Question

If solid $X$ atoms goes to the corners of the cube and two alternate face centers, calculate the effective number of atoms of $X$ in a unit cell?

Answer 1

Given,
Solid $X$ is shared by all corners of the cube. According to the lattice theory, each corner shares only $\frac{1}{8}$ atom and each cube has $8$ corners which gives a total of $1$ atom.
It is also shared by alternate faces. As we know, each face contains $\frac{1}{2}$ atom. So, calculating alternatively, we get a total of $1$ atom.
Therefore, we get the effective number of atoms of $X$ in a unit cell as $2$.