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A compound is formed by two elements, M and N . The element N forms CCP and atoms of M occupy $\large\frac{1}{3}$ rd of tetrahedral voids . What is the formula of the compound?

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Solution :
Suppose atoms of element N present in $CCP= x$
Number of tetrahedral voids $=2x$
Since $\large\frac{1}{3} $ rd of the tetrahedral voids are occupied by atoms of element M.
Number of atoms of elements $M= \large\frac{1}{3}$$\times 2x$
$\qquad= \large\frac{2x}{3}$
Ratio of $M:N=\large\frac{2x}{3}$$:x$
$\qquad=2:3$
Hence the formula of the compound $= M_2N_3$
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