# The unit cell length of sodium chloride crystal is 564 pm. What is its density?

Answer: $2.16 \times 10^6 \; gm^{-3}$
The density is given by the formula $\large\frac{z\;M}{a^3\;N_A}$
Given $a = 564 \;ppm$.
Each unit cell of NaCl has 4 Na$^{-}$ and 4 Cl$^{-}$ ions $\rightarrow z = 4$
Avagadro's number $N_A = 6.022 \times 10^{23} /\; mol$
The total mass of NaCl $= 22.99 + 34.34 = 58.5\; g/mol$
$\Rightarrow$ Density $\rho =\large\frac{z\;M}{a^3\;N_A}$$= \large\frac{4 \times 58.5 }{(564\times10^{-12})^3\;6.022 \times 10^{23}}$$\; gm^{-3} \approx 2.16 \times 10^6 \; gm^{-3}$