Chemistry Basics – Advanced Study Notes
MIT‑Level Treatment from First Principles
(Target Audience: UPTET – General Awareness & Current Affairs)
Why Chemistry Still Matters
- Energy: Lithium‑ion, solid‑state, and flow batteries.
- Environment: Green chemistry, CO₂ capture, circular economy.
- Health: Vaccines, diagnostics, drug design.
- Materials: 2‑D materials, perovskites, MOFs.
These notes trace the subject from the sub‑atomic world to the macroscopic phenomena that shape modern society, offering rigorous derivations, edge‑case discussions, and a challenging problem to test your understanding.
1. Atomic Structure & Quantum Mechanics
| Concept | Key Equations | Remarks |
|---|---|---|
| Subatomic particles | Proton (p^+), Neutron (n^0), Electron (e^-) | Mass: (m_p \approx 1.6726\times10^{-27},\text{kg}); (m_e \approx 9.1094\times10^{-31},\text{kg}). |
| Quantum numbers | (n, \ell, m_\ell, m_s) | Principal, azimuthal, magnetic, spin. |
| Schrödinger Equation (time‑independent) | (\hat H \psi = E \psi) | (\hat H = -\frac{\hbar^2}{2m}\nabla^2 - \frac{Ze^2}{4\pi\varepsilon_0 r}) for hydrogenic atoms. |
| Electron configurations | Aufbau, Pauli, Hund | ([n\ell^{(2\ell+1)}]) notation. |
| Periodic trends | Ionization energy, electron affinity, electronegativity | Derived from quantum numbers and effective nuclear charge (Z_\text{eff}). |
1.1 From Schrödinger to Energy Levels
For the hydrogen atom: [ E_n = -\frac{Z^2 m_e e^4}{2(4\pi\varepsilon_0)^2 \hbar^2 n^2} = -\frac{13.6,\text{eV} \cdot Z^2}{n^2}. ]
Derivation Sketch
- Solve radial part (R_{n\ell}(r)) using spherical harmonics.
- Apply boundary conditions at (r=0,\infty).
- Quantization emerges from the requirement that the wavefunction be normalizable.
1.2 Edge Cases
| Case | Phenomenon | Why it’s an exception |
|---|