Question

A hypothetical AX type of ceramic material is known to have a density of 2.65 g/cm3 and a unit cell of cubic symmetry with a cell edge length of 0.43 nm. The atomic weights of the A and X elements are 86.6 and 40.3 g/mol, respectively. On the basis of this information, which of the following crystal structures is (are) possible for this material:
a. rock salt
b. cesium chloride
c. zinc blende
Justify your choice(s)

Answer 1

Answer: is Cesiun Chloride

Explanation:

Given

●density (ρ) = 2.65 g/cm3

● unit cell has cubic symmetry with edge length (VC) =0.43 nm =4.3 × 10-8 cm

● A atomic weights (AC)= 86.6g/mol

● X atomic weights (AA)= 40.3g/mol

Using Equation

ρVC NA

 n' = --------------------

∑ AC + ∑ AA 

Where

NA is avogadro's number = 6.022 x 10^23

(2.65 g/cm3)[(4.30 × 10^-8 cm)3/unit cell ](6.022 × 10^23 formula units/mol)

= ________________________

(86.6 + 40.3) g/mol 

= 1.00 formula units/unit cell  

only cesium chloride has one formula unit per unit cell

While zinc blende is 4 formula unit per unit cell and rock salt is 0.695 formula unit per unit cell