## Chemistry and Chemical Reactivity (9th Edition)

a) $8\times 1/8=1$ atom in the cell. $l=2.r$ Volume of cell: $l^3=8.r^3$ Volume of sphere: $4\pi/3.r^3$ Coverage: $(4\pi/3)/8\times100\%=52.36\%$ b) (BCC): 2 atoms per cell, $\sqrt3.l=4.r$ Volume of cell: $l^3=64/3\sqrt3.r^3$ Volume of spheres: $2\times4\pi/3.r^3$ Coverage: $(8\pi/3)/(64/3\sqrt3)\times100\%=68.02\%$ (FCC): 4 atoms per cell, $\sqrt2.l=4.r$ Volume of cell: $l^3=64/2\sqrt2.r^3$ Volume of spheres: $4\times4\pi/3.r^3$ Coverage: $(16\pi/3)/(32/\sqrt2)\times100\%=74.05\%$ All else held equal, the FCC arrangement should provide a higher density.