Question

Side-centered cubic (scc) cell Top view 1) (5 points) Walter White who lives in Simeranya (a utopic city in Anarres) prepares blue crystals, named as myth, which adopt a side-centered cubic (scc) cell, where atoms occupy the center of sides of a cubic cell. (The myth molecule is assumed to have a perfect spherical shape.) a) Find out how many atoms are present in each unit cell. b) Calculate the atomic packing factor (APF) of scc unit cell. c) Given the density of the material as 6.184 g/cm and a molar mass of 132 g/mol, determine the radius (in nm) of myth molecule. d) Find the linear density (in nm) of the following vectors in scc; (111), (110), and [100]. (You can choose the origin as one of the corners of scc cell.) e) Determine the number of holes with coordination numbers 6, 8, and 12 per unit cell.

Answer 1

Con D90 - 9 - Microsoft Word - X Home Insert Page Layout References Mailings Review View Cut Ea Copy Paste Format Painter Clipboard Calibri (Body) 11 - A A АавbccDo АавbccDc АаВЫС Аавьсс Аав| Аавьссl АавbccD Аавьссос B I U - abe X, X? Aaab - A E U - P- Normal 1 No Spaci... Heading 1 Heading 2 Title Subtitle Subtle Em... Emphasis Font E Paragraph Styles 1:2:1:1:1: '1:1 A1:27:31:41:51:5:17:18:19: 1.10 | 11 | 12 | 13 | 14 | 15 1A:1:17. 18: = Change Styles # Find - 4ac Replace hf Select Editing As the atoms are present only at the edges (sides) and all these atoms must be shared by other three (total four) unit cells. Therefore it is concluded that each atom is common to four different cubes with their common edge as shown here. 1 2 .1 Therefore the contribution of each atom towards a .3 .1 single cell will be 14 .4 .1 .5 .1 .6 .1 a) Total number of atoms = contribution X number of atoms present at the edges = 44X12 = 3 b) Packing fraction is how much space occupied Top view APF = Volume occupied/Total volume Let the side of the cube = 'a' Radius of the atoms ='' From the picture given, look at the red arrow, it connects the mid points of the two adjacent sides of the square. The mid points are the centers of the atoms (spheres), let the length of red arrow be 'x' 7 1 .8 1 .9 1 Therefore x= )* + (3) 10 Page: 1 of 1 Words: 254 English (United States) ONE 2 130% 0 17:15 = Ato ( 1») ENG 30-10-2019 FA 1 Type here to search

9 - Microsoft Word - 2 x Home Insert Page Layout References Mailings Review View Cut Ea Copy Paste Format Painter Clipboard Calibri (Body) 11 - A A АавbccDo АавbccDc АаВЫС Аавьсс Аав| Аавьссl АавbccD Аавьссос B 1 U abe x x Aa ab- A # E E -- Normal 1 No Spaci... Heading 1 Heading 2 Title Subtitle Subtle Em... Emphasis Font Paragraph Styles 1:2:1:1:1:11A1:27:31:4:15 116 117 118 119 | 10 | 11 | 12 | 13 | 14 | 15 16:1'17' 1 : 18 Change Styles # Find - 4ac Replace hf Select Editing Therefore x- \@* + C) * .e. a = V2 x we notice that the length 'X' = 2r volume of sphere = ar3=1 43) (substituting r =x/2) Total volume of all spheresl = 3x – 1 (3) * Volume of the cube = (a)= (v2 x) 20 119 118 117 116 115 114 113 112 111 1101 APF = Volume occupied/Total volume = 3x1 (15)9 (V2 x) = 0.56 Z.M (c) density of solid crystals is given by, d = where Z = number of formulas per unit cell, M = molar mass, a = edge length, No =Avogadro number Supplying the data, and applying maths we get 6.184 =- 3 X 132 www.a3 X6.023X1023 a = 10.63X10-23 = 4.73X 10-8 cm English (United States) Page: 1 of 1 Words: 252 ONE 2 ^ ° 130% ve ) ENG 0 17:16 30-10-2019 A Type here to search 4