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

Last updated date: 13th Jun 2024
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Hint: The structure of metals can be explained when atoms are packed together. The atoms in metals are considered as spheres of identical size. Close packing is the most efficient arrangement of spheres of identical size and to fill available spaces in which each sphere touches six neighboring spheres.

The number of atoms in face-centered cubic unit cell, ${\text{Z = 4}}$
So the number of tetrahedral voids $= 2{\text{Z}} = 8$
According to the question, ${\text{N}} \to {\text{4}}$ and ${\text{M}} \to \dfrac{1}{3} \times 8 = \dfrac{8}{3}$
Thus the formula will be ${{\text{N}}_4}{{\text{M}}_{\dfrac{8}{3}}}$.
So we have to convert the subscripts to whole numbers. So multiply with three on both, we get ${{\text{N}}_{12}}{{\text{M}}_8}$
On simplifying, we get the formula of the compound as ${{\text{N}}_3}{{\text{M}}_2}$