Consider a hypothetical polymer that has a tetragonal unit cell $($ie$.,===90)$ with the following

unit cell edge lengths: $a=b=0\mathrm{.}731nm,$ and $c=0\mathrm{.}933nm.$ Furthermore, the repeat unit molecular weight

is $64\mathrm{.}0\frac{g}{m}ol,$ and there are $4$ repeat units associated with each unit cell. $(20$ pts $)$

a$)$ Calculate the volume of the unit cell $(4$ pts$).$

b$)$ Calculate the density of a $100\%$ crystalline sample of this polymer $(8$ pts $).$

c$)$ If a specimen of this material having $45$ percent crystallinity has a density of $1\mathrm{.}00\frac{g}{c}m3$ compute

the density of the totally amorphous polymer $(8$ pts $).$