Why does Bohr's model fail for multi-electron atoms?

It ignores electron-electron repulsion and treats orbits as classical. Schrödinger's wave-mechanical picture, with orbitals and probability densities, is required beyond hydrogen.

What is the difference between an orbit and an orbital?

An orbit is a fixed Bohr path; an orbital is a 3-D region of high probability of finding an electron, defined by a wavefunction ψ.

Why does 4s fill before 3d?

By the (n + ℓ) rule: 4s has n + ℓ = 4, 3d has n + ℓ = 5, so 4s is lower in energy in neutral atoms. After filling, 3d drops below 4s, which is why ions remove 4s electrons first.

What does the Heisenberg uncertainty principle imply?

Position and momentum cannot both be known exactly; their uncertainties satisfy Δx·Δp ≥ h/4π. This rules out classical Bohr-style trajectories at atomic scales.

Why is the half-filled d⁵ configuration unusually stable?

Exchange energy is maximised when electrons in degenerate orbitals all have parallel spins, lowering the total energy — the basis of Cr's 4s¹ 3d⁵ anomaly.

The maximum number of electrons in a subshell with ℓ = 2 is:

10. ℓ = 2 is a d sub-shell, with 2(2ℓ+1) = 10 electrons.

The wavelength of the first line of the Balmer series (n = 3 → n = 2) for hydrogen is approximately:

656 nm. 1/λ = R_H(1/4 − 1/9) = 1.097×10⁷ × 5/36; λ ≈ 656 nm (Hα, red).

The ground-state electronic configuration of Cu (Z = 29) is:

[Ar] 4s¹ 3d¹⁰. A fully filled 3d¹⁰ with 4s¹ is more stable than 4s² 3d⁹ due to exchange energy.

Which of the following species is isoelectronic with Ne?

F⁻. F⁻ has 10 electrons, identical to neutral Ne.

The de Broglie wavelength of a 0.05 kg ball moving at 20 m/s is of order:

10⁻³⁴ m. λ = h/mv = 6.626×10⁻³⁴ / (0.05 × 20) ≈ 6.6×10⁻³⁴ m — undetectable, which is why classical objects do not diffract.

Atomic Structure MDCAT 2026 — Notes, Key Concepts & MCQs (Chemistry)

Atomic Structure

Atomic Structure averages 3 MCQs per MDCAT paper — Bohr's model, quantum numbers, and electronic configuration are perennial favourites.

Atomic Structure is a Chemistry chapter on the official PMDC MDCAT 2026 syllabus, contributing roughly 3 MCQs to the 45-MCQ Chemistry section. Mastering the core concepts below typically secures the full chapter weightage.

From Rutherford to Bohr

Rutherford's 1911 α-scattering experiment showed that atoms have a tiny dense positive nucleus with electrons outside. Classical electromagnetism predicted electrons should spiral in; Bohr (1913) postponed the catastrophe with three postulates: electrons orbit only at fixed radii where angular momentum mvr = nh/2π (n = 1, 2, 3…), they radiate only when jumping between orbits, and ΔE = hν. For hydrogen, E_n = −13.6/n² eV and r_n = 0.529 n² Å. The Lyman series (n_f = 1) lies in the UV, the Balmer (n_f = 2) in the visible, the Paschen (n_f = 3) in the IR. Atkins Chapter 7 and FSc XI Chapter 5 derive 1/λ = R_H(1/n_f² − 1/n_i²) with R_H = 1.097×10⁷ m⁻¹.

Wave-particle duality and the uncertainty principle

de Broglie (1924): λ = h/mv. An electron of mass 9.11×10⁻³¹ kg moving at 10⁶ m/s has λ ≈ 7.3×10⁻¹⁰ m — comparable to atomic dimensions, which is why electrons diffract through crystals (Davisson-Germer). Heisenberg: Δx·Δp ≥ h/4π. Localising an electron to within 1 Å forces a momentum uncertainty large enough to make a definite orbit meaningless. Schrödinger's 1926 wave equation Ĥψ = Eψ replaced orbits with orbitals — regions where |ψ|² gives the probability density.

Quantum numbers and orbital shapes

Four quantum numbers specify an electron: principal n (shell, 1, 2, 3…), azimuthal ℓ (subshell, 0 to n−1: s, p, d, f), magnetic m_ℓ (orientation, −ℓ to +ℓ), and spin m_s (±½). Subshell capacities: s = 2, p = 6, d = 10, f = 14. s orbitals are spherical; p orbitals are dumb-bells along x, y, z; d orbitals show four-lobed cloverleaves except d_z². Pauli exclusion: no two electrons share all four numbers. Hund's rule: degenerate orbitals fill singly with parallel spins before pairing. Aufbau: lowest (n + ℓ) first, with ties broken by lower n — explaining 4s before 3d.

Electronic configuration and anomalies

Carbon (Z = 6) is 1s² 2s² 2p². Iron (Z = 26): 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁶ or [Ar] 4s² 3d⁶. The two famous anomalies are Cr ([Ar] 4s¹ 3d⁵) and Cu ([Ar] 4s¹ 3d¹⁰), where a half-filled or fully-filled d sub-shell offers extra exchange-energy stability — a topic Clayden treats in his organometallic-precursor chapters and Atkins in Chapter 9. For ions, remove from the highest-n shell first: Fe²⁺ is [Ar] 3d⁶, not [Ar] 4s² 3d⁴.

Spectra, ionisation, and effective nuclear charge

The hydrogen emission spectrum's discrete lines confirmed quantisation. Ionisation energy generally rises across a period (greater Z_eff) and falls down a group (greater shielding). Small dips: B < Be (2p higher than 2s), O < N (paired 2p electron repulsion). Slater's rules give Z_eff = Z − σ; for the 2p electron in carbon, σ ≈ 2.75, Z_eff ≈ 3.25. The MDCAT often asks which species is isoelectronic with Ne — answer set: F⁻, Na⁺, Mg²⁺, O²⁻, all with 10 electrons.

Key Concepts

Worked MCQs

Frequently Asked Questions

How Atomic Structure Is Tested

MDCAT questions on Atomic Structure are a mix of recall (definitions, classifications), application (predict outcomes, interpret diagrams), and basic numerical/analytical reasoning. PMDC papers from 2020–2025 emphasized the concepts above; older UHS papers (2008–2019) tested them too, with slight variations in question framing.