Atomic Structure and Electron Configuration

Learn about subatomic particles, energy levels, orbitals, and how to write electron configurations for atoms and ions.

Atomic Structure and Electron Configuration

Structure of the Atom

The atom consists of three fundamental particles:

| Particle | Symbol | Charge | Mass (amu) | Location | |----------|--------|--------|------------|----------| | Proton | p⁺ | +1 | 1.007 | Nucleus | | Neutron | n⁰ | 0 | 1.009 | Nucleus | | Electron | e⁻ | -1 | 0.00055 | Electron cloud |

Key Definitions

Atomic number ( $Z$ ): Number of protons (defines the element)
Mass number ( $A$ ): Total protons + neutrons
Isotopes: Atoms of same element with different numbers of neutrons

Notation: $^A_ZX$ where $X$ is element symbol

Example: $^{12}_6C$ (Carbon-12) has 6 protons, 6 neutrons, 6 electrons

Quantum Numbers

Four quantum numbers describe each electron in an atom:

1. Principal Quantum Number ( $n$ )

Values: $n = 1, 2, 3, 4, ...$
Meaning: Energy level (shell)
Capacity: Maximum $2n^2$ electrons per level

2. Angular Momentum Quantum Number ( $\ell$ )

Values: $\ell = 0$ to $n-1$
Meaning: Sublevel (subshell) shape
- $\ell = 0$ : s orbital (spherical)
- $\ell = 1$ : p orbital (dumbbell)
- $\ell = 2$ : d orbital (cloverleaf)
- $\ell = 3$ : f orbital (complex)

3. Magnetic Quantum Number ( $m_\ell$ )

Values: $-\ell$ to $+\ell$ (including 0)
Meaning: Orbital orientation in space
Number of orbitals: $2\ell + 1$

4. Spin Quantum Number ( $m_s$ )

Values: $+\frac{1}{2}$ or $-\frac{1}{2}$
Meaning: Electron spin direction
Pauli Exclusion Principle: No two electrons can have the same four quantum numbers

Orbital Capacity

| Sublevel | Number of Orbitals | Max Electrons | |----------|-------------------|---------------| | s ( $\ell=0$ ) | 1 | 2 | | p ( $\ell=1$ ) | 3 | 6 | | d ( $\ell=2$ ) | 5 | 10 | | f ( $\ell=3$ ) | 7 | 14 |

Electron Configuration

Electron configuration shows how electrons are distributed among orbitals.

Order of Filling (Aufbau Principle)

Electrons fill orbitals in order of increasing energy:

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

Memory aid: Use the diagonal rule or periodic table

Notation

Full configuration: List all sublevels with number of electrons

Example: Oxygen (8 electrons) $1s^2 2s^2 2p^4$

Noble gas configuration: Use previous noble gas in brackets

Example: Calcium (20 electrons) $[Ar] 4s^2$

Orbital diagram: Show each orbital as a box with electron spins

Three Key Rules

1. Aufbau Principle

Electrons fill lowest energy orbitals first.

2. Pauli Exclusion Principle

Maximum 2 electrons per orbital, with opposite spins.

3. Hund's Rule

When filling orbitals of equal energy (like three p orbitals), place one electron in each orbital before pairing.

Example: Nitrogen (7 electrons)

2p orbitals: ↑ ↑ ↑ (one electron in each)

NOT: ↑↓ ↑ (incorrect - violates Hund's rule)

Electron Configurations of Ions

Cations (positive ions)

Remove electrons from highest $n$ value first (usually outermost s)

Example: Fe → Fe²⁺

Fe: $[Ar] 4s^2 3d^6$
Fe²⁺: $[Ar] 3d^6$ (remove 4s² electrons)

Anions (negative ions)

Add electrons following normal filling order

Example: O → O²⁻

O: $1s^2 2s^2 2p^4$
O²⁻: $1s^2 2s^2 2p^6$ (add 2 electrons to 2p)

Exceptions to Filling Order

Some elements have anomalous electron configurations for extra stability:

Chromium (Cr):

Expected: $[Ar] 4s^2 3d^4$
Actual: $[Ar] 4s^1 3d^5$ (half-filled d sublevel is more stable)

Copper (Cu):

Expected: $[Ar] 4s^2 3d^9$
Actual: $[Ar] 4s^1 3d^{10}$ (filled d sublevel is more stable)

Why: Half-filled and fully-filled sublevels have extra stability.

Valence Electrons

Valence electrons are electrons in the outermost shell (highest $n$ ).

They determine:

Chemical properties
Bonding behavior
Reactivity

Example: Nitrogen $[He] 2s^2 2p^3$

Valence electrons: 5 (in $n=2$ shell)

Core vs. Valence Notation

Core electrons: Inner electrons (represented by noble gas) Valence electrons: Outer electrons (written out)

Example: Phosphorus (P)

Full: $1s^2 2s^2 2p^6 3s^2 3p^3$
Noble gas: $[Ne] 3s^2 3p^3$
Core: [Ne] (10 electrons)
Valence: $3s^2 3p^3$ (5 electrons)

📚 Practice Problems

1Problem 1medium

❓ Question:

(a) Write the complete electron configuration for iron (Fe, atomic number 26). (b) Write the noble gas notation for Fe. (c) How many unpaired electrons does Fe have in its ground state? (d) Which orbital subshell is being filled in the transition metals?

💡 Show Solution

Solution:

(a) Complete configuration:

Fe (Z=26): 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁶

(b) Noble gas notation:

Previous noble gas is Ar (Z=18)
Fe: [Ar] 4s² 3d⁶

4s²: 2 paired electrons
3d⁶: ↑↓ ↑ ↑ ↑ ↑ (following Hund's rule)
4 unpaired electrons in the 3d subshell

(d) Subshell being filled:

Transition metals fill the d subshell (specifically the (n-1)d subshell)

2Problem 2easy

❓ Question:

Write the full electron configuration for sulfur (S, atomic number 16).

💡 Show Solution

Solution:

Given: Sulfur (S), $Z = 16$ Find: Full electron configuration

Step 1: Determine number of electrons

Neutral sulfur has 16 electrons (same as protons).

Step 2: Fill orbitals in order

Order: 1s, 2s, 2p, 3s, 3p

1s: 2 electrons → $1s^2$ (total: 2)
2s: 2 electrons → $2s^2$ (total: 4)
2p: 6 electrons → $2p^6$ (total: 10)
3s: 2 electrons → $3s^2$ (total: 12)
3p: 4 electrons → $3p^4$ (total: 16) ✓

Answer: $1s^2 2s^2 2p^6 3s^2 3p^4$

Noble gas notation: $[Ne] 3s^2 3p^4$

Verification:

Total electrons: $2 + 2 + 6 + 2 + 4 = 16$ ✓
Valence electrons: 6 (matches Group 16) ✓

3Problem 3medium

❓ Question:

💡 Show Solution

Solution:

(a) Complete configuration:

Fe (Z=26): 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁶

(b) Noble gas notation:

Previous noble gas is Ar (Z=18)
Fe: [Ar] 4s² 3d⁶

4s²: 2 paired electrons
3d⁶: ↑↓ ↑ ↑ ↑ ↑ (following Hund's rule)
4 unpaired electrons in the 3d subshell

(d) Subshell being filled:

Transition metals fill the d subshell (specifically the (n-1)d subshell)

4Problem 4hard

❓ Question:

(a) Write the electron configuration for Cu²⁺ (copper ion). (b) Explain why copper's electron configuration is [Ar] 4s¹ 3d¹⁰ rather than the expected [Ar] 4s² 3d⁹. (c) Which electrons are removed first when forming the Cu²⁺ ion?

💡 Show Solution

Solution:

(a) Cu²⁺ configuration:

Cu is [Ar] 4s¹ 3d¹⁰
Remove 2 electrons from highest energy levels
Cu²⁺: [Ar] 3d⁹

(b) Copper's anomalous configuration:

Expected: [Ar] 4s² 3d⁹
Actual: [Ar] 4s¹ 3d¹⁰
Explanation: A completely filled d¹⁰ subshell is more stable than d⁹ due to exchange energy. The extra stability from having a filled d subshell outweighs the energy cost of promoting an electron from 4s to 3d.

When forming ions, electrons are removed from the highest n value first (4s before 3d)
Even though Cu fills 3d last, the 4s¹ electron is removed first, then one 3d electron
This is why Cu²⁺ is [Ar] 3d⁹, not [Ar] 4s¹ 3d⁸

5Problem 5hard

❓ Question:

💡 Show Solution

Solution:

(a) Cu²⁺ configuration:

Cu is [Ar] 4s¹ 3d¹⁰
Remove 2 electrons from highest energy levels
Cu²⁺: [Ar] 3d⁹

(b) Copper's anomalous configuration:

Expected: [Ar] 4s² 3d⁹
Actual: [Ar] 4s¹ 3d¹⁰
Explanation: A completely filled d¹⁰ subshell is more stable than d⁹ due to exchange energy. The extra stability from having a filled d subshell outweighs the energy cost of promoting an electron from 4s to 3d.

When forming ions, electrons are removed from the highest n value first (4s before 3d)
Even though Cu fills 3d last, the 4s¹ electron is removed first, then one 3d electron
This is why Cu²⁺ is [Ar] 3d⁹, not [Ar] 4s¹ 3d⁸

6Problem 6medium

❓ Question:

Draw the orbital diagram for carbon (C) and identify any unpaired electrons.

💡 Show Solution

Solution:

Given: Carbon (C), $Z = 6$ Find: Orbital diagram and unpaired electrons

Step 1: Write electron configuration

Carbon: $1s^2 2s^2 2p^2$

Step 2: Draw orbital diagram

1s: ↑↓

2s: ↑↓

2p: ↑ ↑ _ (three orbitals: px, py, pz)

Step 3: Apply Hund's Rule

For the 2 electrons in 2p:

Place one electron in first orbital (↑)
Place one electron in second orbital (↑)
Leave third orbital empty

Complete diagram:

      ↑↓        ↑↓      ↑  ↑  _
      1s        2s      2p

Answer:

Orbital diagram shown above
Unpaired electrons: 2 (both in 2p sublevel)

Explanation:

Hund's rule requires maximizing unpaired electrons in degenerate orbitals
Carbon's 2 unpaired electrons make it chemically reactive
These unpaired electrons form bonds in compounds like CO₂, CH₄

Verification:

Total electrons: 2 + 2 + 2 = 6 ✓
Hund's rule followed ✓

7Problem 7hard

❓ Question:

Write the electron configuration for Fe²⁺ and explain how it differs from neutral Fe.

💡 Show Solution

Solution:

Given: Fe (iron, $Z = 26$ ) and Fe²⁺ Find: Electron configurations and explanation

Step 1: Write configuration for neutral Fe

Iron has 26 electrons.

Following the filling order through 4s and 3d:

$\text{Fe: } [Ar] 4s^2 3d^6$

Expanded: $[Ar] = 1s^2 2s^2 2p^6 3s^2 3p^6$

Step 2: Form Fe²⁺ (remove 2 electrons)

Key concept: When forming cations, remove electrons from the highest $n$ value first.

For Fe: Remove from 4s before 3d

$\text{Fe}^{2+}: [Ar] 3d^6$

NOT $[Ar] 4s^2 3d^4$ (incorrect!)

Step 3: Explain the difference

Neutral Fe: $[Ar] 4s^2 3d^6$ (26 electrons)

4s sublevel: 2 electrons
3d sublevel: 6 electrons

Fe²⁺: $[Ar] 3d^6$ (24 electrons)

4s sublevel: 0 electrons (both removed)
3d sublevel: 6 electrons (unchanged)

Why remove 4s first?

Even though 4s fills before 3d, once the 3d sublevel begins filling, it becomes lower in energy than 4s. When ionizing, electrons are removed from the highest energy orbital, which is 4s.

Answer:

Fe: $[Ar] 4s^2 3d^6$
Fe²⁺: $[Ar] 3d^6$
Difference: Lost both 4s electrons

Verification:

Fe has 26 electrons ✓
Fe²⁺ has 24 electrons (26 - 2) ✓
4s electrons removed before 3d ✓

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Atomic Structure and Electron Configuration

Atomic Structure and Electron Configuration

Structure of the Atom

Key Definitions

Quantum Numbers

1. Principal Quantum Number (nnn)

2. Angular Momentum Quantum Number (ℓ\ellℓ)

3. Magnetic Quantum Number (mℓm_\ellmℓ​)

4. Spin Quantum Number (msm_sms​)

Orbital Capacity

Electron Configuration

Order of Filling (Aufbau Principle)

Notation

Three Key Rules

1. Aufbau Principle

2. Pauli Exclusion Principle

3. Hund's Rule

Electron Configurations of Ions

Cations (positive ions)

Anions (negative ions)

Exceptions to Filling Order

Valence Electrons

Core vs. Valence Notation

📚 Practice Problems

1Problem 1medium

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2Problem 2easy

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3Problem 3medium

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4Problem 4hard

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5Problem 5hard

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6Problem 6medium

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7Problem 7hard

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1. Principal Quantum Number ( $n$ )

2. Angular Momentum Quantum Number ( $\ell$ )

3. Magnetic Quantum Number ( $m_\ell$ )

4. Spin Quantum Number ( $m_s$ )