Packing efficiency

Atoms of metals x, y, and z form face-centred cubic (fcc) unit cell of edge length $L_x$, body-centred cubic (bcc) unit cell of edge length $L_y$, and simple cubic unit cell of edge length $L_z$, respectively.

If $r_z = \dfrac{\sqrt3}{2}r_y$; $r_y = \dfrac{8}{\sqrt3}r_x$; $M_z = \dfrac32 M_y$ and $M_z = 3M_x$, then the correct statement(s) is(are)

[Given: $M_x$, $M_y$, and $M_z$ are molar masses of metals x, y, and z, respectively. $r_x$, $r_y$, and $r_z$ are atomic radii of metals x, y, and z, respectively.]

Atom X occupies the fcc lattice sites as well as alternate tetrahedral voids of the same lattice. The packing efficiency (in %) of the resultant solid is closest to

For the given close packed structure of a salt made of cation $\mathbf X$ and anion $\mathbf Y$ shown below (ions of only one face are shown for clarity), the packing fraction is approximately $\left(\text{packing fraction} = \dfrac{\text{packing efficiency}}{100}\right)$

The cubic unit cell structure of a compound containing cation M and anion X is shown below. When compared to the anion, the cation has smaller ionic radius. Choose the correct statement(s).

The CORRECT statement(s) for cubic close packed (ccp) three dimensional structure is(are)

The arrangement of $\ce{X-}$ ions around $\ce{A+}$ ion in solid AX is given in the figure (not drawn to scale). If the radius of $\ce{X-}$ is 250 pm, the radius of $\ce{A+}$ is

The packing efficiency of the two-dimensional square unit cell shown below is

The volume of this HCP unit cell is

The empty space in this HCP unit cell is