Part 1: Atomic Structure Review

Before we dive into electron configurations, let's make sure the fundamentals of atomic structure are solid. Every atom is built from three subatomic particles, and understanding how they're counted is essential for everything that follows.

The Three Subatomic Particles

Particle	Symbol	Charge	Location	Relative Mass
Proton	p⁺	+1	Nucleus	1 amu
Neutron	n⁰	0	Nucleus	1 amu
Electron	e⁻	−1	Electron cloud	≈ 0 amu (1/1836 amu)

Key relationships:

• The atomic number (Z) = number of protons = number of electrons (in a neutral atom)
• The mass number (A) = protons + neutrons
• Number of neutrons = A − Z

The identity of an element is determined entirely by its number of protons. Change the proton count and you change the element.

Isotope Notation

Atoms of the same element can have different numbers of neutrons. These variants are called isotopes.

We write isotope notation as:

$^{A}_{Z}X$

where A is the mass number (top), Z is the atomic number (bottom), and X is the element symbol.

Example: (^{14}_{6}\text{C}) — Carbon-14

• Protons = 6
• Electrons = 6 (neutral atom)
• Neutrons = 14 − 6 = 8

Isotopes of an element have identical chemical behavior because they have the same number of electrons. Their physical properties (mass, nuclear stability) differ.

Quick Check: Identifying Particles

How many protons are in an atom of phosphorus (P, atomic number 15)?

Calculating Neutrons

Chlorine-37 ((^{37}_{17}\text{Cl})) has a mass number of 37 and an atomic number of 17. How many neutrons does it have?

Remember: neutrons = mass number − atomic number

Ions: Gaining and Losing Electrons

When an atom gains or loses electrons, it becomes an ion:

• Cation (positive ion): atom loses electrons → fewer electrons than protons
  • Na → Na⁺ (11 protons, 10 electrons)
• Anion (negative ion): atom gains electrons → more electrons than protons
  • Cl → Cl⁻ (17 protons, 18 electrons)

Important: Gaining or losing electrons does NOT change the atomic number or the identity of the element. Only changing protons does that.

Ion Particle Counts

How many electrons does the ion Ca²⁺ have? (Calcium has atomic number 20.)

Comprehensive Review

An atom of (^{56}_{26}\text{Fe}) — let's verify you can identify all its particles.

Part 2: Energy Levels and Subshells

Electrons don't just float randomly around the nucleus — they occupy specific energy levels and subshells. Understanding this organization is the foundation of electron configuration.

Principal Energy Levels

The principal quantum number (n) describes the main energy level of an electron:

n	Name	Max Electrons (2n²)
1	First shell	2
2	Second shell	8
3	Third shell	18
4	Fourth shell	32

The formula for the maximum number of electrons in a principal energy level is:

$\text{Max electrons} = 2n^2$

As n increases, the energy level is farther from the nucleus on average and the electrons have higher energy.

Subshells: s, p, d, f

Each principal energy level is divided into subshells, labeled s, p, d, and f.

Subshell	Number of Orbitals	Max Electrons
s	1	2
p	3	6
d	5	10
f	7	14

Each orbital holds a maximum of 2 electrons (with opposite spins — the Pauli exclusion principle).

Which subshells exist in each level?

• n = 1: 1s only
• n = 2: 2s, 2p
• n = 3: 3s, 3p, 3d
• n = 4: 4s, 4p, 4d, 4f

In general, level n contains subshells s through the (n − 1)th letter in the sequence s, p, d, f.

Subshell Capacity Check

How many electrons can the 3d subshell hold at maximum?

The Aufbau Filling Order

Electrons fill subshells in order of increasing energy, not simply by principal quantum number. The filling order is:

1s → 2s → 2p → 3s → 3p → 4s → 3d → 4p → 5s → 4d → 5p → 6s → 4f → 5d → 6p → 7s → 5f → 6d → 7p

Notice that 4s fills before 3d — this is because 4s is lower in energy than 3d for most elements.

The diagonal rule is a visual trick to remember this order:

Write the subshells in a grid and draw diagonal arrows from upper-right to lower-left:

1s
2s 2p
3s 3p 3d
4s 4p 4d 4f
5s 5p 5d 5f
6s 6p 6d
7s 7p

Following the diagonals gives the correct filling order.

Filling Order Practice

Determine which subshell fills next in the Aufbau order.

Maximum Electron Calculations

Use the formula (2n^2) to determine the maximum number of electrons in a principal energy level.

Key Takeaways

1. Principal quantum number (n) determines the main energy level; max electrons = (2n^2).
2. Subshells (s, p, d, f) hold 2, 6, 10, and 14 electrons respectively.
3. The Aufbau filling order follows the diagonal rule — energy order differs from simple numerical order (e.g., 4s fills before 3d).
4. Each orbital holds at most 2 electrons with opposite spins.

In Part 3, we will use these rules to write complete electron configurations for real elements.

Part 3: Writing Electron Configurations

Now that you know the subshells and filling order, it is time to write full electron configurations. Three fundamental rules govern how electrons fill orbitals.

The Three Rules

1. Aufbau Principle

Electrons fill the lowest energy subshell available first.

Filling order: 1s → 2s → 2p → 3s → 3p → 4s → 3d → 4p → ...

2. Pauli Exclusion Principle

Each orbital can hold a maximum of 2 electrons, and those 2 electrons must have opposite spins (↑↓).

No two electrons in the same atom can have the same set of four quantum numbers.

3. Hund's Rule

When filling orbitals of equal energy (degenerate orbitals, such as the three 2p orbitals), electrons fill each orbital singly first with parallel spins before any orbital gets a second electron.

Think of it like a bus: passengers sit in empty seats before doubling up.

Step-by-Step Examples

Hydrogen (H, Z = 1): 1 electron
Configuration: 1s¹

Carbon (C, Z = 6): 6 electrons
1s² 2s² 2p² → 1s² 2s² 2p²
(By Hund's rule, the two 2p electrons occupy two separate p orbitals with parallel spins.)

Sodium (Na, Z = 11): 11 electrons
1s² 2s² 2p⁶ 3s¹

Iron (Fe, Z = 26): 26 electrons
1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁶
Notice: 4s fills before 3d in the Aufbau order, so 4s² appears before 3d⁶.

Tip: Always verify your total by adding the superscripts:
2 + 2 + 6 + 2 + 6 + 2 + 6 = 26 ✓

Identify the Element

Which element has the electron configuration 1s² 2s² 2p⁶ 3s² 3p⁴?

Write the Configuration

Write the full electron configuration for the following elements. Use the format: 1s2 2s2 2p6 (no superscripts needed, just the number after each subshell letter).

More Configuration Practice

Write the full electron configuration. Remember: 4s fills before 3d!

Spot the Error

Which of the following electron configurations is INCORRECT?

Key Takeaways

1. Aufbau principle: Fill lowest energy subshells first.
2. Pauli exclusion: Max 2 electrons per orbital (opposite spins).
3. Hund's rule: Fill degenerate orbitals singly before pairing.
4. Always verify by summing superscripts to match the atomic number.
5. Remember that 4s fills before 3d — this is the most common filling-order mistake.

Next up: Noble gas shorthand notation to simplify these long configurations!

Part 4: Noble Gas (Shorthand) Notation

Writing out 1s² 2s² 2p⁶ 3s² 3p⁶ every time gets tedious. Chemists use noble gas shorthand notation to simplify electron configurations by replacing the inner-shell electrons with the symbol of the preceding noble gas in brackets.

The Noble Gases

Noble Gas	Symbol	Atomic Number	Full Configuration
Helium	He	2	1s²
Neon	Ne	10	1s² 2s² 2p⁶
Argon	Ar	18	1s² 2s² 2p⁶ 3s² 3p⁶
Krypton	Kr	36	1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶
Xenon	Xe	54	[Kr] 4d¹⁰ 5s² 5p⁶
Radon	Rn	86	[Xe] 4f¹⁴ 5d¹⁰ 6s² 6p⁶

To use shorthand notation:

1. Find the noble gas that comes just before your element in the periodic table.
2. Write that noble gas symbol in brackets.
3. Continue the configuration from where the noble gas left off.

Examples

Sodium (Na, Z = 11)
Full: 1s² 2s² 2p⁶ 3s¹
The preceding noble gas is Neon (Z = 10): 1s² 2s² 2p⁶
Shorthand: [Ne] 3s¹

Iron (Fe, Z = 26)
Full: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁶
The preceding noble gas is Argon (Z = 18): 1s² 2s² 2p⁶ 3s² 3p⁶
Shorthand: [Ar] 4s² 3d⁶

Bromine (Br, Z = 35)
Full: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁵
The preceding noble gas is Argon (Z = 18)
Shorthand: [Ar] 4s² 3d¹⁰ 4p⁵

The shorthand is especially useful for heavier elements where the full configuration would be extremely long.

Identify the Noble Gas Core

Which noble gas core would you use for the shorthand notation of Selenium (Se, Z = 34)?

Shorthand Notation

What is the correct noble gas shorthand notation for phosphorus (P, Z = 15)?

Convert to Shorthand

Convert the following full electron configurations to noble gas shorthand. Use the format: [Xx] 3s2 3p5 (brackets around the noble gas symbol, no superscripts).

Noble Gas Shorthand Identification

Match each element with its correct shorthand electron configuration.

Key Takeaways

1. Noble gas shorthand replaces the inner electron core with the preceding noble gas symbol in brackets.
2. Always choose the noble gas that comes immediately before your element in the periodic table.
3. After the bracket, continue writing the remaining subshells in Aufbau filling order.
4. This notation makes it easy to focus on the valence electrons — the outer electrons that participate in bonding and determine chemical properties.

Next: We will tackle the important exceptions to the Aufbau order and learn how to write configurations for ions.

Part 5: Exceptions and Ion Configurations

The Aufbau principle works for most elements, but a handful of important exceptions exist. Additionally, when atoms form ions, the order of electron removal is NOT the same as the filling order. Both concepts are heavily tested on the AP exam.

The Two Critical Exceptions

Chromium (Cr, Z = 24)

Expected: [Ar] 4s² 3d⁴
Actual: [Ar] 3d⁵ 4s¹

Copper (Cu, Z = 29)

Expected: [Ar] 4s² 3d⁹
Actual: [Ar] 3d¹⁰ 4s¹

Why? Half-filled (d⁵) and fully filled (d¹⁰) subshells have extra stability due to:

• Exchange energy: More favorable electron-electron interactions when orbitals are symmetrically occupied.
• Electrons in the 4s and 3d subshells are very close in energy, so the stabilization from a half-filled or fully filled d subshell outweighs the cost of promoting one electron from 4s.

Other elements in the same columns (Mo, Ag, etc.) show similar exceptions, but Cr and Cu are the ones you must know for the AP exam.

Exception Check

What is the correct electron configuration for chromium (Cr, Z = 24)?

Electron Configurations of Ions

Cations (Positive Ions)

When forming cations, electrons are removed from the subshell with the highest principal quantum number (n) first.

Critical rule for transition metals: Remove electrons from 4s before 3d, even though 4s filled first!

Example: Fe²⁺ (Z = 26, 24 electrons)

• Neutral Fe: [Ar] 4s² 3d⁶
• Remove 2 electrons from 4s (highest n = 4)
• Fe²⁺: [Ar] 3d⁶

Example: Fe³⁺ (Z = 26, 23 electrons)

• Start from Fe²⁺: [Ar] 3d⁶
• Remove 1 more electron from 3d
• Fe³⁺: [Ar] 3d⁵

Anions (Negative Ions)

When forming anions, electrons are added to the next available subshell.

Example: Cl⁻ (Z = 17, 18 electrons)

• Neutral Cl: [Ne] 3s² 3p⁵
• Add 1 electron to 3p
• Cl⁻: [Ne] 3s² 3p⁶ (same as Ar — isoelectronic!)

Ion Configuration Practice

What is the electron configuration of Cu²⁺?

Recall: Cu (Z = 29) has the configuration [Ar] 3d¹⁰ 4s¹ (exception).

Write Ion Configurations

Write the noble gas shorthand electron configuration for each ion. Use the format: [Xx] 3d6 (no superscripts, brackets around noble gas).

Remember: Remove electrons from the highest n first!

Tricky Ion Problems

These require careful attention to exception rules and ion formation rules.

Key Takeaways

1. Chromium and copper are the two critical exceptions: they "steal" an electron from 4s to achieve a half-filled (d⁵) or fully filled (d¹⁰) d subshell.
2. When forming cations, remove electrons from the subshell with the highest n first — for transition metals, this means 4s before 3d.
3. When forming anions, add electrons to the next available subshell.
4. Isoelectronic species have the same number of electrons and the same electron configuration.
5. These rules are among the most commonly tested topics on the AP Chemistry exam.

Part 6: Orbital Diagrams and Quantum Numbers

Electron configurations tell us which subshells are occupied. Orbital diagrams and quantum numbers give us a more detailed picture — showing the spin of each electron and the exact "address" of every electron in an atom.

Orbital Diagrams (Box-Arrow Notation)

An orbital diagram represents each orbital as a box (or line) and each electron as an arrow:

• ↑ represents spin-up ((m_s = +\frac{1}{2}))
• ↓ represents spin-down ((m_s = -\frac{1}{2}))

Example: Nitrogen (N, Z = 7)

1s	2s	2p
↑↓	↑↓	↑ ↑ ↑

Each of the three 2p orbitals gets one electron first (Hund's rule) before any pairing occurs. All three unpaired electrons have the same spin direction.

Example: Oxygen (O, Z = 8)

1s	2s	2p
↑↓	↑↓	↑↓ ↑ ↑

Oxygen has 8 electrons. After filling the three 2p orbitals singly (like nitrogen), the 8th electron pairs up in the first 2p orbital.

Hund's Rule Application

How many unpaired electrons does nitrogen (N, Z = 7) have?

The Four Quantum Numbers

Every electron in an atom is described by a unique set of four quantum numbers — like a full mailing address.

1. Principal Quantum Number (n)

• Allowed values: 1, 2, 3, 4, ...
• Describes the main energy level (shell)
• Higher n = higher energy, larger orbital

2. Angular Momentum (Azimuthal) Quantum Number (l)

• Allowed values: 0 to (n − 1)
• Describes the subshell shape
• l = 0 → s, l = 1 → p, l = 2 → d, l = 3 → f

3. Magnetic Quantum Number ((m_l))

• Allowed values: −l to +l (including 0)
• Describes the orientation of the orbital in space
• For p orbitals (l = 1): (m_l) = −1, 0, +1 → three orientations

4. Spin Quantum Number ((m_s))

• Allowed values: (+\frac{1}{2}) or (-\frac{1}{2})
• Describes the spin direction of the electron
• Two electrons in the same orbital must have opposite spins (Pauli exclusion)

Allowed Values Summary

Subshell	n (example)	l	(m_l) values	# orbitals	Max e⁻
1s	1	0	0	1	2
2p	2	1	−1, 0, +1	3	6
3d	3	2	−2, −1, 0, +1, +2	5	10
4f	4	3	−3, −2, −1, 0, +1, +2, +3	7	14

Key relationship: The number of orbitals in a subshell = 2l + 1

Quantum Number Practice

Determine the quantum numbers for specified electrons.

Quantum Number Calculations

Use the relationships between quantum numbers to answer.

Key Takeaways

1. Orbital diagrams show each orbital as a box with arrows for electrons; Hund's rule requires filling singly before pairing.
2. Four quantum numbers (n, l, (m_l), (m_s)) uniquely identify every electron.
3. n determines the energy level; l determines the subshell shape; (m_l) determines the orbital orientation; (m_s) determines the spin.
4. Allowed values: l = 0 to n−1; (m_l) = −l to +l; (m_s) = ±½.
5. Number of orbitals in a subshell = 2l + 1; max electrons = 2(2l + 1).

Next: Part 7 brings it all together with AP-style synthesis problems!

Part 7: Synthesis & AP Review

This final part ties together everything from Parts 1–6 with AP-style questions. Expect multi-concept problems that combine electron configuration with periodic trends, ionization energy, and other core ideas. These are the types of questions that appear on the AP Chemistry exam.

Electron Configuration and Periodic Trends

Electron configurations explain why periodic trends exist:

Atomic Radius:

• Increases down a group (higher n → electrons farther from nucleus)
• Decreases across a period (more protons pull electrons closer)

Ionization Energy (IE):

• Decreases down a group (valence electrons farther from nucleus, easier to remove)
• Generally increases across a period (greater nuclear charge holds electrons tighter)
• Exceptions: IE drops from Group 2 → 13 (removing from higher-energy p vs. s) and from Group 15 → 16 (paired vs. unpaired p electron)

Electronegativity:

• Increases up and to the right (F is most electronegative)
• Noble gases are generally excluded

All of these trends trace back to electron configuration — the number of shells (n), effective nuclear charge ((Z_{eff})), and subshell occupancy.

AP-Style Question 1: Ionization Energy Exception

The first ionization energy of oxygen (Z = 8) is lower than that of nitrogen (Z = 7), even though oxygen has a higher atomic number. Which explanation best accounts for this?

AP-Style Question 2: Identifying an Element

An element has the electron configuration [Kr] 4d¹⁰ 5s² 5p⁴. Which statement about this element is correct?

AP-Style Question 3: Transition Metal Ion

The ion Ti²⁺ is used in some catalytic processes. What is the ground-state electron configuration of Ti²⁺?

Common AP Mistakes to Avoid

Mistake 1: Ion Configurations

❌ Removing electrons from the last-filled subshell (3d)
✅ Remove from the highest n first (4s before 3d for transition metals)

Mistake 2: Forgetting Exceptions

❌ Cr: [Ar] 4s² 3d⁴
✅ Cr: [Ar] 3d⁵ 4s¹ (half-filled d subshell)

❌ Cu: [Ar] 4s² 3d⁹
✅ Cu: [Ar] 3d¹⁰ 4s¹ (fully filled d subshell)

Mistake 3: Wrong Noble Gas Core

❌ Using [Kr] for elements with Z < 36
✅ Always use the noble gas that comes immediately before the element

Mistake 4: Violating Hund's Rule

❌ Pairing electrons in a 2p orbital before all three 2p orbitals have one electron
✅ Fill all degenerate orbitals singly (with parallel spins) before pairing

Challenge Problems

Write the electron configuration in noble gas shorthand. Format: [Xx] 3d5 4s1 (no superscripts, brackets around noble gas).

Synthesis Questions

These questions connect electron configuration to other chemistry concepts.

Final Summary: Electron Configuration Mastery

Congratulations on completing all 7 parts! Here is everything you need to know:

1. Atomic structure: Protons define the element; electrons determine chemical behavior.
2. Energy levels and subshells: n determines the shell; s, p, d, f subshells hold 2, 6, 10, 14 electrons.
3. Three rules: Aufbau (lowest energy first), Pauli (max 2 per orbital, opposite spins), Hund (fill singly before pairing).
4. Noble gas shorthand: Replace inner electrons with [noble gas] bracket.
5. Exceptions: Cr is [Ar] 3d⁵ 4s¹; Cu is [Ar] 3d¹⁰ 4s¹.
6. Ion configurations: Remove from highest n first (4s before 3d for transition metals).
7. Quantum numbers: n, l, (m_l), (m_s) uniquely identify every electron.
8. Periodic trends: Atomic radius, IE, and electronegativity all stem from electron configuration.

You are now prepared for any electron configuration question on the AP Chemistry exam. Good luck!