Solids structures occur in 3-D lattices, where instead of single molecules there are numerous formula units stuck together in a close packing formation in base units called unit cells. While there are numerous unit cells options for solids to form in, we will focus on the cubic unit cells. For the cubes below to show where atoms are located for the following cubic unit cells: How much of a corner atom is in a single unit cell? How much of an atom in the body of a unit cell is inside the cell? How much of an atom in the face of a unit cell is inside the cell? How many atoms make up each cell? Simple cubic: bcc: fcc: In math classes, we learn a lot of theories and manipulations of numbers to solve equations. These skills are tools that can be applied in other disciplines at the correct time. This is one of those times. We will use the Pythagorean theory: a2+b2=c2 Consider the face-centered cubic structure shown here: a. What is the length of the line (labeled c) that runs diagonally across one of the faces of the cube in terms of r (the atomic radius)? b. Use the answer to part a and the Pythagorean theorem to derive the expression for the edge length (I) in terms of r