A) consider a two-dimensional crystal made up of spherical atoms that are packedtogether as tightly as possible in a plane. show that the unit cell may be drawn as a hexagon with an atom in the center and atoms at each of the six corners. how many atoms are there per cell? (5 pts.) show that it is also possible to draw the unit cell as a parallelogram that has an empty center and atoms at each of its corners. how many atoms does this cell contain? how many unit cells of type (b) are contained within a single hexagonal cell of type ( pts.) consider a two-dimensional crystal that has a hexagonal unit cell with an empty center and atoms located at the corners of the hexagon. draw the atom positions generated by several neighboring cells. show that the unit cell used in part (b) is not a correct unit cell for this structure.(5 pts.) draw a proper set of lattice vectors for the structure in (c). indicate the basis vectors that are needed to complete the description of the structure. given your choice of lattice vectors, what atom group is repeated at each lattice point?