Respuesta :
Explanation:
For AX type ceramic material, the number of formula per unit cells is as follows.
[tex]\rho = \frac{n'(A_{c} + A_{A})}{V_{C}N_{A}}[/tex]
or, [tex]n' = \frac{\rho a^{3}N_{A}}{(A_{c} + A_{A})}[/tex]
where, n' = no. of formula units per cell
[tex]A_{c}[/tex] = molecular weight of cation = 90.5 g/mol
[tex]A_{a}[/tex] = molecular weight of anion = 37.3 g/mol
[tex]V_{c}[/tex] = volume of cubic cell = 3.55 [tex]g/cm^{3}[/tex]
a = edge length of unit cell = [tex]3.9 \times 10^{-8} cm[/tex]
[tex]N_{A}[/tex] = Avogadro's number = [tex]6.023 \times 10^{23}[/tex]
[tex]\rho[/tex] = density = 3.55 [tex]g/cm^{3}[/tex]
Now, putting the given values into the above formula as follows.
[tex]n' = \frac{\rho a^{3}N_{A}}{(A_{c} + A_{A})}[/tex]
= [tex]\frac{3.55 g/cm^{3} \times (3.9 \times 10^{-8})^{3} \times 6.023 \times 10^{23}}{(90.5 + 37.3)}[/tex]
= 0.9
= 1 (approx)
Therefore, we can conclude that out of the given options crystal structure of cesium chloride is possible for this material.
