Question

$A_{2}B$ molecules (molar mass $=259.8$ g/mol ) crystallizes in a hexagonal lattice.The lattice constants are $a=5$ $\mathring{A}$ and $b=8$ $\mathring{A}$. If the density of crystal is $5$ g cm${}^{-3}$, then how many molecules are contained in a 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 $2$

As we know,
Density $=\frac{nM}{V{N}_0}$ , where $n$ is the number of atoms per unit cell.

$n=\frac{dV{N}_0}{M}=\frac{5V\times 6.023\times {10}^{23}}{259.8}=2$