Problem. 3 (i) A metal having a cubic structure has a density of 2.6g/cm3, an atomic weight of 87.62g/mol, and a lattice parameter of 6.0849A. Determine the crystal structure of the metal. One A is equal to 108cm, and Avogadro"s number is equal to 6.021023 atomsimol. (ii) Indium has a tetragonal structure with a=0.32517nm and c=0.49.459nm. The density is 7.286g/cm3 and the atomic weight is 114.82g/mol. Does indium have the simple tetragonal or body-centered tetragonal structure? One A is equal to 101cm, and Avogadro's number is equal to 6.021023 atoms/mol. Problem 4 Strontium (Sr) has an FCC crystal structure, an atomic radius of 0.215nm, and an atomic weight of 87,62g/mol. Calculate the theoretical density for Sr. Problem 5 (a) Derive linear density expressions for FCC[100] and [111] directions in terms of the atomic nadrus R. Compute and compare linear density valaes for these same two directions for copper (Cu) which has an atomic radius of 0.128nm. (b) Derive linear density expressions for BCC[110] and [111] directions in terms of the atomic nadius R. Compute and compare linear density values for these same two directions for iron (Fe) which has an atomic radius of 0.124nm. Problem 6 (a) Derive planar density expressions for FCC (100) and (111) planes in lemus of the atomic radius R. Compute and compare planar density values for these same two planes for aluminum (Al) which has an atomic radius of 0.143nm. (b) Derive planar density expressions for BCC(100) and (110) planes in tems of the atomic nadius R. Compute and compare planar density values for these same two planes for molybdenum (Mo) which has an atomic radius of 0.136nm. (c) Derive the planar density expression for the HCP (000t) plane in terms of the atomic radius R. Compute the planar density value for this same plane for titanium (Ti) which has an atomic radius of 0.145nm