The crystal structure of a compound consisting of atoms M and N shows that it has a cubic-packed array of N atoms, with M atoms occupying one-third of the tetrahedral voids. Determine the formula of the compound.

Explanation

In the crystal structure of a compound consisting of M and N atoms, N atoms are present in cubic close-packed array and M atoms present in one-third of tetrahedral voids.
Thus, number of N atoms per unit cell = 4
`therefore` The number of tetrahedral voids = `4xx2=8`
Hence, number of M atoms per unit cell = `8xx1/3=8/3`
Thus, the ratio of M and N atoms per unit cell
`=8/3:4=2:3`
Therefore, the formula of the compound will be `M_(2)N_(3)`.