’s constant (6.626 × 10⁻³⁴ J·s)
  • ν = frequency of light (Hz)
  • KE = kinetic energy of the ejected electron (J)
  • BE = binding energy (ionization energy) of the electron (J)

• Binding Energy (BE): The energy required to remove an electron from an atom. Higher BE = electron is closer to the nucleus (lower energy orbital).

• Example: 1s electrons have higher BE than 2s electrons.

• Kinetic Energy (KE) of Ejected Electrons: The leftover energy after the electron is ejected. KE = hν – BE.

• Key idea: Electrons with higher KE were less tightly bound (lower BE).

• PES Spectrum: A graph of electron count (y-axis) vs. binding energy (x-axis). Peaks represent subshells (e.g., 1s, 2s, 2p).

• Example: A peak at 1300 eV = 1s electrons; a peak at 100 eV = 2s electrons.

• Intensity of Peaks: The height of a peak corresponds to the number of electrons in that subshell.

• Example: A 2p peak with 3× the height of a 2s peak means there are 6 electrons in 2p (vs. 2 in 2s).

• Orbital Energy Order: In multi-electron atoms, s < p < d < f in energy (for the same n). PES confirms this experimentally.

• Exception: In hydrogen (1-electron), all orbitals with the same n have the same energy.

• Koopmans’ Theorem: The binding energy of an electron ≈ its orbital energy (ignoring relaxation effects). Useful for interpreting PES data.

• Work Function (Φ): The minimum energy needed to remove an electron from a metal surface (not the same as BE for atoms).

• Example: In solar panels, light must exceed the work function to eject electrons (photoelectric effect).

• X-ray PES (XPS) vs. UV PES (UPS):

• XPS: Uses X-rays (high energy) → ejects core electrons (e.g., 1s, 2s).

• UPS: Uses UV light (lower energy) → ejects valence electrons (e.g., 2p, 3s).

• Spin-Orbit Coupling: In PES, some peaks split due to electron spin interacting with orbital motion (e.g., p orbitals split into p₁/₂ and p₃/₂).

• AP tip: You won’t need to calculate this, but recognize doublet peaks in spectra.

Step-by-Step: How to Interpret a PES Spectrum

Problem: Given a PES spectrum, identify the element and explain the peaks.

1. Label the axes:
2. x-axis: Binding energy (BE) in eV or MJ/mol (higher BE = left).

3. y-axis: Relative number of electrons (intensity).

4. Identify the peaks:

5. The leftmost peak = 1s electrons (highest BE).

6. Next peaks = 2s, 2p, 3s, 3p, etc. (follow the Aufbau principle).

7. Count electrons per peak:

8. Height of peak ≈ number of electrons in that subshell.

9. Example: A 2p peak with 3× the height of 2s → 6 electrons in 2p (vs. 2 in 2s).

10. Match to electron configuration:

11. Add up electrons from all peaks → total electrons = atomic number.

12. Example: Peaks at 1s² 2s² 2p⁶ 3s² 3p² → 14 electrons → Silicon (Si).

13. Compare orbital energies:

14. Higher BE = lower energy orbital (closer to nucleus).

15. Example: In Na (1s² 2s² 2p⁶ 3s¹), the 3s peak has lower BE than 2p.

16. Check for anomalies:

17. Half-filled/full subshells (e.g., Cr, Cu) may have unexpected peak heights.
18. Spin-orbit splitting → doublet peaks (e.g., p orbitals split into two).

Common Mistakes

• Mistake: Confusing binding energy (BE) with kinetic energy (KE).

• Correction: BE is the energy to remove an electron; KE is the leftover energy after ejection. KE = hν – BE.

• Mistake: Assuming peak height = energy level.

• Correction: Peak height = number of electrons; x-axis position = energy (BE).

• Mistake: Forgetting that PES measures ionization energy, not electron affinity.

• Correction: PES gives ionization energies (energy to remove an electron), not the energy change when an electron is added.

• Mistake: Misordering subshells (e.g., thinking 3d has lower BE than 4s).

• Correction: In multi-electron atoms, 4s has lower BE than 3d (but fills first in Aufbau). PES confirms this experimentally.

• Mistake: Ignoring spin-orbit splitting (e.g., treating p peaks as single peaks).

• Correction: Some spectra show doublet peaks for p, d, f orbitals due to spin-orbit coupling.

AP Exam Insights

1. FRQs often ask you to:
2. Identify an element from a PES spectrum.
3. Compare orbital energies (e.g., “Which has higher BE: 2s or 2p?”).

4. Explain why peaks have different heights (e.g., “Why is the 2p peak taller than 2s?”).

5. Multiple-choice traps:

6. Peak height vs. energy: A tall peak ≠ high energy (it means more electrons).
7. Units: BE is often given in eV or MJ/mol—convert if needed.

8. Core vs. valence electrons: XPS (X-ray PES) ejects core electrons; UPS (UV PES) ejects valence electrons.

9. Tricky distinction:

10. Ionization energy (IE) vs. binding energy (BE):

    
    
    • IE = energy to remove one electron from a neutral atom (e.g., first IE of Na).
    • BE = energy to remove any electron from any orbital (measured by PES).

11. Experimental context:

12. PES is not the same as mass spectrometry (which measures mass/charge ratio).
13. PES does not give info about molecular geometry (use IR or NMR for that).

Quick Check Questions

1. Multiple Choice

The PES spectrum of an element shows peaks at the following binding energies (in MJ/mol): - 2.37 (small peak) - 0.15 (large peak) - 0.08 (medium peak)

Which element is this most likely to be? (A) Carbon (C) (B) Sodium (Na) (C) Magnesium (Mg) (D) Aluminum (Al)

✅ Answer: (B) Sodium (Na)
Explanation: The peaks correspond to 1s² (2.37 MJ/mol), 2s² 2p⁶ (0.15 MJ/mol), and 3s¹ (0.08 MJ/mol)—matching Na’s electron configuration (1s² 2s² 2p⁶ 3s¹).

2. Short FRQ

A PES spectrum for an unknown element has three peaks with relative intensities (heights) in a ratio of 1:2:3. The binding energies of the peaks are 500 eV, 40 eV, and 20 eV.

(a) Identify the element.
(b) Explain why the peak at 20 eV is the tallest.

✅ Answer:
(a) Nitrogen (N)
- Peaks: 1s² (500 eV), 2s² (40 eV), 2p³ (20 eV) → total electrons = 7 → N.
(b) The 20 eV peak is tallest because it represents the 2p subshell, which has 3 electrons (vs. 2 in 2s and 2 in 1s). Peak height corresponds to the number of electrons in that subshell.

Last-Minute Cram Sheet

1. PES measures binding energy (BE) = energy to remove an electron.
2. KE = hν – BE (kinetic energy of ejected electron).
3. Higher BE = electron closer to nucleus (lower energy orbital).
4. Peak height = number of electrons in that subshell.
5. 1s peak is always the leftmost (highest BE).
6. XPS (X-ray PES) → core electrons; UPS (UV PES) → valence electrons.
7. Spin-orbit coupling → doublet peaks (e.g., p orbitals split).
8. ⚠️ Peak height ≠ energy! Tall peak = more electrons, not higher energy.
9. Aufbau order: 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p…
10. ⚠️ In multi-electron atoms, 4s has lower BE than 3d (but fills first).