Radii of `A` and that of `X` and `Y` have been given as
`A = 1.00` pm
`X = 1.00` pm
`Y = 2.00` pm
Thus ratio of volume of AX and AY unit cells is

Options

A. `17.54`
B. `0.057`
C. `1.0`
D. `0.217`

Answer

b

Explanation

Ratio of `r^(+)//r^(-)` will docide the type of unit cell
For `AX= (r_(A))/(r_(X)) = (1)/(1) = 1.0` hence `AX` has fcc structuture
`2(r_(A) + r_(X)) - = asqrt(3)`
`a = (2)/(sqrt(3)) (r_(A^(+)) + r_(X^(-)))`
`= 2 xx (2)/(sqrt(3)) = (4)/(sqrt(3)` pm
Volume `= a^(2) = ((4)/(sqrt(3)))^(2) = (64)/(3sqrt(3)`
For `AY = (r_(A))/(r_(I)) = (1)/(2) = 0.5`
Thus, for octahdral or square plase structure
`r =(1)/(2)`
`a = 2r = 2(r_(A)^(-) + r_(I-)) = 2(1 + 2) = 6` pm
Volume `(AY) = a^(2) = 216 pm^(1)`
`"Ratio" = ("Volume"(AX))/("Volume"(AY)) = (64)/(3sqrt(3) xx 218) = 0.057`