1: Atomic structure and quantum theory

Section 1: Core Principles - 1: Atomic Structure and Quantum Theory

Understanding the atom's structure and the quantum theory governing its behaviour is fundamental to chemistry. Early models evolved significantly: Dalton proposed indivisible atoms; Thomson discovered electrons within a "plum pudding" model; Rutherford's gold foil experiment revealed the dense, positively charged nucleus surrounded by mostly empty space. However, classical physics couldn't explain atomic stability or observed phenomena like atomic emission spectra.

This led to the Bohr model (1913), which postulated electrons orbiting the nucleus in fixed, quantized energy levels. Electrons absorbing energy jump to higher levels; falling back emits light at specific frequencies, explaining line spectra (e.g., hydrogen Balmer series). While revolutionary, Bohr's model failed for multi-electron atoms and couldn't account for orbital shapes or finer spectral details.

The resolution came with quantum mechanics in the 1920s. Key principles include:

• Wave-Particle Duality (de Broglie): Electrons (and all matter) exhibit both particle-like and wave-like properties. The wavelength relates to momentum ($p$) by $\lambda = h/p$ ($h$ = Planck's constant).
• Heisenberg Uncertainty Principle: It's impossible to simultaneously know both the exact position and momentum of an electron. This defines inherent limits in measurement.
• Schrödinger Wave Equation: This mathematical equation describes the electron's wavefunction ($\Psi$), which contains all information about the electron's energy and probable location within an atom. Solving it for the hydrogen atom provides the foundation.

Solutions to the Schrödinger equation introduce quantum numbers defining electron orbitals:

1. Principal Quantum Number ($n$): Energy level/shell ($n = 1, 2, 3...$), determines orbital size and average distance from the nucleus.
2. Angular Momentum Quantum Number ($l$): Subshell/shape ($l = 0$ to $n-1$). $l=0$ (s, spherical), $l=1$ (p, dumbbell), $l=2$ (d), $l=3$ (f).
3. Magnetic Quantum Number ($m_l$): Orientation of the orbital in space ($m_l = -l$ to $+l$, including 0). Defines specific orbitals within a subshell (e.g., three p orbitals: $p_x$, $p_y$, $p_z$).
4. Spin Quantum Number ($m_s$): Intrinsic spin direction of the electron ($+\frac{1}{2}$ or $-\frac{1}{2}$).

The Pauli Exclusion Principle states no two electrons in an atom can have the same set of all four quantum numbers, limiting orbital occupancy to two electrons with opposite spins. Hund's Rule dictates that electrons fill degenerate orbitals (same $n$ and $l$) singly with parallel spins before pairing. These rules govern electron configuration, the distribution of electrons among orbitals (e.g., Oxygen: $1s^2 2s^2 2p^4$), which underpins chemical properties and periodic trends.