A compound formed by elements X & Y. Crystallizes in the cubic structure, where X is at the corners of the cube and Y is at the six face centres. What is the formula of the compound? If side length is `5A^(@)`, estimate the density of the solid assuming atomic weight of X and Y as 60 and 90 respectively.

Explanation

From eight corner atoms one atoms `(X)` contribute to one unit cell.
From six face centers, three atoms `(Y)` contribute to one unit cell.
So, the formula of the compound is `XY_(3)`.
As we know that,
`rho =(n xx M_(m))/(N_(A) xx a^(3))`, here `n=1`
Molar mass of `XY_(3)`
`M = 60 + 3 xx 90 = 330` gm
`a = 5Å = 5 xx 10^(-8)` cm
`rho =(1 xx 330)/(6.023 xx 10^(23) xx (5 xx 10^(-8))^(3)) gm//cm^(3)`
`rho =(330)/(6.023 xx 10^(23) xx 125 xx 10^(-24)) gm//cm^(3) = 4.38 gm //cm^(3)`