Periodic Properties of the Elements

Elemental Patterns and the Periodic Law

The periodic table organizes elements according to recurring patterns in their physical and chemical properties. These patterns, known as periodic properties, allow scientists to predict the behavior of elements and even the existence of undiscovered elements. For example, the density of elements increases as you move down a column, reflecting an increase in the mass-to-volume ratio of atoms.

• Periodic property: A property that exhibits a repeating pattern across periods or groups in the periodic table.

• Example: Aluminum (Al) has a lower density (2.70 g/cm3) compared to indium (In) (7.31 g/cm3), and both belong to the same group.

The Periodic Law and the Development of the Periodic Table

In the nineteenth century, scientists observed that arranging elements by increasing atomic mass revealed recurring patterns in their properties. Dmitri Mendeleev formulated the periodic law, stating that when elements are arranged in order of increasing mass, certain sets of properties recur periodically. Mendeleev's arrangement allowed for the prediction of undiscovered elements and their properties.

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

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

The Modern Periodic Table: Structure and Classification

The modern periodic table arranges elements by increasing atomic number (number of protons), not atomic mass. Rows are called periods, and columns are called groups or families. Elements in the same group have similar properties. The table is divided into metals, nonmetals, and metalloids, as well as main-group elements, transition metals, and inner transition metals.

• Groups (families): Vertical columns with elements of similar properties.

• Periods: Horizontal rows.

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

• Transition/inner transition metals: Properties are less predictable.

Electron Configuration and Quantum Theory

Electron Configuration: Arrangement of Electrons in Atoms

Quantum-mechanical theory describes electrons as existing in orbitals, and the arrangement of these electrons is called the electron configuration. The solution to Schrödinger’s equation for hydrogen shows that electrons fill the lowest energy orbitals first. For multi-electron atoms, electron-electron interactions, electron spin, and energy splitting of sublevels must be considered.

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

• Orbitals: Regions of space where electrons are likely to be found (s, p, d, f).

Electron Spin and the Pauli Exclusion Principle

Each electron has a property called spin, which can be either +1/2 or -1/2. The Pauli exclusion principle states that no two electrons in an atom can have the same set of four quantum numbers, so each orbital can hold a maximum of two electrons with opposite spins.

• Spin quantum number (ms): +1/2 or -1/2.

• Paired electrons: Opposite spins, diamagnetic (not attracted to a magnetic field).

• Unpaired electrons: Paramagnetic (attracted to a magnetic field).

Energy Splitting and the Aufbau Principle

In multi-electron atoms, sublevels split in energy due to electron shielding and penetration. The order of filling is determined by the aufbau principle: electrons fill orbitals from lowest to highest energy. The general order is:

Writing Electron Configurations

Electron configurations are written by listing the occupied orbitals and the number of electrons in each. For example, the configuration for germanium (Ge) is:

Or, using noble gas notation:

Shielding, Penetration, and Effective Nuclear Charge

Coulomb’s Law and Shielding

Coulomb’s law describes the attraction and repulsion between charged particles. In multi-electron atoms, electrons are attracted to the nucleus but repelled by other electrons, leading to shielding. The effective nuclear charge (Zeff) is the net positive charge experienced by an electron.

• Shielding: Core electrons shield valence electrons from the full nuclear charge.

• Penetration: The ability of an electron to get close to the nucleus; s orbitals penetrate more than p, d, or f.

• Effective nuclear charge: (Z = nuclear charge, S = shielding constant)

Periodic Trends in Atomic Properties

Atomic Radius

The atomic radius is the average distance from the nucleus to the outermost electrons. It can be measured as the van der Waals radius (nonbonding), covalent radius (bonding), or metallic radius. Atomic radius decreases across a period (left to right) due to increasing effective nuclear charge, and increases down a group due to the addition of energy levels.

• Trend across a period: Decreases (increased Zeff pulls electrons closer).

• Trend down a group: Increases (more energy levels, electrons farther from nucleus).

Ionization Energy

Ionization energy (IE) is the energy required to remove an electron from an atom in the gas phase. The first ionization energy refers to removing the first electron. IE increases across a period and decreases down a group. Exceptions occur due to sublevel energies and electron repulsions.

• Trend across a period: Increases (higher Zeff).

• Trend down a group: Decreases (electrons farther from nucleus).

• Exceptions: Between groups 2A/3A and 5A/6A due to sublevel and pairing effects.

Electron Affinity

Electron affinity (EA) is the energy change when an atom gains an electron. A more negative EA means the atom more readily accepts an electron. EA generally becomes more negative across a period and is most negative for halogens. Trends down groups are less regular.

• Trend across a period: Becomes more negative (except groups 2A, 5A, 8A).

• Trend down a group: Becomes less negative for group 1A.

Metallic Character

Metallic character describes how closely an element's properties match those of metals (malleable, ductile, good conductors, low ionization energy). Metallic character increases down a group and decreases across a period.

• Trend across a period: Decreases (nonmetals to the right).

• Trend down a group: Increases (metals at the bottom).

Summary Table: Periodic Trends

Key Terms and Concepts

• Periodic Law: Properties of elements recur in a regular pattern when arranged by increasing atomic number.

• Electron Configuration: The arrangement of electrons in an atom's orbitals.

• Shielding: Reduction in effective nuclear charge on an electron due to other electrons.

• Penetration: The extent to which an electron can approach the nucleus.

• Effective Nuclear Charge (Zeff): Net positive charge experienced by an electron.

• Ionization Energy: Energy required to remove an electron from an atom.

• Electron Affinity: Energy change when an atom gains an electron.

• Metallic Character: How closely an element's properties match those of a metal.