Atomic Structure and Properties

• Atomic number (Z) = protons = electrons (neutral atom)
• Mass number (A) = protons + neutrons
• Isotopes: same Z, different A
• Mass spectrometry determines isotopic abundances and average atomic mass

$\text{Average atomic mass} = \sum(\text{mass}_i \times \text{fractional abundance}_i)$

Filling order: $1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s...$

Rules: Aufbau principle, Hund's rule, Pauli exclusion principle.

Examples:

• C (Z=6): $1s^2 2s^2 2p^2$
• Fe (Z=26): $[\text{Ar}] 3d^6 4s^2$
• Cu (Z=29): $[\text{Ar}] 3d^{10} 4s^1$ (exception)

Ion configurations: remove from highest principal quantum number first.

• Fe²⁺: $[\text{Ar}] 3d^6$

PES measures the binding energies of all electrons in an atom.

• X-axis: binding energy (decreasing left to right)
• Y-axis: relative number of electrons
• Each peak corresponds to a subshell
• Height of peak = number of electrons in that subshell
• Position = binding energy (how tightly held)

Higher binding energy = closer to nucleus = harder to remove.

Explaining Trends

Coulomb's law: $F = k\frac{q_1 q_2}{r^2}$

Applied to atoms: the force on a valence electron depends on:

• Effective nuclear charge ($Z_{eff}$): nuclear charge minus shielding
• Distance from the nucleus (atomic radius)

Across a period: $Z_{eff}$ increases, radius decreases → stronger attraction → higher IE Down a group: more shells → larger radius → weaker attraction → lower IE

IE Anomalies

• Be → B: 2p electron is higher energy than 2s
• N → O: paired electron in 2p experiences repulsion

• Electron configuration follows Aufbau, Hund's, and Pauli rules
• PES provides direct evidence for subshell electron structure
• Periodic trends explained by $Z_{eff}$ and atomic radius (Coulomb's law)
• IE anomalies: subshell energy (s→p) and electron pairing effects