Lithium chloride crystallizes in a face-centered cubic structure.The unit cell length is 5.14 × 10^-8 cm.The chloride ions are touching each other along the face diagonal of the unit cell.The lithium ions fit into the holes between the chloride ions.What is the radius of the chloride ion?

Question

Quizplus · Accepted Answer

In a face-centered cubic structure, the face diagonal is equal to $4r$, where $r$ is the radius of the ions assuming they are touching each other. The face diagonal can also be calculated using the unit cell length ($a$) by the formula $\sqrt{2}a$. Given that $a = 5.14 \times 10^{-8}$ cm, the face diagonal is $\sqrt{2} \times 5.14 \times 10^{-8}$ cm. Solving for $r$, we get $r = \frac{\sqrt{2} \times 5.14 \times 10^{-8}}{4}$ cm, which simplifies to approximately $1.82 \times 10^{-8}$ cm.

Lithium Chloride Crystallizes in a Face-Centered Cubic Structure