#### The concentration of Schottky defects in a crystal with a density of $6.022 \times 10^{28} m^{-3}$ is ;Option: 1 $1.661 \times 10^{18} \mathrm{~m}^{-3}$Option: 2 $6.022 \times 10^{22} \mathrm{~m}^{-3}$Option: 3 $1.661 \times 10^{22} \mathrm{~m}^{-3}$Option: 4 $6.022 \times 10^{18} m^{-3} \mid$

The concentration of Schottky defects  can be calculated using the formula:$C_s=\frac{n}{N} \mathrm{C}_{-} \mathrm{s}=\mathrm{n} / \mathrm{N}$where $n$ is the number of Schottky defects and $N$  is the total number of lattice sites.

The density of the crystal $(p)$ can be calculated using the formula:

$p=N \times \frac{m}{V}$, where m is the mass of one unit cell and $V$ is the volume of one unit cell.

The number of lattice sites $(N)$ can be calculated using the formula:

$N=p \times \frac{V}{m}$

Substituting the value of $N$ in the formula for $C_s$, we get:

$C_s=\frac{n}{\left(p \times \frac{V}{m}\right)}$

Rearranging the above equation, we get:

$n=C_s \times p \times \frac{V}{m}$

Substituting the given values, we get:

$n=\frac{1}{2} \times 6.022 \times 10^{28} \times 1.58 \times 10^{-29} \times \frac{\left(5.642 \times 10^{-10}\right)^3}{\left(6.023 \times 10^{23}\right)}$

$n=1.661 \times 10^6$

Therefore, the concentration of Schottky defects is

$1.661 \times 10^{18} m^{-3}$