Enter the charge number and the number of electrons into the calculator to determine the ionic radius of an ion. The ionic radius is an estimate of the size of an ion in a crystal lattice.

Ionic Radius Formula

The following formula is used to calculate the ionic radius. 

IR = 0.34 * (N^{(1/3)}) / (Z^{(1/2)})

Variables:

  • IR is the ionic radius (picometers, pm)
  • Z is the charge number of the ion
  • N is the number of electrons in the ion

To calculate the ionic radius, multiply the cube root of the number of electrons by 0.34, then divide by the square root of the charge number.

What is Ionic Radius?

The ionic radius is a measure of the size of an ion’s electron cloud when the ion is part of a crystal lattice. It varies with the ion’s charge, the number of electrons, and the arrangement of the surrounding ions in the lattice. The ionic radius is crucial for understanding the properties of ionic compounds, including their stability, solubility, and melting points.

How to Calculate Ionic Radius?

The following steps outline how to calculate the Ionic Radius.

  1. First, determine the charge number (Z) of the ion.
  2. Next, determine the number of electrons (N) in the ion.
  3. Use the formula IR = 0.34 * (N^(1/3)) / (Z^(1/2)) to calculate the ionic radius (IR).
  4. Finally, calculate the Ionic Radius (IR) in picometers (pm).
  5. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

Charge number (Z) = 2

Number of electrons (N) = 18