A solid is made up of two elements \(X\) and \(Y\). \(X\) occupies \(2/3\)rd of the octahedral voids and \(Y\) has ccp arrangement. What is the formula of the compound \(X\) and \(Y\)?

\(X_2Y_3\)

The correct answer is option 2. \(X_2Y_3\).

Let us break down the problem step by step to understand how the formula \(X_2Y_3\) is derived:

Y atoms: The problem states that element \(Y\) has a cubic close-packed (ccp) arrangement. In a ccp structure, there are 4 atoms of \(Y\) per unit cell.

X atoms: Element \(X\) occupies \(2/3\) of the octahedral voids in the structure.

In a ccp structure: For every atom of \(Y\) in the ccp arrangement, there is 1 octahedral void. So, with 4 \(Y\) atoms in the unit cell, there are also 4 octahedral voids.

Since \(X\) occupies \(2/3\) of the octahedral voids, the number of \(X\) atoms per unit cell is:

\(\text{Number of \(X\) atoms} = \frac{2}{3} \times 4 = \frac{8}{3} \approx 2.67\)

The ratio of the number of \(X\) atoms to \(Y\) atoms is approximately \(2.67 : 4\).

Simplifying this ratio by multiplying both terms by 3 to eliminate the fraction, we get:

\(2.67 \times 3 : 4 \times 3 = 8 : 12\)

Simplifying further:

\(\frac{8}{4} : \frac{12}{4} = 2 : 3\)

The simplified ratio gives us the formula \(X_2Y_3\), indicating that for every 2 atoms of \(X\), there are 3 atoms of \(Y\).

Therefore, the correct formula of the compound is \(X_2Y_3\).