Question

silver iodide has the same structure as zinc sulfide, and its density is 5.67g/cm^3. the edge length of the unit cell is

Answer 1

Answer:

The unit cell edge length is $6.50\times 10^{-8} m$

Explanation:

ZnS has FCC structure. and so is the AgI.

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

Density of AgI= $5.67 g/cm^3$

Edge length = a

Atomic mass of AgI (M) = 234.77 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'.

$5.76 g/cm3=\frac{4\times 234.77 g/mol}{6.022\times 10^{23} mol^{-1}\times a^{3}}$

$a = 6.50\times 10^{-8} m$

The unit cell edge length is $6.50\times 10^{-8} m$