Question

A compound of formula $A_2{B}_3$ has the hcp lattice. Which atom forms the hcp lattice and what fraction of tetrahedral voids is occupied by the other atoms?
(JEE Main 2019)

• A. $\text{hcp lattice - B,}\frac{2}{3}\text{Tetrahedral voids- A}$
• B. $\text{hcp lattice - A,}\frac{2}{3}\text{Tetrahedral voids- B}$
• C. $\text{hcp lattice - B,}\frac{1}{3}\text{Tetrahedral voids- A}$
• D. $\text{hcp lattice - A,}\frac{1}{3}\text{Tetrahedral voids- B}$

Answer 1

The correct option is C $\text{hcp lattice - B,}\frac{1}{3}\text{Tetrahedral voids- A}$

$A_2{B}_3\text{has hcp lattice}$ If $A$ form hcp, then $\frac{3}{4}$ of tetrahedral void must occupied by B to form $A_2{B}_3$. If $B$ form hcp, then $\frac{1}{3}$ of tetrahedral void must occupied by $A$ to form $A_2{B}_3$.