A compound consists of element A and B. It crystallises in a cubic crystal structure with unit cell having A atoms at the corners of the cell and B atom at the face centres of the cell. If the edge-length of the unit cell is 5Å, and the atomic masses of A and B are 60 and 90 respectively, then calculate the density of the compound.

Explanation

Formula of the compound: No. of A atoms per unit cell = `8xx1/8=1` & no. of B atoms per unit cell = `6xx1/2=3`
Therefore, ratio of A and B atoms = 1 : 3
Hence, the formula of the compound = `AB_(3)`
`therefore" "`Molar mass of the compound = `(60+3xx90)g*mol^(-1)`
`=330g*mol^(-1)`
Number of formula unit of `AB_(3)` per unit cell = 1
Hence, mass of a unit cell = `(1xx330)/(6.022xx10^(23))=5.48xx10^(-22)g`
Volume of the unit cell = `a^(3)=(5xx10^(-8))^(3)=125xx10^(-24)cm^(3)`
`therefore" "`Density of the unit cell = `(5.48xx10^(-22))/(125xx10^(-24))=4.384g*cm^(-3)`
`therefore" "`Density of the compound = `4.384g*cm^(-3)`