Chapter 3: Periodic Properties of the Elements – Structured Study Notes

Periodic Properties of the Elements

Elemental Patterns and the Periodic Law

The periodic law describes the recurring patterns in the physical and chemical properties of elements, which are fundamental for predicting the behavior of undiscovered elements and understanding elemental properties.

• Periodic Property: A property that exhibits a repeating pattern across the periodic table, such as density, atomic radius, and ionization energy.

• Example: Density increases as you move down a column in the periodic table, as seen in the comparison between aluminum (Al) and indium (In).

• Mass-to-volume ratio: Increases down a column, contributing to higher density.

To be periodic means to exhibit a repeating pattern.

Discovery and Organization of the Periodic Table

In the nineteenth century, scientists observed that certain groups of elements had similar properties when arranged in order of increasing mass. Mendeleev summarized these observations in the periodic law:

• Periodic Law: When elements are arranged in order of increasing mass, certain sets of properties recur periodically.

• Mendeleev’s Table: Organized elements so that those with similar properties fell within the same vertical columns, leaving gaps for undiscovered elements.

• Prediction: Mendeleev predicted the existence and properties of elements such as eka-silicon (later discovered as germanium).

The Modern Periodic Table

The modern periodic table lists elements in order of increasing atomic number, not mass. Rows are called periods, and columns are called groups or families. Elements in a group have similar properties.

• Main-group elements: Properties are largely predictable based on position.

• Transition and inner transition elements: Properties are less predictable.

• Quantum theory: Explains why periodic patterns occur.

Electron Configuration and Quantum Theory

Electron Configuration: How Electrons Occupy Orbitals

Quantum-mechanical theory describes the behavior of electrons in atoms. Electrons exist in orbitals, and their arrangement is described by the electron configuration.

• Electron configuration: The distribution of electrons among the orbitals of an atom.

• Schrödinger’s equation: For hydrogen, the electron occupies the lowest energy orbital.

• Multi-electron atoms: Electron–electron interactions complicate the solution, but orbitals remain hydrogen-like.

Electron Spin and the Pauli Exclusion Principle

Electron spin is a fundamental property, quantized as either +½ or −½. The Pauli exclusion principle states that no two electrons in an atom can have the same set of four quantum numbers.

• Spin quantum number (ms): Describes electron spin direction.

• Orbital diagrams: Use half-arrows to represent electron spins.

• Paired spins: Diamagnetic (no net magnetic field).

• Unpaired spins: Paramagnetic (net magnetic field).

Sublevel Energy Splitting and the Aufbau Principle

In multi-electron atoms, sublevels split in energy due to charge interaction, shielding, and penetration. Electrons fill orbitals from lowest to highest energy (Aufbau principle).

• Degenerate orbitals: Orbitals with the same energy.

• Energy order: $E(s) < E(p) < E(d) < E(f)$

• Hund’s Rule: Electrons occupy degenerate orbitals singly before pairing.

Shielding, Penetration, and Effective Nuclear Charge

Electrons experience both attraction to the nucleus and repulsion from other electrons. Shielding reduces the net attraction, and penetration describes how close an electron can get to the nucleus.

• Effective nuclear charge (Zeff): The net positive charge felt by an electron.

• Shielding: Inner electrons block the attraction from the nucleus.

• Penetration: s orbitals penetrate more than p, d, or f orbitals.

• Formula: $Z_{\text{eff}} = Z - S$

Electron Configuration and the Periodic Table

Core and Valence Electrons

Electrons in lower-energy shells are called core electrons, while those in the highest principal energy shell are valence electrons. Valence electrons determine chemical and physical behavior.

• Valence electrons: Participate in bonding and ion formation.

• Core electrons: Do not participate in bonding.

Orbital Blocks and Periodic Table Organization

The periodic table is divided into four blocks (s, p, d, f) based on the filling of quantum sublevels. The group number of a main-group element equals its number of valence electrons; the row number equals the highest principal quantum number.

Transition and Inner Transition Metals

Transition metals (d block) and inner transition metals (f block) exhibit trends differing from main-group elements. Sublevel splitting causes anomalies in electron configurations, often requiring experimental determination.

• Example: Cr, Mo, Cu, Ag have irregular electron configurations.

Periodic Trends and Elemental Properties

Effective Nuclear Charge and Periodic Trends

Effective nuclear charge increases across a period and decreases down a column. s orbitals shield better than p, d, or f orbitals.

Atomic Radii

Atomic radius is the average distance from the nucleus to the outermost electron. It decreases across a period and increases down a group.

• Van der Waals radius: Nonbonding radius.

• Covalent radius: Bonding radius.

Periodic Trends: Atomic Radii in Main-Group and Transition Elements

Atomic size increases down a group due to higher principal quantum numbers. Across a period, increased effective nuclear charge pulls electrons closer, decreasing size. Transition metals show less variation across the d block.

Magnetic Properties of Ions

Atoms or ions with unpaired electrons are paramagnetic (attracted to a magnetic field), while those with all paired electrons are diamagnetic (slightly repelled).

Radii of Atoms and Their Ions

Cations are smaller than their neutral atoms due to increased effective nuclear charge after electron loss. Anions are larger than their neutral atoms due to increased electron–electron repulsion.

Ionization Energy

Ionization energy is the minimum energy required to remove an electron from an atom in the gas phase. It decreases down a group and increases across a period.

• First ionization energy: Energy to remove the first electron.

• Successive ionization energies: Increase as more electrons are removed.

Exceptions to Ionization Energy Trends

Exceptions occur between groups 2A and 3A, and 5A and 6A, due to differences in orbital type and electron repulsion.

Electron Affinity

Electron affinity is the energy change associated with adding an electron to an atom. It generally becomes more negative across a period, with halogens having the highest electron affinity.

Metallic Character

Metallic character describes how closely an element’s properties match those of a metal. It decreases across a period and increases down a group.

Summary of Elemental Periodic Properties

The periodic table organizes elements by recurring properties, explained by quantum theory and electron configuration. Understanding these trends is essential for predicting chemical behavior.