Question

The density of crystalline sodium chloride is 5.85 g cm. What is the edge length of the unit cell​

Answer 1

Answer:  The edge length is  $9.51\times 10^{-8} m$

Explanation:

NaCl has FCC structure

Number of atom in unit cell of FCC (Z) = 4

Density of $NaCl$ = $5.85 g/cm^3$

Edge length = a

Atomic mass of $NaCl$ (M) = 58.5 g/mol

Formula used :  

$\rho=\frac{Z\times M}{N_{A}\times a^{3}}$

where,

$\rho$ = density

Z = number of atom in unit cell

M = atomic mass

$(N_{A})$ = Avogadro's number  

a = edge length of unit cell

On substituting all the given values , we will get the value of 'a'.

$5.85 g/cm3=\frac{4\times 758.5g/mol}{6.022\times 10^{23} mol^{-1}\times a^{3}}$

$a =9.51\times 10^{-8}m$

The edge length is  $9.51\times 10^{-8} m$