Introduction
Chemistry begins with the atom, and modern atomic structure cannot be understood without quantum mechanics. This chapter sets the foundation for the entire subject: how electrons are arranged determines bonding (Chapter 8 onward), reactivity, and the periodic trends that organise all of inorganic and organic chemistry.
1. Wave nature of matter and basic quantum concepts
Just as de Broglie proposed that matter has an associated wavelength (λ = h/p, covered in Physics Chapter II), electrons in atoms must be described as standing waves rather than particles on fixed orbits. This wave nature is the reason electron energies in atoms are quantized — only specific “standing wave” patterns around the nucleus are self-consistent, analogous to only certain wavelengths fitting a vibrating string.
2. The Schrödinger equation and interpretation of the wavefunction
Solving the time-independent Schrödinger equation for an electron in the Coulomb potential of a nucleus gives both the allowed energy levels and the corresponding wavefunctions (orbitals). The wavefunction, ψ, has no direct physical meaning itself, but |ψ|² gives the probability density of finding the electron at a given point — chemists visualise orbitals as three-dimensional probability clouds rather than fixed paths.
3. Quantum numbers and atomic orbitals
Each orbital is labelled by three quantum numbers arising naturally from solving the equation: principal (n = 1, 2, 3…, determines overall size/energy), azimuthal (l = 0 to n−1, determines shape: l=0 is s, spherical; l=1 is p, dumbbell-shaped; l=2 is d, more complex), and magnetic (mₗ, determines orientation in space). A fourth, spin (mₛ = ±½), comes from relativistic quantum mechanics and distinguishes the two electrons that can occupy any one spatial orbital.
4. Electronic configuration and the governing principles
Electrons fill orbitals according to three rules: the Aufbau principle (lowest-energy orbitals fill first), the Pauli exclusion principle (no two electrons in an atom share all four quantum numbers, so each orbital holds at most two electrons, with opposite spin), and Hund’s rule (electrons occupy separate orbitals of equal energy singly, with parallel spins, before pairing up — this minimises electron–electron repulsion). Together these rules generate the electronic configurations (e.g., 1s² 2s² 2p⁶…) that determine an atom’s chemical behaviour.
5. Hydrogen-like atoms, many-electron atoms, and periodic trends
The Schrödinger equation can be solved exactly only for one-electron (“hydrogen-like”) systems; many-electron atoms require approximations because electrons repel each other as well as being attracted to the nucleus. Nonetheless, the resulting shell structure explains the major periodic trends:
- Atomic radius decreases across a period (increasing nuclear charge pulls electrons in more tightly) and increases down a group (additional electron shells).
- Ionization energy (energy to remove an electron) generally increases across a period and decreases down a group, for the same reasons, with some exceptions caused by extra stability of half-filled or fully-filled subshells.
- Electronegativity (an atom’s tendency to attract shared electrons in a bond) follows similar trends and underlies bond polarity, discussed further in inorganic and organic bonding chapters.
Key Takeaways
- Electrons in atoms are described by wavefunctions (orbitals) rather than fixed classical orbits; |ψ|² gives the probability of finding the electron at a location.
- Four quantum numbers (n, l, mₗ, mₛ) specify each electron’s state; the Aufbau principle, Pauli exclusion principle, and Hund’s rule together determine how electrons fill orbitals in an atom.
- Periodic trends in atomic radius, ionization energy, and electronegativity follow directly from how effectively increasing nuclear charge and additional electron shells balance each other across the periodic table.