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key points to crake this question : First of all we have to calculate tetrahedral voids present in this lattice , because as we know that the number of tetrahedral voids = 2 x number of atoms present in lattice. now calculate the number of atoms present and then calculate the ratio atoms of M and N because the chemical formula represents the number of atoms present in compound and there ration creates the compound formula. After that we can easily calculate the chemical formula of compound in which M and N will present.

Solution :

Let us suppose the number of atoms of element N which are present in CCP (Cubic Closed Packing) = x

Then the number of tetrahedral voids will be = 2x

Given that the 1/3rd of the tetrahedral voids are occupied by atoms of element M.

It means we can say that –

number of atoms of element M are = 2x /3

now what we have find here :

N = x

M = 2x /3

the the ratio of M and N = 2x/3 : x = 2 : 3

hence the formula of compound on given conditions is = M2N3

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