A compound formed by elements X and Y crystallizes in the cubic structure where X is at the corners of the cube and Y is at the 6 face centres if the length is 5A° estimate the density of the solid asuming atomic weight of X and Y as 60 and 90 respectively

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Solution

Solution: From eight corner atoms one atoms (X) contributes to one unit cell.

From six face centres, three atoms (Y) contributes to one unit cell.

So, the formula of the compound is XY3.

As we know that,

p = n × Mm / NA × a3 =, here n = 1

Molar mass of XY3

Mm = 60 + 3 × 90 = 330 gm

p = 1×330 / 6.023 ×1023 × (5×10–8)3 gm/cm3

a = 5Å = 5 × 10–8 cm

= 330 / 6.023 ×1023 × 125 × 10–24 gm/cm3 = 4.38 gm / cm3

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