Revision Notes - Structure of Atom

Table of Contents
1. Introduction
2. Discovery of Subatomic Particles
3. Atomic Models
4. Atomic Number and Mass Number
5. Developments Leading to Bohr's Model
6. Bohr's Model for Hydrogen Atom (1913)
7. Towards Quantum Mechanical Model
8. Quantum Mechanical Model
9. Shapes of Atomic Orbitals
10. Energies of Orbitals
11. Filling of Orbitals
12. Summary
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Introduction

Atoms are fundamental units of matter, once thought indivisible but now known to consist of subatomic particles: electrons, protons, and neutrons. Understanding atomic structure is key to explaining chemical and physical properties of elements.

Discovery of Subatomic Particles

1. Electron (J.J. Thomson, 1897):

• Identified via cathode ray experiments; negatively charged, mass ~1/1837 of H atom.
• Charge: -1.602 × 10⁻¹⁹ C; Mass: 9.109 × 10⁻³¹ kg.

2. Proton (Rutherford, 1919):

• Found via anode rays (canal rays); positively charged, mass ~1836 times electron.
• Charge: +1.602 × 10⁻¹⁹ C; Mass: 1.672 × 10⁻²⁷ kg.

3. Neutron (James Chadwick, 1932):

• Neutral particle, slightly heavier than proton; Mass: 1.675 × 10⁻²⁷ kg.
• Charge and Mass Comparison:

Atomic Models

 1. Thomson's Model (1904)

• Atom as a positively charged sphere with embedded electrons (plum pudding model).
• Limitation: Could not explain electron stability or spectral lines.

2. Rutherford's Model (1911)

• Based on alpha particle scattering:
  • Nucleus: Small, dense, positively charged center containing most mass.
  • Electrons: Orbit nucleus like planets around the sun.
• Limitation: Electrons should emit energy and spiral into nucleus, contradicting atomic stability.

Atomic Number and Mass Number

• Atomic Number (Z): Number of protons (defines element), e.g., H (Z=1), C (Z=6).
• Mass Number (A): Protons + neutrons, e.g., ¹²C (A=12, Z=6, neutrons=6).
• Isotopes: Same Z, different A (e.g., ¹²C, ¹⁴C).
• Isobars: Same A, different Z (e.g., ¹⁴C, ¹⁴N).
• Notation: ⁿₘX, where X is element, m is A, n is Z (e.g., ¹²₆C).

Developments Leading to Bohr's Model

• Electromagnetic Waves: Maxwell's theory; light as waves with wavelength (λ), frequency (ν), speed (c = λν).
• Planck's Quantum Theory (1900): Energy emitted/absorbed in quanta (E = hν, h = 6.626 × 10⁻³⁴ J s).
• Einstein's Photoelectric Effect (1905): Light quanta (photons) eject electrons; energy threshold required.
• Atomic Spectra:
  • Emission: Light emitted by energized atoms (e.g., hydrogen's line spectrum).
  • Absorption: Light absorbed by atoms, forming dark lines.
• Hydrogen Spectrum: Lyman (UV), Balmer (visible), Paschen, Brackett, Pfund (IR); Rydberg formula: 1/λ = R(1/n₁² - 1/n₂²), R = 109677 cm⁻¹.

Bohr's Model for Hydrogen Atom (1913)

• Postulates:
  • Electrons orbit nucleus in fixed energy levels (orbits) without radiating energy.
  • Energy levels quantized: Eₙ = -2.18 × 10⁻¹⁸/n² J (n = principal quantum number).
  • Electron transitions emit/absorb energy: ΔE = E₂ - E₁ = hν.
• Radius: rₙ = 0.529 × n²/Z Å (H: n=1, r=0.529 Å).
• Velocity: vₙ = 2.188 × 10⁶ × Z/n m/s.
• Success: Explained hydrogen spectrum, atomic stability.
• Limitations: Failed for multi-electron atoms, ignored electron spin, contradicted Heisenberg's uncertainty principle.

Towards Quantum Mechanical Model

Dual Nature of Matter:

• de Broglie (1924): Particles have wave properties; λ = h/mv (h = Planck's constant, m = mass, v = velocity).
• Example: Electron at 100 V, λ = 1.227/√V nm.

Heisenberg's Uncertainty Principle (1927): Cannot know exact position and momentum simultaneously; Δx × Δp ≥ h/4π.

Quantum Mechanical Model

• Schrödinger's Wave Equation: Treats electrons as waves, solved for orbitals (probability regions).
• Orbitals: Defined by quantum numbers:
  • Principal (n): Energy level (1, 2, 3, ...).
  • Azimuthal (l): Subshell (0 to n-1; s, p, d, f).
  • Magnetic (mₗ): Orbital orientation (-l to +l).
  • Spin (mₛ): Electron spin (+1/2 or -1/2).
• Probability Density: ψ² gives electron likelihood.

Shapes of Atomic Orbitals

• s-Orbital (l=0): Spherical, size increases with n.
• p-Orbital (l=1): Dumbbell-shaped, three orientations (p_x, p_y, p_z).
• d-Orbital (l=2): Five orientations, complex shapes.
• Nodes: Regions of zero electron density (e.g., 2s has one spherical node).

Energies of Orbitals

• Hydrogen: Energy depends only on n (Eₙ = -13.6/n² eV).
• Multi-electron Atoms: Energy depends on n and l (e.g., 3s < 3p < 3d due to penetration effect).Energy Level Diagram

Filling of Orbitals

• Aufbau Principle: Electrons fill lowest energy orbitals first (1s, 2s, 2p, 3s, ...).
• Pauli Exclusion Principle: No two electrons have identical four quantum numbers; max 2 electrons per orbital with opposite spins.
• Hund's Rule: Electrons pair only after singly occupying degenerate orbitals with parallel spins.
• Configurations: e.g., C (Z=6): 1s²2s²2p²; exceptions like Cr (3d⁵4s¹) for stability.Order of filling of orbitals

Summary

Atoms consist of electrons, protons, and neutrons. Thomson's plum pudding model evolved into Rutherford's nuclear model, refined by Bohr's quantized orbits for hydrogen. Quantum mechanics, with de Broglie's wave-particle duality and Schrödinger's orbitals, describes electron probability via quantum numbers (n, l, mₗ, mₛ). Orbital shapes (s, p, d) and energy levels guide electron filling per Aufbau, Pauli, and Hund's rules, explaining atomic properties.