Summary

This chapter replaced the simple, purely classical picture of an atom with the quantum mechanical model that chemistry actually uses.

Bohr's model first correctly predicted the hydrogen line spectrum by quantising the electron's angular momentum ($mvr = nh/2\pi$) and postulating stationary, non-radiating orbits, with a photon emitted or absorbed exactly matching the energy difference between orbits ($\Delta E = h\nu$). It fails, however, for any atom with more than one electron, cannot explain fine spectral structure or the Zeeman/Stark effects, and -- most fundamentally -- assumes a fixed, precisely known orbit that directly contradicts the uncertainty principle.

Shells and subshells. Each shell (principal quantum number $n$) is divided into subshells ($l = 0$ to $n-1$, labelled s, p, d, f), each subshell made of one or more orbitals.

Wave-particle duality and uncertainty. De Broglie's relation $\lambda = h/mv$ shows every moving particle has an associated wavelength, confirmed experimentally for electrons by the Davisson-Germer diffraction experiment. Heisenberg's uncertainty principle, $\Delta x \cdot \Delta p \geq h/4\pi$, shows that an electron's exact position and momentum can never both be known -- ruling out Bohr's fixed orbits and motivating a probabilistic description instead.

The Schrödinger equation and orbitals. Solving $\hat{H}\psi = E\psi$ gives wave functions $\psi$ (orbitals) whose square, $\psi^2$, gives the probability of finding the electron at a point in space -- replacing Bohr's orbit with a three-dimensional probability distribution.

Quantum numbers $n$ (shell/energy), $l$ (subshell/shape), $m_l$ (orbital orientation) and $m_s$ (electron spin, $\pm\tfrac{1}{2}$) together specify every electron in an atom uniquely. Orbital shapes follow directly from $l$: spherical for s, dumbbell-shaped for p, and mostly four-lobed (with $d_{z^2}$ as the exception, having two lobes plus a torus) for d. …