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In a compound, nitrogen atoms (N) make c...

In a compound, nitrogen atoms (N) make cubic close packed lattice and metal atoms (M) occupy one-third of the tetrahedral voids present. Determine the formula of the compound formed by M and N?

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Suppose, number of N-atoms in ccp structure = x. So, no. of tetrahedral voids in the ccp structure = 2x. Now, 1/3rd of the tetrahedral voids are occupied by M-atoms. Hence, number of M-atoms in the close-packed structure = `2/3x`. Therefore, ratio of M and N-atoms per unit cell of the crystal = `2/3x:x=2:3" "therefore` Formula of the compound is `M_(2)N_(3)`.
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