Ionic Radii Calculator

What is an Ionic Radius?

An ionic radius is simply the size of an ion in a crystal. When atoms gain or lose electrons to become ions, their size changes. Positive ions (cations) are usually smaller than their original atoms, while negative ions (anions) are typically larger. Understanding these sizes is crucial for predicting how ions will pack together to form solid materials, like salts and minerals.

The size of an ion is influenced by several factors:

• Atomic Number: More protons in the nucleus pull electrons closer, generally making ions smaller across a period.
• Charge State: A higher positive charge (more electrons lost) means a smaller ion, as the remaining electrons are pulled more tightly. A higher negative charge (more electrons gained) means a larger ion due to increased electron repulsion.
• Coordination Number: This is the number of ions directly surrounding a central ion in a crystal. A higher coordination number (more neighbors) can slightly increase the apparent ionic radius.
• Electronic Configuration: The arrangement of electrons in shells affects the overall size.
• Spin State (for transition metals): For certain metals, how electrons fill orbitals can also impact their ionic size.

Trends in Ionic Radii on the Periodic Table

Ionic radii follow predictable patterns across the periodic table:

• Across a Period (Left to Right): For ions with the same charge, the ionic radius generally decreases. This is because as you move right, the number of protons in the nucleus increases, pulling the electrons closer to the center.
• Down a Group (Top to Bottom): The ionic radius generally increases. This happens because as you go down a group, new electron shells are added, making the ion larger.
• Isoelectronic Series: These are groups of ions and atoms that have the same number of electrons (e.g., O²⁻, F⁻, Na⁺, Mg²⁺ all have 10 electrons). In such a series, the radius decreases with increasing nuclear charge (more protons pull the same number of electrons tighter). For example, Mg²⁺ is smaller than Na⁺.
• Effect of Charge: Cations (positive ions) are always smaller than their parent atoms, and the more positive the charge, the smaller the ion (e.g., Fe³⁺ is smaller than Fe²⁺). Anions (negative ions) are always larger than their parent atoms, and the more negative the charge, the larger the ion (e.g., S²⁻ is larger than Cl⁻).

The Radius Ratio Rule and Crystal Geometry

The radius ratio rule is a simple but powerful concept that helps predict the arrangement of ions in an ionic crystal. It's calculated by dividing the radius of the smaller ion (usually the cation, r⁺) by the radius of the larger ion (usually the anion, r⁻): Radius Ratio = r⁺ / r⁻.

This ratio helps determine the coordination number (how many ions surround a central ion) and the resulting crystal geometry (the shape formed by these surrounding ions):

• Radius Ratio > 0.732: The central ion can be surrounded by 8 other ions, forming a cubic arrangement (8-coordinate).
• 0.414 - 0.732: The central ion can be surrounded by 6 other ions, forming an octahedral arrangement (6-coordinate).
• 0.225 - 0.414: The central ion can be surrounded by 4 other ions, forming a tetrahedral arrangement (4-coordinate).
• < 0.225: The central ion can be surrounded by 3 other ions, forming a triangular arrangement (3-coordinate).

This rule is a useful guide for understanding the packing efficiency and stability of ionic compounds.