Question

Atomic densities and atomic volumes Problem 3. In this problem, we will calculate the atomic density ) and atomic volume () of two different pure metallic solids, Iron (Fe) and aluminum (AI). We will compare and contrast two different calculation methods flabeled Method I and Method II below. We will exploit the technique of "DIMENSIONAL ANALYSIS in our calculations. Method I. Calculate p and n based on knowledge of the mass density of the solid (the symbol for mass density is p.). (a) Calculate the atomic density.pke, of iron (Fe) in units of one and the corresponding atomic volume, 5. of Fe in units of A3/atom, based on knowledge that the mass density of Fe is given by p = 7.874 while the molecular weight of Fe is given by M.W.Fe = 55.845 mele (b) Calculate the atomic density, pal, of aluminum (AI) in units of "con, and the corresponding atomic volume, 1. of Al in units of A/atom, based on knowledge that the mass density of Al is given by pl = 2.70 while the molecular weight of Al is given by M.W.A1 = 26.982

Answer 1

a mode Method-a M.Wife = 55.845 g - - 1 mole of fe = 55.845g. on, 6.02381623 ato my of fe = 55.845 g oh, I alom of fe= 55.845 6.62381023 g me 2 Pure = 7.874 de mai = 9.27 *10-25 g Now - 9.27X 10 23 g .= I alom . 7-874 g = 7.874 .. . 3.27 x 103 atoms . = 8.5 x 1222 alones .: Atomie density pre z 8.5*1022 atoms/cm3

8.5 410 22 ÅR Now 1 cm² ³ 8.50.1022 atoms. D. and a cm = 108 Å items = 1024 À 3 . 8.5x1922 atoms = 1024 À 3 on t atom = 1024 11.36 Å3 ... Abome volume need = 11.76 Å3 /arom i 6 P = 2.70 g and M. W A1 = 26.982 in love I more of Al= 26.982 g . atome it Al a 26.982 - 6.023X1023 g. - i ems . = 4.47 x 10 2.2 = t + S 8 Nowo Mow. na 2.7 6.47x0o23 117 x 1623 atoms 2604 x 1022 atoms :1 Pane = 5.041012 atoms /ema .6.048 1022 atoms = 1024 A3 on t stay alom = 1024 16.55 $3 i 16.55 m) atom. ÅR 6.0 48 1022

* Method- of o Bec crystal structure contains 2 tony per unit cell... Now volume of a unit cell in Bcc struchine is = a8 cao= lattice parametery .= (2.8665)3 Å . = 23:55 83 so 2 atory 23.554 23.55 . 23.55 Å » 2 atoms. op, de a 2 ato na . = 0.084 atom atouts Atomie demity, Atle: 0.084 atom (83 Now I Å = 108 cm + Å = 1024 cm? .: pre 0.084 1026 arom emi 8 .4 x cm3

2 afony → 23.5 5 A 23. 55 2 03 1 Nom LA at > -11.77 ÁS = 11.77 A/atom :: Rate © In cell Comel 4.0995 Å fee structure, no. of atomy pin unit too is 4. volume of a unit cell in .fee Now 03 =66.40 A. ... 66.40 Ås & į atoms on, 18 y o atomes = 0.06 atoms Pa = 0.06 atony/ År DAL = 0.06 1024 1 cm PA = 6X1022 Nom cm3 Now 4 atoms atom? = # 66:40 ÅR 166.40 m3 120*= 16.6 #%/ atom