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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 six face centers. What is the formula of the compound? If side length is 5$A^{\large\circ}$, estimate the density of the solid assuming atomic weight of X and Y as 60 and 90 respectively.

1 Answer

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 $XY_3$.
As we know that, $\rho =\large\frac{n\times M_m}{N_A\times a^3}$ , here n = 1
Molar mass of $XY_3$
$M_m = 60 + 3 × 90 = 330$ gm
$\rho=\large\frac{1\times 330}{6.023\times 10^{23}\times (5\times 10^{-8})^3}$$gm/cm^3$
a = $5A^{\large\circ} = 5 × 10^{–8} $cm
$\Rightarrow \large\frac{330}{6.023\times 10^{23}\times 125\times 10^{-24}}$$gm/cm^3=4.38gm/cm^3$
Hence (B) is the correct answer.
answered Jun 2, 2014 by sreemathi.v

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