Question

Atoms of element X form hcp lattice and those of element Y occupy `2/3` of its tetrahedral voids. The percentage of element X in the lattice is ______ (Nearest integer).

Answer 1

Atoms of element X form hcp lattice and those of element Y occupy `2/3` of its tetrahedral voids. The percentage of element X in the lattice is 43% (Nearest integer).

Explanation:

Given: Element X forms an hcp lattice.

Element Y occupies `2/3` of the tetrahedral voids.

We are to find the percentage of element X in the resulting solid.

In any close-packed structure (like hcp or fcc) Number of tetrahedral voids = 2 × number of atoms of element X

So, if the number of atoms of element X = 1,

The number of tetrahedral voids = 2

= Number of Y atoms = `2/3 xx 2`

= `4/3`

Total atoms in the compound = X + Y

= `1 + 4/3`

= `7/3`

Percentage of X = `1/(7/3) xx 100`

= `3/7 xx 100`

= 42.86 ≈ 43%