Question

$A_{2}B$ molecules (molar mass =259.8 g/mol) crystallises in a hexagonal lattice as shown in figure. The lattice constants were $a=5\mathring{A}$ and $b=8\mathring{A}$. If density of crystal is 5 $g/c{m}^3$ then how many molecules are contained in given unit cell? (use $N_A=6\times {10}^{23}$)

• A. 6
• B. 4
• C. 3
• D. 2

Answer 1

The correct option is D 2

Volume of unit cell$=a^2\sin {60}^o\times b$

$=173.2\times {10}^{-24}$

$\Rightarrow a=5\stackrel{o}{A}$

Mass of unit cell= $173.2\times {10}^{-24}\times 5\times 6\times {10}^{23}=519.6g$

Number of molecules presenr in given cell= $\frac{519.6}{259.8}=2$ .