JEE Main · 2023 · 25 Jan 2023 · Shift 1 · Solid State

In the cubic unit cell X sits on the alternate corners and at the body centre. The four alternate corners contribute $4\times \frac{1}{8}=\frac{1}{2}$ and the body-centre atom contributes $1$, so the amount of X is $\frac{1}{2}+1=\frac{3}{2}$. Y occupies two-thirds of the six faces, that is four face-centres, each shared between two cells, giving $4\times \frac{1}{2}=2$. The atom ratio is $X:Y=\frac{3}{2}:2$, so the empirical formula is $X_{1.5}{Y}_2$.