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A solid compound contains X,Y and Z at...

A solid compound contains X,Y and Z atoms in a cubic lattice with x atom occupying the corners Y atoms in the body centred positions and Z atoms at the centres of faces of the unit cell . What is empirical formula of the compound ?

A

a) `XY_(2)Z_(3)`

B

b) `XYZ_(3)`

C

c) `X_(2)Y_(2)Z_(3)`

D

d) `X_(8)YZ_(6)`

Text Solution

Verified by Experts

The correct Answer is:
B
Since atom X is present at corner and one corner is shared by eight unit cells ,
Number of X atoms per unit cell `=(1)/(8)xx8=1`
Atom Y is present at body centred position and used by only one unit cell .So ,
number of Y atoms per unit cell =1
Atom Z is present at rhe centre of each face , so shared by two unit cell ,
thus number of Z atoms per unit cell `=(1)/(2)xx6=3` ,br> Hence , the formula of compound `=XYZ_(3)`
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