Chapter 7.1, Problem 7.1E

Calculate the number of atoms in each unit cell (Figure 7.1) of
a. A body-centered cubic structure
b. A hexagonal structure

The positions of atoms are frequently described m lattice points expressed as fractions of the unit cell dimensions. For example, the body-centered cube has atoms at the origin [the corner at which $x=0,y=0,z=0$ , or $\left(0,0,0\right)$ ] and at the center of the cube $\left[x=\mathrm{½},y=\mathrm{½},z=\mathrm{½},\left(\mathrm{½},\mathrm{½},\mathrm{½}\right)\right]$ .The other atoms can be generated by moving these two atoms in each direction in increments of one cell length.