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Question

A certain solid has a structure in which X atoms are located at the corners of the cubic cell, O at the edge centres and Y at the body centres. Then the formula of the cell is XaYbOc.
If O atoms are missing from any two edge centres per unit cell, the formula is XxYyOz.
Find the value of (a+b+c)+(x+y+z).

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Solution


a=18×8=1
b=1×1=1
c=14×12=3
Then the formula of the cell is X1Y1O3.
When O is missing from any two edge centre, total of 10 atoms are left. So here x=a, y=b, and z=14×10=2.5
We get Molecular formula as XYO2.5
Since the molecular formula can never be a fraction, so multiply it by 2.
Now Molecular formula becomes as X2Y2O5 and
(a+b+c)+(x+y+z)=14

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