Lecture Notes on Atomic Structure and Quantum Mechanics

Definition and Nature of an Atom

• Atom: The smallest particle of an element that retains the properties of that element.
• Periodic Table: Contains elements like sodium, oxygen, etc. An atom of an element like oxygen retains all properties of oxygen.

Composition of an Atom

• Neutrons: No charge (neutral).
• Protons: Positively charged.
• Electrons: Negatively charged.
• In a neutral atom, the number of electrons equals the number of protons.
• Mass Number: Represents the number of protons and neutrons.
• Atomic Number: Represents the number of protons.

Structure of an Atom

• Nucleus: Contains protons and neutrons.
• Electron Shells: Surround the nucleus; contain electrons.
• Electrons in shells closer to the nucleus have less energy compared to those farther away.
• Electron Configuration: The distribution of electrons across different shells.

Electron Configuration

• Electron Shells: First shell (max 2 electrons), second shell (max 8 electrons), etc.
• Formula: 2n² for maximum electrons per shell.
• Example: Sodium with atomic number 11 has electron configuration 1s² 2s² 2p⁶ 3s¹.

Bohr's Atomic Model

• Nucleus: Small and positively charged.
• Electrons: Surround the nucleus in shells (energy levels).
• Electrons farther from the nucleus have more energy.
• Energy Levels: Represented by integers (n = 1, 2, 3, etc.). The lowest energy level (n=1) is the ground state.
• Electron Transitions: Movement between energy levels requires energy gain or loss.

Wave Properties of Electrons

• Wave: A repetitive disturbance that carries energy.
• Wavelength (λ): Distance between successive identical points of a wave.
• Amplitude: Maximum displacement from the neutral position.
• Frequency (ν): Number of repetitions per second.
• Wave Number: Reciprocal of wavelength (1/λ).
• Relationship: ν = c/λ where c is the speed of light.

Planck’s Quantum Theory

• Energy (E): Emitted or absorbed in discrete quantities (quanta).
• Photon Energy: E = hν where h is Planck's constant.
• Planck's Constant (h): 6.626 x 10⁻³⁴ J·s.

Photoelectric Effect

• Emission of electrons from metal surfaces when light strikes them.
• Threshold Frequency: Minimum frequency required for electron emission.
• Intensity and Frequency: Above threshold frequency, electron emission increases with light intensity.
• Kinetic Energy (K.E.): K.E. = hν - hν₀ (ν₀ is the threshold frequency).

Particle-Wave Duality

• Dual Nature: Light exhibits both wave and particle characteristics.
• de Broglie Wavelength (λ): λ = h / (mv) where m = mass, v = velocity.

Hydrogen Spectrum

• Emission Spectra: Discrete frequencies of radiation emitted by excited hydrogen atoms.
• Series: Lyman (UV), Balmer (Visible), Paschen, Brackett, Pfund (Infrared).
• Rydberg Equation: 1/λ = R (1/n₁² - 1/n₂²) where R is Rydberg constant.

Electron Configuration Using Orbitals

• Orbitals: Regions where electrons are likely to be found (s, p, d, f).
• Max Electrons: s (2), p (6), d (10), f (14).
• Order: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, etc.
• Noble Gas Configuration: Shortened form using noble gases as references (e.g., [Ne] 3s² for Mg).

Quantum Numbers

• Principal Quantum Number (n): Energy level (1, 2, 3, ...).
• Angular Momentum Quantum Number (l): Shape of the orbital (0, 1, 2, ... up to n-1).
• Magnetic Quantum Number (ml): Orientation of the orbital (-l to +l).
• Spin Quantum Number (ms): Direction of the electron spin (+½ or -½).
• Pauli Exclusion Principle: No two electrons in an atom can have the same set of four quantum numbers.

Exceptions in Electron Configuration

• Chromium and Copper: More stable with half-filled or fully filled d orbitals.
• Example: Chromium ([Ar] 4s¹ 3d⁵) and Copper ([Ar] 4s¹ 3d¹⁰).

Uncertainty Principle

• Heisenberg's Uncertainty Principle: Impossible to precisely measure both position and momentum of a particle simultaneously.