If the length of the body diagonal of a FCC unit cell is \( x \, \text{Å} \), the distance between two octahedral voids in the cell in \( \text{Å} \) is:
Show Hint
In FCC crystals, the relationship between the body diagonal and the edge length is \( \text{Body Diagonal} = \sqrt{3} \cdot \text{Edge Length} \). This can be used to compute the distance between voids.
In a face-centered cubic (FCC) unit cell, octahedral voids occupy the body center and edge centers. The distance between two such voids is calculated as follows:
Step 1: The length of the body diagonal is determined by:
\[
x = \sqrt{3}a,
\]
where \( a \) represents the edge length of the unit cell.
Step 2: The edge length \( a \) can be expressed in terms of the body diagonal length \( x \) as:
\[
a = \frac{x}{\sqrt{3}}.
\]
Step 3: The distance between two octahedral voids lies along the body diagonal. Given their positions at the body center and edge centers, this distance is:
\[
\text{Distance} = \frac{a}{\sqrt{2}}.
\]
Substituting the expression for \( a \) from Step 2:
\[
\text{Distance} = \frac{\frac{x}{\sqrt{3}}}{\sqrt{2}} = \frac{x}{\sqrt{3} \cdot \sqrt{2}} = \frac{x}{\sqrt{6}}.
\]
Final Answer:
\[
\boxed{\frac{x}{\sqrt{6}}}
\]