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 :

Options

A. `A_(5)B_(7)`
B. `A_(7)B_(5)`
C. `AB`
D. `AB_(3.75)`

Explanation

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.