Which arrangement is most suitable for the uniform packing of atoms in a layer?

In a compound,nitrogen atoms $(N)$ make a cubic close-packed lattice and metal atoms $(M)$ occupy one-third of the tetrahedral voids present. Determine the formula of the compound formed by $M$ and $N$.

$A$ solid is made of two elements $X$ and $Y$. Atoms of $X$ are in $FCC$ arrangement and $Y$ atoms occupy all tetrahedral sites. What is the possible formula of the compound?

What is the type of hole occupied if the limiting value of $\frac{r+}{r-}$ is in the range of $0.225$ to $0.414$?

Find the number of tetrahedral voids per atom in a crystal lattice.

The maximum radius of a sphere that can be fitted in the octahedral hole of a cubical closed packing of spheres of radius $r$ is $..............$ $r$.