Question

A crystal is made of particles A and B. A forms FCC packing and B occupies all the octahedral voids. If all the particles along the plane as shown in figure are removed, then the formula of the crystal would be :
A. `A_(5)B_(7)`
B. `A_(7)B_(5)`
C. `AB`
D. `AB_(3.75)`

Answer 1

4A long from corner and 2A ions from face center (PR and Qs are removed)
2B ions from edge center (PQ and RS) and one ion from body center are removed.
`therefore` Number of A ions removed.
`=4xx(1)/(8)` (corner share) `+2xx(1)/(2)` (face center share) `=(1)/(2)+1=1(1)/(2)`.
Number of B ions removed.
`=2xx(1)/(4)` (edge center share) `+(1)/(1)`
(body center share) `=(1)/(2)+1=1(1)/(2)`.
Number of A ions left `=4-1(1)/(2)=2.5`
Number of B ions left `=4-1(1)/(2)=2.5`
Thus, formula`=A_(2.5)B_(2.5)=2.5AB`
Simplest formula=AB.