Atomic structure and quantized description

Atomic Structure & Numbers

Matter is built from atoms, featuring a dense nucleus of protons and neutrons surrounded by electrons in quantized energy levels. An electron's state is defined by four quantum numbers.

Electron configuration rules govern how these states fill:

• Aufbau principle: Fill lowest energy orbitals first.
• Pauli exclusion: No two electrons share all four quantum numbers.
• Hund's rule: Maximize unpaired spins within a subshell.

Models & Stoichiometry

In the Bohr model, electrons inhabit fixed paths with quantized angular momentum $L = n\hbar$ ($n = 1, 2, \ldots$). Transitions emit or absorb photons where $\Delta E = E_f - E_i$.

Key Relationships

• Amount of substance: $n = m/M$ ($m$ = mass, $M$ = molar mass).
• Avogadro's number: $N_A = 6.022\times 10^{23}\;\text{mol}^{-1}$.
• Ideal gas law: $PV = nRT$.
• Hydrogen energy: $E_n = -13.6/n^{2}\;\text{eV}$ (from the Schrödinger equation).

Common pitfall: Electron orbits are a cartoon. Orbitals are probability clouds, and transitions are instantaneous quantum jumps, not gradual spirals.