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In a crystalline solid, atoms of X form ...

In a crystalline solid, atoms of X form fcc packing and atoms of Y occupy all octahedral voids. If all the atoms along one body diagonal are removed, what is the simplest formula of the crystalline lattice solid?

Text Solution

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No. of A atoms `= 8xx(1)/(8)+6 xx(1)/(2)=4`
No. of atoms of B in octahedral void = 4
Along one body diagonal there are two A atoms and one B atoms
No. of effective atoms of A after removal `= 4-2xx(1)/(8)=(15)/(4)`
No. of effective atoms of B after removal `= 4-1=3`
`A : B = (15)/(4) : 3 = 5 : 4`
`therefore` Simplest formula `= A_(5)B_(4)`
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