A cubic solid is made up of two elements X and Y. Atoms of X are present on every alternate corner and one at the center of cube. Y is at $$\frac{1}{3}$$rd of the total faces. The empirical formula of the compound is

A cubic solid is made up of two elements X and Y. We need to find the empirical formula.

X is present on every alternate corner and one at the center of the cube.

A cube has 8 corners. Every alternate corner means 4 corners are occupied by X.

Contribution from corners = $$4 \times \dfrac{1}{8} = \dfrac{1}{2}$$

Contribution from body center = $$1$$

Total X per unit cell = $$\dfrac{1}{2} + 1 = \dfrac{3}{2} = 1.5$$

Y is at $$\dfrac{1}{3}$$rd of the total faces.

A cube has 6 faces. $$\dfrac{1}{3} \times 6 = 2$$ face-centered positions are occupied by Y.

Contribution from face centers = $$2 \times \dfrac{1}{2} = 1$$

Total Y per unit cell = $$1$$

X : Y = 1.5 : 1 = 3 : 2

The empirical formula is $$\text{X}_3\text{Y}_2$$ or equivalently $$\text{X}_{1.5}\text{Y}$$.

The correct answer is Option B: $$\text{X}_{1.5}\text{Y}$$.