Question

The distance between any two tetrahedral voids formed on any body diagonal of a closest packed structure is $x\times a$, where a is the edge length of closest packed structure.
The value of $x$ is :

• A. $\frac{1}{3}$
• B. $\frac{1}{2}$
• C. $2$
• D. $\frac{3}{2}$

Answer 1

The correct option is B $\frac{1}{2}$

If $a$ is the edge length of the cube, then the length of the body diagonal will be $\sqrt{3}a$.
On one body diagonal, two tetrahedral holes are present.
The distance between these two tetrahedral holes is $\frac{1}{2}$.