Q$6,07$ and $08($ Note $-$ for linear density and planar densities, show or sketch the

directions or planes with the atoms on them for full credit. Refer to the class note for

examples$)$

Q$6.(10$ pts$)($a$,7$pts$)$ Derive linear density expressions for FCC $[100]$ and $[111]$ directions in

terms of the atomic radius R$.($b$,3$pts$)$ Compute and compare linear density values for these same

two directions for copper $(Cu).$ Take the radius of Cu atom as $0\mathrm{.}128$ nm

Q$7.(10$ pts$)(($a$)7pts,$ part b $3pts$ Derive planar density expressions for FCC $(100)$ and $(111)$

planes in terms of the atomic radius R$.($b$)$ Compute and compare planar density values for these

same two planes for aluminum $(Al).$ Take radius of Al atom $=0\mathrm{.}143nm.$

Q$8.(5$pts$)($a$)$ Calculate the planar density of $(100)$ in NaCl crystal. $($b$)$ Calculate the linear

density of $[100]$ in NaCl $.$ Assume radii of $N{a}^{+}$and $C{l}^{-}$are $0\mathrm{.}102$ nm and $0\mathrm{.}181$ nm respectively.