Atomic Structure

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your exam.

Atomic Structure — Quick Facts

Atomic structure forms the foundation of chemistry — understanding electrons, orbitals, and atomic spectra is essential for NEET.

Key Definitions:

• Quantum numbers: Four numbers (n, l, mₗ, mₛ) that completely describe an electron in an atom
• Principal quantum number (n): Energy level, 1 to ∞; determines shell (K, L, M, N…)
• Azimuthal quantum number (l): Subshell shape, 0 to (n−1); s(0), p(1), d(2), f(3)
• Magnetic quantum number (mₗ): Orbital orientation, −l to +l
• Spin quantum number (mₛ): Electron spin, +½ or −½

Electronic Configuration:

• Aufbau principle: Fill orbitals in order of increasing (n + l) value; for ties, lower n first
• Hund’s rule: Maximise unpaired electrons in degenerate orbitals before pairing
• Pauli exclusion principle: No two electrons can have all four quantum numbers identical

Key Formulas:

• Maximum electrons in shell n = 2n²
• Maximum electrons in subshell l = 2(2l + 1)
• de Broglie wavelength: λ = h/mv
• Photoelectric equation: E = hν = hc/λ; KEₘₐₓ = hν − Φ

⚡ Exam tip: For d-block elements (Groups 3–12), (n−1)d is filled after ns but before (n−1)p. For Cr (Z=24): [Ar] 3d⁵ 4s¹, not [Ar] 3d⁴ 4s² — this is because half-filled d-subshell (d⁵) has extra stability.

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🟡 Standard — Regular Study (2d–2mo)

Standard content for students with a few days to months.

Atomic Structure — NEET/JEE Study Guide

Bohr’s Model and its Limitations: Bohr proposed that electrons revolve in fixed circular orbits with quantized energy. The radius of the nth orbit: $$r_n = \frac{\epsilon_0 h^2 n^2}{\pi m e^2} = 0.529 \times n^2 \text{ Å}$$

Energy of electron in nth orbit: $$E_n = -\frac{me^4}{8\epsilon_0^2 h^2} \times \frac{1}{n^2} = -13.6 \frac{Z^2}{n^2} \text{ eV}$$

Bohr model successfully explained hydrogen spectrum but failed for:

• Multi-electron atoms (fine structure)
• Zeeman effect (splitting in magnetic field)
• Stark effect (splitting in electric field)

Quantum Mechanical Model: Heisenberg’s uncertainty principle: Δx · Δp ≥ h/4π. For electrons, we can never simultaneously know exact position and momentum — this is why Bohr’s precise orbits are impossible.

Quantum Numbers and Electron Configurations:

Shell	n	Subshells	Max e⁻
K	1	1s	2
L	2	2s, 2p	8
M	3	3s, 3p, 3d	18
N	4	4s, 4p, 4d, 4f	32

** Aufbau order by (n+l):**

• 1s: n+l = 1+0 = 1
• 2s: n+l = 2+0 = 2
• 2p: n+l = 2+1 = 3
• 3s: n+l = 3+0 = 3
• 3p: n+l = 3+1 = 4
• 4s: n+l = 4+0 = 4
• 3d: n+l = 3+2 = 5

Order: 1s → 2s → 2p → 3s → 3p → 4s → 3d → 4p → 5s → 4d → 5p → 6s → 4f → 5d → 6p → 7s → 5f…

⚡ Exception: Copper (Cu, Z=29) is [Ar] 3d¹⁰ 4s¹ — the 3d¹⁰ configuration (full d-subshell) is extra stable. Similarly, Zn is 3d¹⁰ 4s², not 3d⁸ 4s².

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🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for students on a longer study timeline.

Atomic Structure — Comprehensive Notes

Derivation of de Broglie Wavelength: From Einstein’s mass-energy equivalence: E = mc² and photon momentum: p = E/c Therefore: p = mc = h/λ → λ = h/mc = h/p

For a particle of mass m moving at velocity v: λ = h/mv

Heisenberg’s Uncertainty Principle (Derivation): From photon diffraction thought experiment: Δx · Δp ≥ h/4π For an electron in an orbit of radius r, if position uncertainty is Δx, then angular momentum uncertainty is ΔL = r · Δp. Minimum uncertainty: ΔL ≈ h/4π But quantised angular momentum: L = n·h/2π → ΔL ≥ h/2π This contradicts Bohr’s assumption of precise orbits — hence electrons cannot have defined circular paths.

Hydrogen Spectrum: When hydrogen atom electrons transition between energy levels, photons are emitted or absorbed.

Balmer series (visible): Transitions from n > 2 to n = 2 $$ \frac{1}{\lambda} = R \left(\frac{1}{2^2} - \frac{1}{n^2}\right) $$ where R = 1.097 × 10⁷ m⁻¹

Lyman series (UV): n > 1 to n = 1 Paschen series (IR): n > 3 to n = 3

Quantum Mechanical Treatment: The Schrödinger equation for hydrogen atom: $$\hat{H}\psi = E\psi$$ Where $\hat{H} = -\frac{\hbar^2}{2m}\nabla^2 - \frac{e^2}{4\pi\epsilon_0 r}$

Solutions require three quantum numbers. The wave function ψ describes the probability amplitude — |ψ|² gives the probability density of finding an electron.

Orbital Shapes:

• s-orbital: Spherical, 1 orbital per subshell
• p-orbital: Dumbbell-shaped, 3 orbitals (pₓ, pᵧ, p_z) per subshell
• d-orbital: Double-dumbbell/cloverleaf, 5 orbitals per subshell
• f-orbital: Complex 3D shape, 7 orbitals per subshell

Slater’s Rules for Effective Nuclear Charge: Zₑff = Z − S, where S is the screening constant:

1. Write configuration as (1s)(2s,2p)(3s,3p)(3d)(4s,4p)(4d)…
2. Electrons to the right of the target electron contribute 0 to S.
3. For ns or np electron: same group (ns,np) electrons contribute 0.35 each (0.30 for 1s); (n−1) shell contributes 0.85; (n−2) or lower contributes 1.00.
4. For nd or nf electron: all electrons to the left contribute 1.00.

Example: For a 3p electron in Cl (Z=17): Slater gives Zₑff = 17 − (6×0.35 + 8×0.85 + 2×1.00) = 17 − 10.5 = 6.5

NEET Pattern Analysis: Atomic structure typically contributes 1–2 questions per year. High-yield areas: quantum numbers (identifying valid/invalid combinations), electronic configuration exceptions (Cu, Cr, Ag, etc.), de Broglie wavelength calculations, and photoelectric effect. Always check if the electron is in ground state or excited state when determining configuration.

⚡ NEET 2022 Qn: Which of the following sets of quantum numbers is not allowed for an electron? (a) n=2, l=1, mₗ=0, mₛ=+½ → ALLOWED. (b) n=2, l=2, mₗ=0, mₛ=+½ → NOT ALLOWED (l must be < n).