Atomic Structure and Electron Configuration

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:

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

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 → ...

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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.

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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 ✓

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.

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

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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)

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?

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?