A hypothetical ceramic, Marylandium Oxide $($MdO$),$ has a $3\mathrm{.}5\frac{g}{c}m3$ density and a cubic unit cell with a cell edge length of $0\mathrm{.}396$

nm $.$ The Md and O atomic weights are $19\mathrm{.}9$ and $13\mathrm{.}0\frac{g}{m}ol,$ respectively.

$(10$ points$)$What crystal structure$($s$)$ is$($are$)$ possible for this material: rock salt, cesium chloride, or zinc blende? Explain your

answer, showing calculations as appropriate.

$(10$ points$)$ If Marylandium's ionic radius is $0\mathrm{.}056$ nm $,$ what is the crystal structure of MdO? Explain your answer, showing

calculations as appropriate. $($Hint: Oxygen's ionic radius is $0\mathrm{.}140$ nm $)$

$(10$ points$)$ Draw the arrangement for the ions on the $(110)$ plane, showing where the ions touch $($if they touch$)$ in the MdO

structure. Mark allclose$-$packed directions and label them with the appropriate Miller$-$Bravais directional indices.