In simple cubic lattice the side of the solid structure is equal to twice the radius of atom. Hence the correct answer is simple cubic.

The packing efficiency of both types of close packed structure is 74%, i.e. 74% of the space in hcp and ccp is filled. The hcp and ccp structure are equally efficient; in terms of packing. The packing efficiency of simple cubic lattice is 52.4%. And the packing efficiency of body centered cubic lattice (bcc) is 68%.

The constituent particles i.e. atoms, molecules and ions are assumed to be spheres.

Let the radius of the octahedral void be r and radius of the atoms in close-packing be R and the edge length be a.

In the right angle triangle ABC,

AB = BC = a

For the diagonal AC,

Using Pythagoras Theorem we get;

Also, 

And, AB = 2R

AC = R + 2r + R = 2R + 2r
∴
r = 0.414R

Hence, the relation is r = 0.414R.

A tetrahedral void is formed when one sphere or particle is placed in the depression formed by three particles.
Definition of Tetrahedral Void: The vacant space or void among the four constituent particles having tetrahedral arrangement in the crystal lattice is called tetrahedral void.

• Magnesium has hexagonal close-packed (HCP) crystal structure.
• Bonding is non-directional metallic bonding.
• Magnesium is metallic solid. The units occupying lattice sites are Mg ions and these ions are surrounded by mobile or delocalised electrons.
• The arrangement of ions in one plane the arrangement of ions is a hexagonal array or closed packed layer. Thus each metal ion is touching six adjacent ions in one plane.

AC = Diameter of void + (2× Radius of sphere) 》AC = 2r + 2R = 2(R+r)

HCP = 74% packing efficiency
BCC = 68% packing efficiency
Simple cubic = 52.4% packing efficiency 

In ccp structure: number of atoms per unit cell is

► 8 corners × 1/8 per corner atom = 8 × 1/8 = 1 atom
► 6 face-centred atoms × 1/2 atom per unit cell = 3 atoms
Therefore, the total number of atoms in a unit cell = 4 atoms.

For a bcc unit cell, number of atoms per unit cell = (8 *1/8) + 1 = 2