Master AP Chemistry Topic 1.6 with our PES practice quiz. Practice interpreting photoelectron spectroscopy graphs and understanding binding energy to ace your AP Chemistry exam.
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H₂
H₂ is a molecule containing two hydrogen atoms.
- Each H atom has 1 electron.
- H₂ therefore contains 2 electrons.
- Each hydrogen atom has one occupied 1s orbital.
- Understanding H₂ begins with understanding electron energy levels, shells, subshells, and orbitals.
1. Electron Shells
1.1 What is an electron shell?
An electron shell is a principal energy level containing electrons around the nucleus.
Shells are identified by the principal quantum number, n:
- First shell → n = 1
- Second shell → n = 2
- Third shell → n = 3
- Fourth shell → n = 4
The maximum number of electrons in a shell is:
2n²
Therefore:
- n = 1 → maximum 2 electrons
- n = 2 → maximum 8 electrons
- n = 3 → maximum 18 electrons
- n = 4 → maximum 32 electrons
AP Chemistry distinction
The number tells you the shell.
Examples:
- 1s → first shell
- 2s → second shell
- 2p → second shell
- 3p → third shell
- 3d → third shell
2. Subshells
2.1 What is a subshell?
A subshell is a subdivision within an electron shell.
There are four types:
- s
- p
- d
- f
Each type contains a specific number of orbitals and can hold a specific maximum number of electrons.
| Subshell | Number of orbitals | Maximum electrons |
|---|---|---|
| s | 1 | 2 |
| p | 3 | 6 |
| d | 5 | 10 |
| f | 7 | 14 |
Every orbital can contain a maximum of 2 electrons.
Therefore:
- s → 1 orbital × 2 = 2 electrons
- p → 3 orbitals × 2 = 6 electrons
- d → 5 orbitals × 2 = 10 electrons
- f → 7 orbitals × 2 = 14 electrons
2.2 Shell vs. subshell vs. orbital
These terms are not interchangeable.
The hierarchy is:
Shell → subshell → orbital → electron
For example, 2p means:
- 2 → second shell
- p → p subshell
- p subshell → 3 orbitals
- each orbital → maximum 2 electrons
- 2p subshell → maximum 6 electrons
2.3 Subshells within each shell
| Shell | Subshells | Maximum electrons |
|---|---|---|
| n = 1 | 1s | 2 |
| n = 2 | 2s, 2p | 8 |
| n = 3 | 3s, 3p, 3d | 18 |
| n = 4 | 4s, 4p, 4d, 4f | 32 |
A shell with principal quantum number n contains n subshells.
3. Electron Configuration
Electron configuration describes how electrons are distributed among orbitals.
For example, oxygen has 8 electrons:
1s² 2s² 2p⁴
The superscript tells you the number of electrons in that subshell.
3.1 Orbital filling order
Electrons generally fill lower-energy orbitals before higher-energy orbitals.
Important order for AP Chemistry:
1s → 2s → 2p → 3s → 3p → 4s → 3d → 4p
Know this order well.
3.2 Three rules for electron configurations
Aufbau principle
Electrons occupy lower-energy orbitals before higher-energy orbitals.
Pauli exclusion principle
An orbital can contain a maximum of 2 electrons, and those electrons must have opposite spins.
Hund’s rule
When electrons occupy orbitals of equal energy, they occupy the orbitals individually before pairing.
For example, 2p⁴ is arranged conceptually as:
↑↓ ↑ ↑
not:
↑↓ ↑↓ —
Hund’s rule minimizes electron-electron repulsion.
4. Photoelectron Spectroscopy (PES)
4.1 What is PES?
Photoelectron spectroscopy is an experimental technique used to determine the energies of electrons in atoms.
PES provides information about:
- electron binding energies
- electron configurations
- relative energies of subshells
- number of electrons in each occupied subshell
- differences between core and valence electrons
4.2 How PES works
The basic process is:
- A photon with known energy strikes an atom.
- The photon transfers energy to an electron.
- The electron is ejected from the atom.
- The kinetic energy of the ejected electron is measured.
- The electron’s binding energy can then be determined.
The energy relationship is:
Photon energy = Binding energy + Kinetic energy
Therefore:
Binding energy = Photon energy − Kinetic energy
This relationship is fundamental for PES calculations.
5. Binding Energy
5.1 Definition
Binding energy is the energy required to remove an electron from an atom.
High binding energy means:
- the electron is strongly attracted to the nucleus
- more energy is required to remove it
- the electron is generally closer to the nucleus
Low binding energy means:
- the electron is less strongly attracted
- less energy is required to remove it
- the electron is generally farther from the nucleus
Therefore:
Higher binding energy → harder to remove
Lower binding energy → easier to remove
5.2 Why does binding energy change?
Two major factors are important:
Distance from the nucleus
Electrons closer to the nucleus experience stronger electrostatic attraction.
Therefore:
Closer electron → stronger attraction → higher binding energy
Farther electron → weaker attraction → lower binding energy
Shielding
Inner electrons repel outer electrons and partially shield them from the nucleus.
As a result, outer electrons do not experience the full attractive force of the nucleus.
This is related to effective nuclear charge, Zₑff.
Greater effective nuclear charge generally means:
greater attraction → greater binding energy
5.3 Binding-energy order
For a typical atom, inner subshells have higher binding energies than outer subshells.
For example:
1s > 2s > 2p > 3s > 3p
Here, “>” means greater binding energy.
The 1s electrons are closest to the nucleus, so they are the most strongly bound.
6. PES Graphs
6.1 What does a PES graph show?
A PES graph usually provides two key pieces of information:
- Peak position → binding energy
- Peak size/area → relative number of electrons
This distinction is extremely important.
Remember:
Peak position = energy
Peak size = electrons
Always check the actual axis labels because graphs can be presented with different orientations.
6.2 What does each peak represent?
Each major PES peak generally represents an occupied subshell.
For example:
1s² 2s² 2p⁶
has three occupied subshells:
- 1s
- 2s
- 2p
Therefore, its PES spectrum should have three major peaks.
The relative electron populations are:
1s → 2 electrons
2s → 2 electrons
2p → 6 electrons
So the 2p peak should represent three times as many electrons as either the 1s or 2s peak.
7. Identifying Peaks on a PES Graph
Suppose an atom has the configuration:
1s² 2s² 2p⁶
The binding-energy order is:
1s > 2s > 2p
Therefore:
- highest binding energy peak → 1s
- next highest → 2s
- lowest → 2p
Why?
1s electrons are closest to the nucleus and therefore require the most energy to remove.
2p electrons are farther from the nucleus and are therefore less strongly bound.
7.1 Peak size
Peak size tells you how many electrons occupy the subshell.
For example:
Peak representing 2 electrons → likely an s subshell
Peak representing 6 electrons → likely a p subshell
Peak representing 10 electrons → likely a d subshell
However, always use the full spectrum and electron configuration rather than identifying a peak from size alone.
8. Using PES to Determine Electron Configuration
This is one of the most important AP Chemistry skills.
Suppose a PES spectrum shows four occupied subshells with electron populations:
2, 2, 6, 1
The electron configuration is:
1s² 2s² 2p⁶ 3s¹
Total electrons:
2 + 2 + 6 + 1 = 11
A neutral atom with 11 electrons is sodium, Na.
8.1 General method
When given a PES graph:
- Count the major peaks.
- Determine the relative binding energies.
- Match the peaks to subshells.
- Use peak size/area to determine the number of electrons in each subshell.
- Write the electron configuration.
- Add the electrons.
- Identify the element or ion if required.
9. PES and Valence Electrons
PES can help identify valence electrons.
For main-group elements, valence electrons are generally the electrons in the outermost occupied shell.
Example:
1s² 2s² 2p⁶ 3s² 3p³
The outermost shell is n = 3.
Therefore:
3s² 3p³
contains the valence electrons.
Number of valence electrons:
2 + 3 = 5
The remaining electrons are core electrons.
Core electrons are closer to the nucleus and generally have higher binding energies.
10. Comparing Atoms and Ions Using PES
PES can also be used to compare species with similar electron configurations.
Consider:
Na⁺ → 1s² 2s² 2p⁶
Ne → 1s² 2s² 2p⁶
Both have 10 electrons, so they are isoelectronic.
However:
- Na⁺ has 11 protons.
- Ne has 10 protons.
The electrons in Na⁺ experience greater attraction to the nucleus.
Therefore, Na⁺ generally has higher electron binding energies than Ne.
General rule
For species with the same number of electrons:
More protons → greater nuclear attraction → higher binding energy
11. PES Calculations
11.1 Using photon energy
The fundamental equation is:
Photon energy = Binding energy + Kinetic energy
Therefore:
Binding energy = Photon energy − Kinetic energy
If photon energy and kinetic energy are given, subtract kinetic energy from photon energy.
11.2 Photon energy from wavelength
If wavelength is provided:
Photon energy = hc / λ
where:
- h = Planck’s constant
- c = speed of light
- λ = wavelength
Then use:
Binding energy = Photon energy − Kinetic energy
Unit warning
Keep units consistent.
If photon energy and kinetic energy are both in eV, binding energy will be in eV.
If they are in joules, keep all energies in joules.
12. Common AP Chemistry PES Mistakes
Mistake 1: Bigger peak means higher binding energy
Incorrect.
Peak size indicates the relative number of electrons.
Peak position indicates binding energy.
Mistake 2: Outer electrons have higher binding energy
Incorrect.
Outer electrons are generally easier to remove.
Outer electrons → lower binding energy
Inner electrons → higher binding energy
Mistake 3: One peak represents one electron
Incorrect.
One peak generally represents an occupied subshell.
For example:
2p⁶
is one subshell containing 6 electrons, so it corresponds to one major PES peak.
Mistake 4: 2p has one orbital
Incorrect.
A p subshell contains 3 orbitals.
Therefore:
3 orbitals × 2 electrons per orbital = 6 electrons
Mistake 5: Shell and subshell are the same
Incorrect.
In 3p:
3 = shell
p = subshell
The p subshell contains 3 orbitals.
13. High-Yield AP Chemistry Summary
Electron structure
Shell → subshell → orbital → electron
Shell
Identified by n.
Maximum electrons:
2n²
Subshell capacities
s → 2 electrons
p → 6 electrons
d → 10 electrons
f → 14 electrons
Orbitals
Each orbital holds a maximum of 2 electrons.
Important filling order
1s → 2s → 2p → 3s → 3p → 4s → 3d → 4p
14. PES: What You Must Know
PES purpose
PES measures electron binding energies and provides evidence for electron configurations.
Fundamental relationship
Photon energy = Binding energy + Kinetic energy
Therefore:
Binding energy = Photon energy − Kinetic energy
Reading a PES graph
Peak position → binding energy
Peak size/area → relative number of electrons
Binding-energy trend
Closer to nucleus → higher binding energy
Farther from nucleus → lower binding energy
Greater nuclear attraction → higher binding energy
Greater shielding → lower binding energy
Determining an electron configuration
PES peaks → occupied subshells
Peak sizes → number of electrons
Peak positions → relative binding energies
Together, these allow you to determine the electron configuration.
15. Essential Exam Checklist
Before an AP Chemistry exam, make sure you can:
- Distinguish shells, subshells, and orbitals.
- State the maximum electrons in s, p, d, and f subshells.
- State the maximum electrons in a shell using 2n².
- Write electron configurations.
- Apply Aufbau, Pauli, and Hund’s rules.
- Explain what PES measures.
- Define binding energy.
- Explain why inner electrons have greater binding energy.
- Explain the role of shielding and effective nuclear charge.
- Read binding energy from a PES graph.
- Determine electron populations from PES peak sizes.
- Identify which subshell corresponds to each PES peak.
- Construct an electron configuration from a PES spectrum.
- Determine the element or ion from the total number of electrons.
- Identify valence and core electrons.
- Compare binding energies of isoelectronic species.
- Use Photon energy = Binding energy + Kinetic energy.
- Calculate photon energy using E = hc/λ when required.