Atomic Structure

Atomic structure governs all of chemistry, and NEET tests it heavily through calculation-based problems. Electromagnetic radiation travels at the speed of light (c = 3 × 10⁸ m/s) with energy E = hν = hc/λ, where Planck's constant h = 6.626 × 10⁻³⁴ J·s. The photoelectric effect (Einstein) showed that light behaves as particles (photons): kinetic energy of emitted electrons = hν − hν₀, where ν₀ is the threshold frequency. No emission occurs below ν₀ regardless of intensity.

The hydrogen spectrum is quantized. The Rydberg formula 1/λ = $R_{H}$(1/n₁² − 1/n₂²), where $R_{H}$ = 1.097 × 10⁷ m⁻¹, predicts all five series: Lyman (n₁=1, UV), Balmer (n₁=2, visible), Paschen (n₁=3, IR), Brackett (n₁=4, IR), and Pfund (n₁=5, IR). The total number of spectral lines emitted from level n is n(n−1)/2.

Bohr's model for hydrogen-like atoms gives: energy $E_{n}$ = −13.6 Z²/n² eV, radius $r_{n}$ = 0.529 n²/Z Å, and velocity $v_{n}$ = 2.18 × 10⁶ Z/n m/s. Energy is always negative (bound state); more negative = more stable.

Solved Example 1: First line in Balmer series of hydrogen (n₂=3 → n₁=2): 1/λ = 1.097 × 10⁷ ($\frac{1}{4}$ − $\frac{1}{9}$) = 1.097 × 10⁷ × $\frac{5}{36}$ = 1.524 × 10⁶ m⁻¹ λ = 6.56 × 10⁻⁷ m = 656 nm (red light) ✓

Solved Example 2: de Broglie wavelength of an electron at 1% speed of light: λ = h/mv = 6.626 × 10⁻³⁴ J·s / (9.1 × 10⁻³¹ kg × 3 × 10⁶ m/s) Dimensional analysis: J·s / (kg·m/s) = (kg·m²/s²)·s / (kg·m/s) = m ✓ λ = 6.626 × 10⁻³⁴ / 2.73 × 10⁻²⁴ = 2.43 × 10⁻¹⁰ m = 2.43 Å

Solved Example 3: Energy emitted when electron jumps from n=3 to n=1 in He⁺ (Z=2): ΔE = 13.6 × Z² × (1/n₁² − 1/n₂²) = 13.6 × 4 × ($\frac{1}{1}$ − $\frac{1}{9}$) = 54.4 × $\frac{8}{9}$ = 48.36 eV

The Heisenberg uncertainty principle (Δx·Δp ≥ h/4π) forbids simultaneously knowing exact position and momentum. This led to the quantum mechanical model with four quantum numbers: n (shell, 1,2,3...), l (subshell, 0 to n−1), mₗ (orientation, −l to +l), mₛ (spin, ±½). Orbital capacity: subshell holds 2(2l+1) electrons; shell holds 2n².

Node formulas (derivation): Total nodes = n−1. Angular nodes = l (from the angular part of the wave function). Radial nodes = total − angular = n−l−1.

Electrons fill orbitals following: Aufbau principle (lowest n+l first; if equal, lower n first), Pauli exclusion (no two electrons share all four quantum numbers), and Hund's rule (maximize spin multiplicity). Anomalous configurations arise from half-filled/fully-filled d-orbital stability: Cr = [Ar] 3d⁵ 4s¹ (not 3d⁴ 4s²), Cu = [Ar] 3d¹⁰ 4s¹ (not 3d⁹ 4s²).

The key testable concept is Bohr model energy calculations for hydrogen-like atoms and quantum number assignments.