Atomic Structure and Electron Configuration

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your NECO exam.

Subatomic Particles:

Particle	Symbol	Mass	Charge
Proton	$p^+$	1 unit	+1
Neutron	$n^0$	1 unit	0
Electron	$e^-$	$\frac{1}{1836}$ unit	−1

Atomic Number ($Z$): Number of protons in the nucleus. Unique to each element. Mass Number ($A$): Total number of protons + neutrons. $$A = Z + N \quad \text{(where } N = \text{number of neutrons)}$$

Isotopes: Atoms of the same element with different mass numbers (different number of neutrons). Example: ${}^{12}\text{C}$ and ${}^{14}\text{C}$ — both have $Z = 6$ but $A = 12$ and $A = 14$.

Electron Configuration Notation: Using the $n + l$ rule (Aufbau principle):

$$1s^2,\ 2s^2,\ 2p^6,\ 3s^2,\ 3p^6,\ 4s^2,\ 3d^{10},\ 4p^6,\ 5s^2,\ 4d^{10},\ 5p^6,\ 6s^2,\ 4f^{14},\ 5d^{10},\ 6p^6,\ 7s^2$$

Memory aid: Some Old Archaeans Looked Very Carefully — ‘s’ comes before ‘p’, ‘p’ before ‘d’, ‘d’ before ‘f’.

⚡ NECO Tip: When writing electron configurations, remember that $4s$ is filled before $3d$ because it has lower energy. For ions, remove electrons from the highest $n$ level first. For $\text{Fe}^{3+}$, remove from $4s$ before $3d$: $\text{Fe} = [Ar] 3d^6 4s^2$, so $\text{Fe}^{3+} = [Ar] 3d^5$.

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🟡 Standard — Regular Study (2d–2mo)

Standard content for NECO Chemistry students with a few days to months.

Bohr’s Model of the Atom:

Electrons orbit the nucleus in discrete shells (energy levels). Energy absorbed → electron moves to higher shell. Energy emitted → electron falls to lower shell, releasing a photon of specific wavelength.

$$E_n = -\frac{13.6}{n^2} \text{ eV} \quad \text{(hydrogen-like atoms)}$$

Energy Levels and Line Spectra:

When electrons transition between levels, photons are emitted: $$\Delta E = h\nu = \frac{hc}{\lambda}$$

• Lyman series (UV): electron falls to $n=1$
• Balmer series (visible): electron falls to $n=2$
• Paschen series (IR): electron falls to $n=3$

Quantum Numbers:

1. Principal quantum number ($n$): Shell number ($1, 2, 3…$); determines energy level and average distance from nucleus.
2. Azimuthal quantum number ($l$): Sub-shell ($0 = s, 1 = p, 2 = d, 3 = f$).
3. Magnetic quantum number ($m_l$): Orbital orientation (from $-l$ to $+l$).
4. Spin quantum number ($m_s$): Electron spin ($+\frac{1}{2}$ or $-\frac{1}{2}$).

Maximum Electrons per Shell: Shell $n$ holds maximum $2n^2$ electrons:

• $n=1$: 2, $n=2$: 8, $n=3$: 18, $n=4$: 32

Orbital Filling Rules:

• Aufbau: Fill lowest energy orbitals first
• Hund’s Rule: For degenerate orbitals ($p, d, f$), put one electron in each orbital before pairing
• Pauli Exclusion Principle: No two electrons in an atom can have all four quantum numbers identical

Example — Nitrogen ($Z=7$): $1s^2 2s^2 2p^3$ Orbital diagram: ↑↓ in each box for $1s, 2s$; one ↑ in each of three $2p$ boxes (Hund’s rule).

⚡ NECO Common Mistakes:

• Forgetting that $4s$ is filled before $3d$ (though $4s$ is higher in energy once filled)
• Writing the wrong number of electrons in a sub-shell (e.g., $p$ can hold maximum 6, $d$ maximum 10)
• Mixing up atomic number and mass number
• Forgetting that ions have different electron configurations from neutral atoms

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🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for NECO and JAMB Chemistry preparation.

de Broglie Wavelength:

Matter has wave-particle duality: $$\lambda = \frac{h}{mv} = \frac{h}{p}$$

Example: An electron (mass $= 9.11 \times 10^{-31}$ kg) moving at $1%$ of speed of light ($3 \times 10^6$ m/s): $$\lambda = \frac{6.63 \times 10^{-34}}{(9.11 \times 10^{-31})(3 \times 10^6)} = 2.43 \times 10^{-10} \text{ m} = 0.243 \text{ nm}$$ This is comparable to X-ray wavelengths — electron diffraction confirms wave nature.

Heisenberg’s Uncertainty Principle: $$\Delta x \cdot \Delta p \geq \frac{h}{4\pi}$$ You cannot simultaneously know the exact position and momentum of a particle.

Wave Mechanics / Schrödinger Equation:

The Schrödinger equation describes electrons as wave functions: $$\hat{H}\psi = E\psi$$ Solutions give quantum numbers and orbital shapes.

Shielding and Effective Nuclear Charge:

Inner electrons shield outer electrons from the full nuclear charge. $$Z_{\text{eff}} = Z - S$$ where $S$ is the shielding constant (approximately 0.35 for each other electron in the same $ns$ or $np$ group, 0.85 for each electron in $(n-1)$ shell, 1.00 for each electron in $(n-2)$ or lower).

Slater’s Rules for Shielding: Group electrons by: $(1s), (2s,2p), (3s,3p), (3d), (4s,4p), (4d), (4f), (5s,5p)$…

Atomic Radius Trends:

Across a period: $Z_{\text{eff}}$ increases → atomic radius decreases. Down a group: new shells added → atomic radius increases.

Ionisation Energy:

Energy required to remove one electron from a neutral gaseous atom. First ionisation energy: $\text{M(g)} \rightarrow \text{M}^+\text{(g)} + e^-$

Trends: Increases across a period (except minor drops at Group 13 and 16), decreases down a group. The drops at $Z=13$ (B → C) and $Z=16$ (S → Cl) occur because removing an electron from a $p$-orbital is slightly easier than from a half-filled $p$-subshell.

Electron Affinity:

Energy released when an electron is added to a neutral gaseous atom: $\text{X(g)} + e^- \rightarrow \text{X}^-\text{(g)}$. Most negative value (most exothermic) is at chlorine. Oxygen has a less negative value than expected due to electron–electron repulsion in the $2p^4$ configuration.

NECO/JAMB Patterns:

• NECO often asks: write electron configurations for elements up to $Z=36$; identify isotopes from nuclear notation; calculate wavelength/frequency of emitted photons using $\Delta E = hc/\lambda$
• Be able to draw orbital diagrams for the first 20 elements
• Know how ionisation energy varies across periods and down groups

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