Question

please help me with 7, 8, and 9 only

For the questions 3-10 of simple cubic unit cell in Exp. 9 Crystal Structure, show your answers with detailed calculations (7 pts) 3. What fraction of the volume of each sphere is inside the unit cell? 9110.25 What is the total number of spheres within the unit cell? 4 spheres 0 5. In terms of the radiusr of one of the spheres, what is the total volume of the spheres inside the unit cell? (The volume V of a sphere of radius r is given by V = ) v=o524.4 sphers a 2.09 6. In terms of the sphere radius r, what is the side length a of the unit cell? 1.2=4 0.5.2=A IFA 7. In terms of the sphere radius r, what is the cell volume ? 8. What is the fraction of space occupied by the spheres in a simple cubic unit cell? y ! 9. What is the coordination number of a particle in a simple cubic structure?

Answer 1

7. Volume of simple cubic unit cell = 8r³​​​​​​

8. Fraction of space occupied by spheres in a simpke cubic cell = 0.523

9. Coordination number of a particle in simple cubic unit cell = 6.

- 7 for a simple cubic unit cell, - side of cube, a = 2 6 where r= radius of sphere So, volume of unit cell = (22)% = [8837 8) for simple cubic unit cell, fraction of space occupied by the spheres = volume of spheres simple cubic cenet volume of unit cell l cell has one sphere) = 1x/ą) ar3 per unit cell 873 = 4 * 3:14 0.523 = 4719 x = 4*34 - 0.523] 24 1 9. Coordination number of a particle in a simple . cubic unit cell is 76 . Reason: In a simple cubic cenit cell each particle is in contact with four other particles in the plane along with one particle each above the layer and the layer below. Hence, the coordination nuinber = 4+1+1 = 6