Atomic Structure & Periodic Table

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Atomic Structure & Periodic Table — Key Facts for Makerere University (Uganda) Core concept: Understanding atomic composition, electron configuration, and periodic trends is essential for all chemistry topics High-yield points: Electron configurations, periodic trends (atomic radius, ionization energy, electronegativity), quantum numbers, and the Aufbau principle ⚡ Exam tip: Drawing electron configurations and predicting periodic trends are very common short-answer questions

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Atomic Structure & Periodic Table — Makerere University (Uganda) Study Guide

1. Atomic Structure

Sub-atomic Particles

All atoms consist of three fundamental particles:

Particle	Symbol	Mass	Charge	Location
Proton	p⁺	1.67 × 10⁻²⁷ kg	+1	Nucleus
Neutron	n⁰	1.67 × 10⁻²⁷ kg	0	Nucleus
Electron	e⁻	9.11 × 10⁻³¹ kg	−1	Electron cloud

Atomic number (Z) = number of protons in the nucleus. This determines the element’s identity. Mass number (A) = protons + neutrons in the nucleus. Isotopes are atoms of the same element with the same atomic number but different mass numbers (different number of neutrons). Example: ₁₂H and ₁₃H (protium and deuterium).

Electronic Configuration

Electrons occupy shells (energy levels) around the nucleus: K (n=1), L (n=2), M (n=3), N (n=4), etc.

Maximum electrons per shell: 2n²

• K shell (n=1): maximum 2 electrons
• L shell (n=2): maximum 8 electrons
• M shell (n=3): maximum 18 electrons (but only 8 in outermost atoms)

The Aufbau Principle: Electrons fill orbitals in order of increasing energy. Order: 1s → 2s → 2p → 3s → 3p → 4s → 3d → 4p → 5s → 4d → 5p → 6s → 4f → 5d → 6p → 7s

Example — Electron Configuration:

• Oxygen (Z=8): 1s² 2s² 2p⁴
• Iron (Z=26): 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁶ or [Ar] 4s² 3d⁶
• Copper (Z=29): [Ar] 4s¹ 3d¹⁰ (anomalous configuration due to extra stability of filled d-subshell)

Quantum Numbers

Every electron is described by four quantum numbers:

1. Principal quantum number (n): Shell (1, 2, 3…) — indicates energy level and average distance from nucleus
2. Azimuthal quantum number (l): Sub-shell (s=0, p=1, d=2, f=3) — determines orbital shape
3. Magnetic quantum number (mₗ): Orbital orientation (−l to +l) — specifies which orbital within a subshell
4. Spin quantum number (mₛ): Electron spin (+½ or −½) — two electrons per orbital must have opposite spins

Pauli Exclusion Principle: No two electrons in an atom can have the same set of all four quantum numbers.

Orbital Shapes

• s orbital: Spherical shape; 1 per subshell (holds 2 electrons)
• p orbital: Dumbbell shape; 3 per subshell (holds 6 electrons)
• d orbital: Cloverleaf shape; 5 per subshell (holds 10 electrons)
• f orbital: Complex shape; 7 per subshell (holds 14 electrons)

2. The Periodic Table

Organization

The periodic table is arranged by:

• Groups (columns): Elements in the same group have similar chemical properties (same valence electron configuration)
• Periods (rows): Elements in the same period have the same number of electron shells
• Blocks: s-block, p-block, d-block (transition metals), f-block (lanthanides and actinides)

Periodic Trends

Atomic Radius

Atomic radius decreases across a period (left to right) because increasing nuclear charge pulls electrons closer. Atomic radius increases down a group because electrons are added to higher shells, increasing distance from nucleus.

Ionization Energy (IE)

Energy required to remove one electron from a neutral gaseous atom. IE increases across a period (higher nuclear charge holds electrons more tightly). IE decreases down a group (outer electrons are farther from nucleus and shielded by inner electrons). Trend exceptions: IE drops at Group 13 (removing p-electron is easier than losing a paired s-electron) and Group 16 (removing paired p-electron is harder due to repulsion).

First ionization energy of some elements (kJ/mol):

• Na: 496 | Mg: 738 | Al: 578 | Si: 786 | P: 1011 | S: 1000 | Cl: 1251 | Ar: 1520

Electronegativity (EN)

Tendency of an atom to attract bonding electrons. EN increases across a period and decreases down a group. Fluorine is the most electronegative element (EN = 4.0 on Pauling scale). Noble gases have no EN value (they don’t form bonds in normal conditions).

Electron Affinity (EA)

Energy released when an electron is added to a neutral gaseous atom. Most atoms release energy when gaining an electron (negative EA). Chlorine has the highest EA among common elements.

Shielding (Screening) Effect

Inner-shell electrons partially shield outer-shell electrons from the nuclear positive charge. More inner shells = more shielding = less attraction for valence electrons.

Key Periodic Groups to Know

• Group 1 (Alkali metals): Li, Na, K, Rb, Cs, Fr — highly reactive, lose 1 electron to form +1 ions, low IE, low EN
• Group 2 (Alkaline earth metals): Be, Mg, Ca, Sr, Ba — lose 2 electrons to form +2 ions
• Group 17 (Halogens): F, Cl, Br, I, At — highly reactive, gain 1 electron to form −1 ions, high EN, high EA
• Group 18 (Noble gases): He, Ne, Ar, Kr, Xe — full valence shells, very unreactive

3. Bonding and the Periodic Table

Ionic Bonding

Occurs between metals (low IE, low EN) and non-metals (high EN). Metal atoms lose electrons → cations; non-metal atoms gain electrons → anions. Electrostatic attraction holds ions together.

Example: Na (1s² 2s² 2p⁶ 3s¹) loses 1 e⁻ → Na⁺ (1s² 2s² 2p⁶ = [Ne]). Cl (1s² 2s² 2p⁶ 3s² 3p⁵) gains 1 e⁻ → Cl⁻ ([Ar]). Result: NaCl lattice.

Covalent Bonding

Occurs between non-metals that share electrons. The overlapping orbitals create bonding and antibonding molecular orbitals. Diatomic molecules: H₂, O₂, N₂, Cl₂.

Electronegativity Difference and Bond Type

EN Difference	Bond Type
0	Pure covalent (nonpolar)
0.1 – 1.7	Polar covalent
> 1.7	Ionic

4. Exam-Style Questions & Tips

Common exam question patterns at Makerere:

1. “Write the electron configuration of [element] and state how many unpaired electrons it has”
2. “Explain the trend in atomic radius/IE/EN across Period 2/Group 1/Group 17”
3. “Explain why the atomic radius of Na is larger than that of Cl”
4. “Define ionization energy and explain why IE₁ < IE₂ < IE₃ for an element”
5. “Draw the shapes of s and p orbitals”
6. “Identify the block in the periodic table for element [X]”

⚡ Exam tips:

• Always check the atomic number (Z) from the periodic table before writing electron configurations
• Remember: 4s fills before 3d (but 3d fills before 4p)
• When answering trend questions, always mention: (1) nuclear charge, (2) shielding, (3) distance from nucleus
• Isotopes have same chemical properties but different physical properties (mass, density, radioactive decay)

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🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for students on a longer study timeline.

Detailed Quantum Mechanical Theory

de Broglie Equation

All matter exhibits wave-particle duality. The wavelength of a particle is given by: λ = h/mv where h = Planck’s constant (6.626 × 10⁻³⁴ J s), m = mass (kg), v = velocity (m/s).

Example: Calculate the wavelength of an electron (mass = 9.11 × 10⁻³¹ kg) moving at 1 × 10⁷ m/s. λ = (6.626 × 10⁻³⁴) / (9.11 × 10⁻³¹ × 1 × 10⁷) = 7.27 × 10⁻¹¹ m = 72.7 pm

Heisenberg’s Uncertainty Principle

It is impossible to simultaneously know the exact position and momentum of a subatomic particle. Δx · Δp ≥ h/4π This limits the accuracy of orbital predictions for electrons.

Schrödinger Wave Equation (1926)

The modern description of electrons in atoms comes from solving the Schrödinger equation: ĤΨ = EΨ

• Ĥ = Hamiltonian operator (total energy)
• Ψ = wave function (contains information about the electron’s behavior)
• E = energy of the orbital

The solutions give us atomic orbitals with specific energies and shapes.

Hund’s Rule of Maximum Multiplicity

When filling degenerate (equal energy) orbitals, electrons fill singly first with parallel spins before pairing up.

Example — Nitrogen (Z=7): 1s² 2s² 2p³ Orbital diagram:

N:  ↑↓  ↑↓  ↑  ↑  ↑
    1s  2s  2px 2py 2pz

Each p electron occupies a different orbital with parallel spin.

Example — Oxygen (Z=8): 1s² 2s² 2p⁴

O:  ↑↓  ↑↓  ↑↓  ↑  ↑
    1s  2s  2px 2py 2pz

One orbital has paired electrons.

Effective Nuclear Charge (Zₑff)

The actual positive charge experienced by a valence electron after accounting for shielding. Zₑff = Z − S (where S = screening constant)

For 2p electrons across Period 2:

• B (Z=5): Zₑff ≈ 5 − 0.85 = 4.15
• C (Z=6): Zₑff ≈ 6 − 0.85 = 5.15
• N (Z=7): Zₑff ≈ 7 − 0.85 = 6.15
• O (Z=8): Zₑff ≈ 8 − 0.85 = 7.15

This explains why properties like atomic radius decrease and ionization energy increases across a period.

Screening Constants (Slater’s Rules)

For ns or np electrons:

1. Electrons in the same group (same n): each other electron contributes 0.35 (0.30 for 1s)
2. Electrons in (n−1) shell: each contributes 0.85
3. Electrons in (n−2) or lower: each contributes 1.00
4. For nd or nf electrons: all electrons to the left contribute 1.00

Example: Calculate Zₑff for a 3p electron in phosphorus (Z=15): [1s² 2s² 2p⁶ 3s² 3p³] Same group (3s² 3p³): 4 × 0.35 = 1.40 n−1 shell (2s² 2p⁶): 8 × 0.85 = 6.80 n−2 shell (1s²): 2 × 1.00 = 2.00 Total S = 1.40 + 6.80 + 2.00 = 10.20 Zₑff = 15 − 10.20 = 4.80

Successive Ionization Energies

The energy required to remove successive electrons increases dramatically when moving from one shell to the next (after inner shell electrons are removed, Zₑff increases sharply).

Example — Magnesium (Mg):

Stage	IE (kJ/mol)	Observation
IE₁	738	Remove 3s¹
IE₂	1451	Remove 3s¹ (now Mg²⁺)
IE₃	7733	Remove 2p⁶ — huge jump!

The large jump between IE₂ and IE₃ confirms that Mg has 2 valence electrons (Group 2).

The s, p, d, f Blocks

s-block (Groups 1 & 2 + He): ns¹ and ns² configuration p-block (Groups 13–18): np¹ to np⁶ configuration d-block (Transition metals, Groups 3–12): (n−1)d¹ to (n−1)d¹⁰ ns⁰ to ns² f-block (Lanthanides & Actinides): (n−2)f¹ to (n−2)f¹⁴

Important transition metal electron configurations:

• Cr (Z=24): [Ar] 4s¹ 3d⁵ (instead of 4s² 3d⁴) — half-filled d subshell is extra stable
• Cu (Z=29): [Ar] 4s¹ 3d¹⁰ (instead of 4s² 3d⁹) — filled d subshell is extra stable
• Mn (Z=25): [Ar] 4s² 3d⁵

Oxidation States

The oxidation state is the charge an atom would have if all bonds were ionic.

• Group 1 elements: almost always +1
• Group 2 elements: almost always +2
• Halogens: usually −1 (but can be positive with oxygen/fluorine)
• Oxygen: usually −2 (except in peroxides O₂²⁻ where it’s −1, and OF₂ where it’s +2)
• Hydrogen: +1 with non-metals, −1 with metals (metal hydrides)

Practice Problems

Q1: Write the electron configuration for: (a) Ca (Z=20) → (b) Zn (Z=30) → (c) Br (Z=35) → (d) Sr (Z=38)

Q2: Explain why the first ionization energy of Al (578 kJ/mol) is lower than that of Mg (738 kJ/mol).

Q3: Arrange the following in order of increasing atomic radius: F, Cl, Br, I. Explain your reasoning.

Q4: Define electronegativity and explain why fluorine has the highest electronegativity of all elements.

Q5: The successive ionization energies for element X are: 737, 1450, 7730, 10540 kJ/mol. Identify element X and explain your answer.

Common Mistakes to Avoid

1. Writing d-block configuration incorrectly: Remember Cr and Cu have anomalous configurations — write out the actual distribution, not the “expected” one.
2. Confusing shells, subshells, and orbitals: n=1,2,3 are shells; s, p, d, f are subshells within shells; orbitals are specific distributions within subshells.
3. Forgetting that 4s fills before 3d but 3d is placed after 4s in the configuration notation: [Ar] 4s² 3d⁶ (not [Ar] 3d⁶ 4s²).
4. Not explaining trends properly: Always mention nuclear charge AND shielding AND distance — all three factors.
5. Thinking isotopes have different chemical properties: They have identical chemical properties because chemical behavior depends on electron configuration, not nuclear composition.

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