B.Sc. 1st Semester Chemistry: Atomic Structure Complete Notes
Welcome to the complete study guide for Atomic Structure (Unit-I). These notes are designed to help you master your B.Sc. Semester 1 syllabus while building a rock-solid foundation for future competitive exams like CSIR-NET, RPSC, and JET.
Table of Contents
1. Classical Atomic Theory & Its Downfall
Review of Bohr’s Theory
Niels Bohr proposed that electrons revolve around the nucleus in specific, allowed circular orbits with quantized angular momentum (mvr = nh/2π). Electrons do not radiate energy while in these stationary states.
Limitations of Bohr’s Theory
- Multi-electron atoms: It only successfully explains the single-electron hydrogen spectrum.
- Zeeman & Stark Effects: It cannot explain the splitting of spectral lines in magnetic (Zeeman) or electric (Stark) fields.
- Wave Nature: It treats electrons strictly as particles.
- Uncertainty: It assumes precise, predictable orbits, directly violating the Heisenberg Uncertainty Principle.
2. The Foundations of Quantum Mechanics
Dual Behaviour of Matter (de Broglie’s Relation)
Just as light exhibits both wave-like and particle-like properties, Louis de Broglie proposed that matter also possesses this dual nature. Any moving particle has an associated wavelength (λ):
Heisenberg Uncertainty Principle
It is fundamentally impossible to simultaneously determine both the exact position (Δx) and the exact momentum (Δp) of a microscopic particle.
3. The Schrödinger Equation & Wave Functions
Erwin Schrödinger developed a mathematical equation to describe the wave-like behavior of electrons. Using the Hamiltonian operator (Ĥ), it is written as:
Significance of ψ and ψ2
- ψ (Psi): The wave function of the electron. It is an amplitude function with no direct physical significance.
- ψ2 (Probability Density): The probability of finding an electron in a specific, small volume of space around the nucleus. It is always a positive value.
4. Quantum Numbers, Orbitals & Nodes
Solving the Schrödinger equation yields a set of numbers that completely describe the energy and location of an electron.
| Quantum Number | Symbol | Describes |
|---|---|---|
| Principal | n | Main energy level (shell) and size. |
| Azimuthal | l | Subshell and 3D shape (s, p, d, f). |
| Magnetic | ml | Spatial orientation of the orbital. |
| Spin | ms | Spin state of the electron (+1/2 or -1/2). |
Shapes of Atomic Orbitals & Nodal Planes
- s-orbitals (l=0): Spherical, non-directional. 0 angular nodes.
- p-orbitals (l=1): Dumbbell-shaped (px, py, pz). 1 angular node (nodal plane).
- d-orbitals (l=2): Double-dumbbell shaped (except dz2). 2 angular nodes.
Total Nodes Formula: n - 1
5. Electronic Configuration & Stability
Rules for Filling Orbitals
- Aufbau Principle: Electrons fill the lowest energy orbitals first.
- Pauli’s Exclusion Principle: An orbital can hold a maximum of two electrons with opposite spins.
- Hund’s Rule of Maximum Multiplicity: Degenerate orbitals must be singly occupied with parallel spins before pairing begins.
Stability of Half-Filled and Completely Filled Orbitals
Configurations like p3, d5 (half-filled) and p6, d10 (completely filled) are exceptionally stable due to:
- Symmetrical Distribution: Minimizes electron-electron repulsion.
- High Exchange Energy: Electrons with parallel spins can exchange positions, releasing energy and increasing stability (e.g., Chromium and Copper anomalies).
Effective Nuclear Charge (Zeff)
Outer electrons do not feel the full positive charge of the nucleus due to the shielding effect of inner electrons. Zeff = Z - S (where Z is atomic number, S is shielding constant).
