Learning Objectives
- Understand subatomic particles and atomic models
- Study Bohr's model and its limitations
- Learn quantum mechanical model and quantum numbers
- Understand electron configuration and orbital shapes
- Apply Aufbau principle, Pauli's exclusion principle, and Hund's rule
Key Concepts
Subatomic Particles
Electron: e⁻, mass = 9.1 × 10⁻³¹ kg, charge = -1.6 × 10⁻¹⁹ C. Discovered by J.J. Thomson (cathode rays).
Proton: p⁺, mass = 1.672 × 10⁻²⁷ kg, charge = +1.6 × 10⁻¹⁹ C. Discovered by Goldstein (anode/canal rays).
Neutron: n⁰, mass ≈ proton mass, charge = 0. Discovered by Chadwick.
Atomic Models
Thomson's plum pudding model: Positive charge uniformly distributed with electrons embedded. Failed to explain Rutherford's scattering.
Rutherford's nuclear model: Positive charge and most mass in a tiny nucleus; electrons orbit. Could not explain stability or line spectra.
Bohr's Model (Hydrogen-like atoms)
Electrons revolve in fixed orbits without radiating. Angular momentum: L = nh/2π.
Energy: Eₙ = -2.18 × 10⁻¹⁸/n² J = -13.6/n² eV (for hydrogen).
Radius: rₙ = 0.529 n²/Z Å. Velocity: vₙ = 2.18 × 10⁶ Z/n m/s.
Limitations: works only for single-electron species, cannot explain fine structure, Zeeman effect, or multi-electron spectra.
Dual Nature and de Broglie Equation
λ = h/mv = h/p. Heisenberg Uncertainty Principle: Δx × Δp ≥ h/4π.
Quantum Mechanical Model
Schrodinger wave equation: Ĥψ = Eψ. Solutions give wavefunctions (ψ) and energy levels.
|ψ|² gives the probability density of finding the electron.
Quantum Numbers
- Principal (n): 1, 2, 3, ... Determines energy and size. Shell: K, L, M, N...
- Azimuthal (l): 0 to (n-1). Determines shape. l = 0 (s), 1 (p), 2 (d), 3 (f).
- Magnetic (mₗ): -l to +l. Determines orientation. Number of orbitals = 2l + 1.
- Spin (mₛ): +½ or -½. Determines spin direction.
Maximum electrons in a shell = 2n². Maximum in a subshell = 2(2l + 1).
Orbital Shapes
s orbital: Spherical. One per shell. p orbital: Dumbbell-shaped. Three per shell (px, py, pz). d orbital: Cloverleaf/double dumbbell. Five per shell. f orbital: Complex shape. Seven per shell.
Nodes: Radial nodes = n - l - 1. Angular nodes = l. Total nodes = n - 1.
Electronic Configuration Rules
Aufbau Principle: Electrons fill orbitals in order of increasing energy: 1s → 2s → 2p → 3s → 3p → 4s → 3d → 4p → 5s → 4d → ... (use n+l rule; if n+l same, lower n fills first).
Pauli's Exclusion Principle: No two electrons can have all four quantum numbers identical. Maximum 2 electrons per orbital.
Hund's Rule: Electrons fill degenerate orbitals singly with parallel spins before pairing.
Exceptions: Cr = [Ar]3d⁵4s¹ and Cu = [Ar]3d¹⁰4s¹ (half-filled and fully filled d-subshells are extra stable).
Summary
Atoms consist of electrons, protons, and neutrons. Bohr's model successfully explained hydrogen spectrum but failed for multi-electron atoms. The quantum mechanical model describes electrons as wavefunctions with probability distributions. Four quantum numbers (n, l, mₗ, mₛ) completely describe an electron. Electronic configurations follow Aufbau, Pauli's, and Hund's rules.
Important Terms
- Orbital: Region of space with high probability of finding an electron
- Quantum Numbers: Set of four numbers describing an electron's state
- Aufbau Principle: Electrons fill lowest energy orbitals first
- Pauli's Exclusion Principle: No two electrons with identical quantum numbers
- Hund's Rule: Maximum multiplicity in degenerate orbitals
- Heisenberg Uncertainty: Cannot simultaneously know exact position and momentum
Quick Revision
- Eₙ = -13.6 Z²/n² eV; rₙ = 0.529 n²/Z Å
- λ = h/mv; Δx·Δp ≥ h/4π
- n: shell, l: subshell shape, mₗ: orientation, mₛ: spin
- Max electrons: shell = 2n², subshell = 2(2l+1)
- Filling order: 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f 5d 6p
- Exceptions: Cr [Ar]3d⁵4s¹, Cu [Ar]3d¹⁰4s¹