Structure of Atom

Introduction

• Highly scoring chapter
• Consists of concepts like atomic structure and related principles
• Detailed study of the arrangement of electrons, energy, and structure of atoms

Discovery of Sub-Atomic Particles

Electron Discovery

• Discovered by J.J. Thomson using Cathode Ray Tube experiment
• Set-up: glass tube, low-pressure gas, and high voltage
• Cathode rays (electrons) move towards the anode, showing a negatively charged particle
• Properties: Independent of gas nature, travel in a straight line, create shadows, deflect in electric and magnetic fields

Proton Discovery

• Observed when positive particles move towards the cathode in the opposite direction of electrons
• Known as Anode Rays or Canal Rays
• Discovered using Goldstein's Canal Ray Tube experiment
• Charge and Mass: 1.672 * 10^{-27} kg and +1.6 * 10^{-19} C

Neutron Discovery

• Discovered by James Chadwick by bombarding beryllium with alpha particles
• Neutral particle with a mass similar to protons: 1.675 * 10^{-27} kg

Atomic Models

Thomson's Model

• Plum pudding model: Electrons in positively charged 'pudding'

Rutherford's Model

• Gold foil experiment identified a dense positively charged nucleus
• Electrons revolve around the nucleus in circular orbits

Bohr's Model

• Electrons revolve in specific orbits with quantized energy levels
• Energy emitted or absorbed when electrons jump between orbits

Quantum Mechanical Model

• Developed to address limitations of Bohr’s Model
• Considers wave-particle duality of electrons
• Uses Schrödinger's wave equation to determine the probability distribution of electrons

Quantum Numbers

Principal Quantum Number (n)

• Describes the energy level of an electron in an atom
• Values: n = 1, 2, 3, ...

Azimuthal Quantum Number (l)

• Describes the shape of the orbital
• Values: l = 0, 1, 2, ... (n-1)

Magnetic Quantum Number (m)

• Describes orientation of the orbital within a subshell
• Values: m = -l to +l

Spin Quantum Number (s)

• Describes the spin of the electron
• Values: +1/2, -1/2

The Dual Nature of Electrons

De Broglie Hypothesis

• Particles such as electrons exhibit both wave and particle properties
• Wavelength (λ) = h / (mv)

Heisenberg Uncertainty Principle

• Impossible to simultaneously determine the exact position and momentum of an electron
• Δx * Δp ≥ h / (4π)

Electron Configuration

• Follow Aufbau principle (build-up rule): Electrons fill orbitals starting from the lowest energy level
• Pauli Exclusion Principle: No two electrons in an atom can have the same set of four quantum numbers
• Hund's Rule of Maximum Multiplicity: Electrons fill degenerate orbitals singly first, with parallel spins

Important Concepts and Formulas

Electron Discovery (J.J. Thomson)

• Charge of electron: -1.6 * 10^{-19} C
• Mass of electron: 9.1 * 10^{-31} kg

Proton Discovery (E. Rutherford/Goldstein)

• Charge of proton: +1.6 * 10^{-19} C
• Mass of proton: 1.673 * 10^{-27} kg

Neutron Discovery (James Chadwick)

• Neutral particle
• Mass of neutron: 1.675 * 10^{-27} kg

De Broglie's Wavelength Formula

• λ = h / (mv)

Heisenberg's Uncertainty Principle

• Δx * Δp ≥ h / (4π)

Aufbau Principle (Electron Configuration)

• Electrons populate orbitals starting from the lowest energy to higher energy

Hund's Rule

• Electron pairing in degenerate orbitals occurs after each orbital is singly occupied

Pauli Exclusion Principle

• No two electrons in an atom can have the same four quantum numbers