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(C) In a $ccp$ lattice,let the number of $Y$ atoms be $N = 4$. Number of octahedral voids $= N = 4$. Number of tetrahedral voids $= 2N = 8$. Atoms of

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$50$

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(C) In a $ccp$ lattice,let the number of $Y$ atoms be $N = 4$. Number of octahedral voids $= N = 4$. Number of tetrahedral voids $= 2N = 8$. Atoms of $X$ occupy $50\%$ of octahedral voids $= 0.5 	imes 4 = 2$. Atoms of $X$ occupy $x\%$ of tetrahedral voids $= \frac{x}{100} 	imes 8 = 0.08x$. Total atoms of $X = 2 + 0.08x$. Given formula is $X_3Y_2$,so the ratio $X:Y = 3:2$. Since $Y = 4$,$X = \frac{3}{2} 	imes 4 = 6$. $2 + 0.08x = 6$ $\Rightarrow 0.08x = 4$ $\Rightarrow x = 50$. Percentage of occupied tetrahedral voids $= 50\%$. Percentage of unoccupied tetrahedral voids $= 100 - 50 = 50\%$.

The molecular formula of a crystalline solid is $X_3Y_2$. Atoms of $Y$ form $ccp$ lattice,and atoms of $X$ occupy $50\%$ octahedral voids and $x\%$ of tetrahedral voids. What is the percentage of unoccupied tetrahedral voids?

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