Question

A compound formed by atoms A and B crystallises in the cubic structures. The atoms A occupy the corners while atoms Y the face-centres of the cube. Find the formula of the compound. If the side length is 5 Å, calculate the density of the solid. (Atomic masses: A = 60, B = 90.)

Answer 1

Number of atoms A per unit cell = `8 xx 1/8 = 1`

Number of atoms B per unit cell = `6 xx 1/2 = 3`

Hence, the formula of the compound = AB₃, and the unit cell contains one unit of AB₃, i.e., Z = 1.

For the given system,

Z = 1

a = 5 Å

= 5 × 10⁻⁸ cm

M = 60 + 90 × 3

= 330

Therefore, the density of the solid 

`rho =(Z xx M)/(a^3 xx N_A)`

= `(1 xx 330)/((5 xx 10^-8)^3 xx 6.022 xx 10^23`

= `(330)/(125 xx 10^-24 xx 6.022 xx 10^23`

= `(330)/(752.75 xx 10^-1)`

= `330/75.275`

= 4.38 g cm⁻³