Problen 2 Gallium has an exthothombic structure, with a=0.45268=0.b=0.45186am, and c=0.76570mm. The atoenic radius is 0.121s m. The densily is 5.904gcm3 and the atonic weight is 69,72g mol. Avogadro's mumer is equal to 6.021027 atens mol. Determine: (a) The namber of aloms in each werit cell and (b) The packing factor in the unit eell. Eroblemen 3 (i) A metal having a cubic structure has a demaly of 2.6scm ', an atoeic weight of 87.62g/mol, and a lattice parameter of 6.0849A. Determine the crycal serakture of the metal. One A is equal to 102cm and Avegadro's number is equal to 6.02103 atoms inot. (ii) Indium has a tetragonal structure with a 0.032517mn and c=0.49659nm. The density is 7.266gcm3 and the atseic weipht is 114.82gmol. Does indium have the simpie tetragoeal or bedy-eeotered ietmponal structure? One A is aqual to 107cm, and Avogadro's nember is oqual to 6621027 atomsimol. Froblen 4 Strontium (Sir) has an FCC crystal strocture, an itomic rafias of 0.215 and, and an atoenic weight of 87.62jmol. Calculate the theoretical deniity for 8t. Problem 5 (a) Derive finear demity expression for FCC [100] and [111] drections in lemms of the afomic radias R. Congunte and cenppare linear density valies for these sance two directions for copper (Cu) which has an atomic nalas of 0.178nm. (b) Derive linear density erpessions fir BCC [110] and [111] deectiens in terns of the atomic radius R. Congute and concoure lisear dening value for these same Fwo dirsctions for ifon (Fe) which has an atomic ralive of 0.134mm. Problem 6 (a) Derive planar density expressions for FCC (100) and (111) plasos in lerms of the planes for aluminum (A)) whicth has an akomic nafins of 0.143mm. (b) Derive planar deasity expreswions for BCC(10) and (110) planes in terms of the atomic radius R. Conpuite and compore planur density valses for these sune two planes for molytdenum (Mo) which has an atomic madiss of 0.136mm. (c) Derive the planar density expressice fer the HCP (0001) plune in terms of the ateenic radias R. Cempuse the planar density valioe for this same pluse for titanium (Ti) which has an alomic radius of 0.145nm