Atomic Structure — JEE Main & Advanced Notes

Master Bohr model, spectra, de Broglie wavelength, uncertainty principle, quantum numbers and orbital filling.

Priority: High Yield. Unit: Physical Chemistry. Level: Foundation.

How the uploaded material was used: Mapped from atomic model, spectrum, de Broglie, quantum number and electronic configuration practice sets. The final student-facing notes and questions are original, rewritten and copyright-safe.

These are the ideas that decide most correct answers in Atomic Structure.

• Historical models and why they failed: Thomson's plum-pudding model had electrons scattered in positive charge — disproved by Rutherford's gold-foil experiment (large deflections required a compact nucleus). Rutherford's nuclear model couldn't explain atomic stability (electrons would spiral inward radiating energy) or line spectra. Bohr fixed this by postulating quantised circular orbits with defined energy levels. Bohr's model, in turn, fails for multi-electron atoms because it ignores electron–electron repulsion.
• Bohr model for hydrogen-like species: The Bohr model gives exact results only for one-electron species: H, He⁺, Li²⁺, Be³⁺, etc. Key results: energy Eₙ = −13.6Z²/n² eV (negative because bound), radius rₙ = 0.529n²/Z Å, velocity vₙ = 2.18×10⁶Z/n m/s. Emission spectral series: Lyman (UV, n₁=1), Balmer (visible, n₁=2), Paschen (IR, n₁=3), Brackett (n₁=4), Pfund (n₁=5). Energy of emitted photon = E_higher − E_lower = ΔE (always positive for emission).
• de Broglie's wave-particle duality: Particles have wave-like properties. The de Broglie wavelength λ = h/mv = h/p. For a macroscopic object (large m), λ is negligible. For electrons, λ is comparable to atomic dimensions — this is why electrons diffract and why atomic orbitals are probability clouds rather than definite paths. For an electron accelerated through potential V volts: λ = 12.27/√V Å.
• Heisenberg's uncertainty principle: It is fundamentally impossible to know both the exact position and exact momentum of a particle simultaneously. The minimum uncertainty product is Δx·Δp ≥ h/4π. This principle, not measurement limitations, is the reason electrons cannot have definite circular orbits. It also means the concept of exact electron trajectories is wrong — orbitals are probability distributions instead.
• Quantum numbers — the four labels of an electron: (1) Principal quantum number n: determines the shell (n=1,2,3,…) and the energy (approximately). Maximum electrons = 2n². (2) Azimuthal quantum number l: 0 to n−1, determines subshell (l=0→s, 1→p, 2→d, 3→f) and orbital shape. (3) Magnetic quantum number mₗ: −l to +l (2l+1 values), determines orientation of orbital. (4) Spin quantum number ms: +½ or −½. No two electrons in an atom can have all four quantum numbers identical — Pauli's exclusion principle.
• Aufbau, Pauli and Hund's rules — filling orbitals: Aufbau principle: fill orbitals in order of increasing (n+l); for equal (n+l), fill the lower-n orbital first. Order: 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p … Pauli's exclusion principle: each orbital holds at most 2 electrons with opposite spins. Hund's rule: within a degenerate subshell (e.g., 2p which has 3 orbitals), distribute electrons one per orbital with parallel spins before pairing. Exceptions to expected configuration: Cr is [Ar]3d⁵4s¹ (not 3d⁴4s²) and Cu is [Ar]3d¹⁰4s¹ (not 3d⁹4s²) due to extra stability of half-filled and fully-filled d subshells.
• Shapes and sizes of orbitals: s orbitals are spherical. p orbitals are dumbbell-shaped with a nodal plane. d orbitals have more complex shapes (four-lobed or torus-lobed). Number of radial nodes = n−l−1; number of angular nodes = l; total nodes = n−1. These nodes are regions of zero electron probability. Orbitals further from the nucleus are larger and higher in energy. For many-electron atoms, subshell energy order is 1s < 2s < 2p < 3s < 3p < 4s < 3d (shielding effect).
• Spectral series and energy transitions: When an electron falls from a higher to a lower energy level in a H-like atom, a photon is emitted with energy = |E_higher − E_lower|. The wavelength is given by 1/λ = RZ²(1/n₁² − 1/n₂²) where n₁ < n₂. Lyman series (n₁=1): UV region. Balmer (n₁=2): visible. Paschen (n₁=3), Brackett (n₁=4), Pfund (n₁=5): infrared. Absorption: electron absorbs photon and moves to a higher level.

• Bohr energy: Eₙ = −13.6 Z²/n² eV (valid only for H-like one-electron species)
• Bohr radius: rₙ = 0.529 n²/Z Å (radius of nth orbit)
• Orbital velocity: vₙ = 2.18×10⁶ Z/n m/s
• Rydberg formula: 1/λ = RZ²(1/n₁² − 1/n₂²) where R = 1.097×10⁷ m⁻¹
• Energy of photon: E = hν = hc/λ where h = 6.626×10⁻³⁴ J·s
• de Broglie wavelength: λ = h/mv = h/p; for electron accelerated through V volts: λ = 12.27/√V Å
• Heisenberg uncertainty: Δx·Δp ≥ h/4π; ΔE·Δt ≥ h/4π
• Orbital angular momentum: L = √(l(l+1)) · h/2π
• Magnetic quantum number: mₗ ranges from −l to +l (integer steps), giving 2l+1 values
• Spin: ms = +½ or −½; maximum electrons in shell n = 2n²
• Maximum electrons in subshell: s→2, p→6, d→10, f→14

Derivation / logic hint: Do not plug values blindly. Start from conservation of mass/charge, equilibrium definition, energy balance, electron movement, structure-property relation, or stability of the product/intermediate.

Most negative marks in this chapter come from condition errors, not lack of memory.

• Applying Bohr energy formula (Eₙ = −13.6Z²/n² eV) to multi-electron atoms: this formula is valid ONLY for H-like species (1 electron). For Na, Ca, Fe etc., electron-electron repulsion makes the formula completely wrong.
• Forgetting Z² in energy and Z in radius/velocity: for He⁺ (Z=2), E₁ = −13.6×4/1² = −54.4 eV, not −13.6 eV. Similarly r₁ = 0.529/2 Å. Every formula has Z dependence that cannot be dropped.
• Assigning impossible quantum number combinations: l must be in [0, n−1], mₗ must be in [−l, l], and ms can only be ±½. e.g., n=2, l=2 is impossible (l max = n−1 = 1). n=3, l=1, mₗ=2 is impossible (mₗ max = l = 1).
• Confusing emission and absorption: emission = electron falls DOWN → photon released. Absorption = electron moves UP → photon absorbed. In the Rydberg formula, for emission n₁ < n₂ (lower level is n₁); the wavelength calculated is always positive.
• Wrong electronic configuration due to 4s/3d ordering confusion: 4s fills before 3d (lower n+l = 4 for 4s, = 5 for 3d). But when an electron is removed (ionisation), 4s is removed first because it has higher energy in the presence of the 3d electrons. So Fe is [Ar]3d⁶4s² but Fe²⁺ is [Ar]3d⁶, not [Ar]3d⁴4s².

For JEE Main, prioritise direct formula use, NCERT-aligned facts, named-reaction recognition, trend comparison and quick elimination. Target 60–90 seconds per question.

• Bohr model — H-like species
• Hydrogen spectrum and series
• de Broglie wavelength
• Heisenberg uncertainty principle

For JEE Advanced, combine ideas. Expect assertion-reason, integer, multiple-correct, paragraph-style and hidden-condition problems. Before finalising, ask which assumption the question is testing.

• de Broglie wavelength
• Heisenberg uncertainty principle
• Quantum numbers (n, l, mₗ, ms)
• Orbital shapes and nodes
• Electronic configuration (Aufbau, Pauli, Hund)
• Exceptions: Cr, Cu and other anomalies

Use this block in the final 24–48 hours before a mock.

• H-like species only: Eₙ = −13.6Z²/n² eV. Radius rₙ = 0.529n²/Z Å. Both scale as Z²/n² (energy) or n²/Z (radius).
• Spectral series: Lyman (n₁=1, UV), Balmer (n₁=2, visible), Paschen onward (IR). Longest wavelength in a series = smallest energy jump = adjacent levels (n₁ to n₁+1).
• Quantum numbers: n → shell; l → subshell shape (0=s,1=p,2=d,3=f); mₗ → orientation; ms → spin ±½.
• Filling order: 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p … Exceptions: Cr=[Ar]3d⁵4s¹, Cu=[Ar]3d¹⁰4s¹.
• Uncertainty: Δx·Δp ≥ h/4π. de Broglie: λ = h/mv. Both reflect wave nature of particles.