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A hypothetical AX type of ceramic material is known to have a density of 3.15 g/cm3 and a unit cell of cubic symmetry with a cell edge length of 0.41 nm. The atomic weights of the A and X elements are 90.5 and 37.3 g/mol, respectively. On the basis of this information, which one of the following crystal structures is possible for this material?

a. Sodium chloride
b. Cesium chloride
c. Zinc blende

Sagot :

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Answer:

b.

Explanation:

From the given information:

[tex]p = \dfrac{zM}{N_oa^3}[/tex]

where;

a = 0.41 nm = [tex]4.1 \times 10^{-8} \ cm[/tex]

M = 90.5 + 37.3 = 127.8 g/mol

[tex]N_o = 6.023 \times 10 ^{23}[/tex]

p = 3.15 g/cm³

∴

[tex]3.15 = \dfrac{z \times 127.8}{(6.02 \times 10^{23}) \times (4.1 \times 10^{-8} )^3}[/tex]

Z = 1

Thus, the ceramic material has a simple cubic crystal system and the crystal structure is possible to be Cesium chloride.

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