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

#### Solution 1

The ccp lattice is formed by the atoms of the element N.

Here, the number of tetrahedral voids generated is equal to twice the number of atoms of the element N.

According to the question, the atoms of element M occupy 1/3 rd of tetrahedral voids.

Therefore, the number of atoms of M is equal to `2 xx 1/3 = 2/3` rd of the number of atoms of N

Therefore, ratio of the number of atoms of M to that of N is M: N = `2/3 : 1` = 2:3

Thus, the formula of the compound is M_{2} N_{3}.

#### Solution 2

Atoms of N from ccp, therefore, if the lattice points are n, then

No . of atoms of N = n

No. of oct voids = n

No. of td voids = 2n= 2 x 1n/3 = 2n/3

∴ Formula of compound is: M : N

2/3 n : n

2n: 3n

2: 3

i.e., M_{2}N_{3}