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Question


The cubic unit cell structure of a compound containing cation M and anion X is shown below. When compared to the anion, the cation has a smaller ionic radius. Choose the correct statement(s).

A
The empirical formula of the compound is MX.
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B
The cation M and anion X have different coordination geometries.
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C
The ratio of MX bond length to the cubic unit cell edge length is 0.866.
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D
The ratio of the ionic radii of cation M to anion X is 0.414.
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Solution

The correct option is C The ratio of MX bond length to the cubic unit cell edge length is 0.866.
According to the given diagram, the structure seems to be BCC.

(1) Empirical formula MX

(2) Coordination number of M ion =8 [same co-ordination geometry]
Coordination geometry of X ion = 8 [same co-ordination Geometry]


(3) MX Bond Length =  (a2)2+(a2)2

MX Bond Length=a=14+12
MX bond lengtha(edge length)=32a=0.866

(4) As it is BCC.

rx+rm=32a

0.732rm+rx<1


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