Question

In the lithium iodide crystal, the Li-I distance is \(3.02 \AA\) Calculate the iodide radius, assuming that the iodide ions are in contact.

Short answer

The iodide radius in a Lithium Iodide crystal is 226 pm.

Step-by-step solution

Conversion of Li-I distance to a common unit

First, convert the Li-I distance from \(\AA\) to picometers (pm), because the radius of an atom is typically expressed in pm. To do this, recall that \(1 \AA = 100 \, pm\). Hence, the Li-I distance is \(3.02 \, \AA \times 100 = 302 \, pm\).

Calculation of Iodide Radius

Next, subtract the radius of the Lithium ion from the Li-I distance to find the Iodide radius. The generally accepted radius of a Lithium ion is 76 pm. Therefore, the Iodide radius would be \(302 \, pm - 76 \, pm = 226 \, pm\). This means the radius of the Iodide ion in a lithium iodide crystal is 226 pm.

Key concepts

Crystal Structure

A crystal structure is essentially the arrangement of atoms or ions within a crystal. It's like a 3D blueprint showing how the particles are organized. Imagine stacking spheres in a way that they closely fit together, forming a specific and repeating pattern. In crystals, such as lithium iodide, the ions are arranged in a specific geometric pattern.
The arrangement of these ions affects the chemical and physical properties of the substance. Different types of crystal structures exist, each with a unique formation.

• Think of it like a team coordination strategy where each team member, or ion in this case, has a specific place and role.
• This organization maximizes stability and minimizes energy use, making the crystal structurally sound.

Understanding crystal structures helps chemists predict how compounds behave and interact with each other. That's how scientists know properties like melting points or hardness.

Lithium Iodide

Lithium iodide (\( ext{LiI} \)) is a chemical compound that forms when lithium and iodine come together. In its solid state, lithium iodide takes on a crystal structure. This compound is interesting because it's made up of positively charged lithium ions and negatively charged iodide ions.
The interaction between these ions keeps the crystal structure intact. It's like a dance where each partner knows its step, both contributing to the stability of the system.
Lithium iodide is often used in various applications like electrolytes in batteries and optical materials. Its properties as a solid are largely determined by the arrangement of its ions in the crystal structure. This arrangement significantly impacts its use in technology and industry. From electrical properties to mechanical strength, lithium iodide showcases the importance of crystal structure in material science.

Atomic and Ionic Size

The size of atoms and ions plays a crucial role in how substances function and react. Atomic size is the distance from the atom's nucleus to the boundary of the surrounding cloud of electrons.
Ionic size, however, changes when an atom loses or gains electrons. When an atom becomes an ion, its size might increase or decrease. For instance, a lithium ion is smaller than a lithium atom because it loses an electron.

• In a crystal lattice like that of lithium iodide, these sizes are key because they affect how closely ions can pack together.
• The lithium ion size can influence the overall crystal structure's dimensions and properties.

Understanding atomic and ionic sizes helps us predict interactions between different elements and compounds, impacting everything from solubility to conductivity.

Unit Conversion

Unit conversion is a standard practice in science, allowing measurements to be expressed in different units while maintaining their value. It helps make calculations easier and more universal.
For sizes like atomic or ionic radii, the most common unit is the picometer (\( ext{pm} \)). Although Ångström (\( ext{Å} \)) units are sometimes used, converting between these units is straightforward. This is useful because it standardizes measurements, easing communication and calculations.
For example:

• 1 Ångström = 100 picometers
  Converting \( 3.02 ext{Å} \) to picometers, we get \( 302 ext{pm} \).
  
• Easily converting units is crucial for accurately applying measurements in scientific contexts.

Accurate unit conversion ensures that scientists use a common language, crucial for collaborations and understanding across different scientific disciplines.