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Which of the following statements are Correct:-
  • a)
    Coordination number of simple Cubic structure is 6
  • b)
    Packing fraction of bcc structure is 68%
  • c)
    Coordination number of fee structure is 8
  • d)
    Packing fraction for simple cubic structure is 52%
Correct answer is option 'A,B,D'. Can you explain this answer?
Verified Answer
Which of the following statements are Correct:-a)Coordination number o...
Coordination number is the number of nearest neighbours to a lattice point.

packing fraction
BCC :-   
simple Cubic structure :-
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Which of the following statements are Correct:-a)Coordination number o...
Coordination number of simple Cubic structure is 6:
- The coordination number refers to the number of nearest neighboring atoms or ions surrounding a particular atom or ion in a crystal structure.
- In a simple cubic structure, each atom in the lattice is surrounded by 6 nearest neighboring atoms.
- This can be visualized as a cube with an atom at each corner and each corner atom being shared by 8 unit cells, thus contributing 1/8th of its presence to the central unit cell.
- Each corner atom is shared by 8 unit cells, and each unit cell has only 1 atom, hence the coordination number is 6.

Packing fraction of bcc structure is 68%:
- Packing fraction refers to the ratio of the total volume occupied by atoms to the total volume of the unit cell.
- In a body-centered cubic (bcc) structure, each atom is located at the center of the cube and is surrounded by 8 neighboring atoms.
- The atoms touch each other along the body diagonal of the cube, which has a length of 4r (where r is the radius of each atom).
- The edge length of the cube can be calculated using the relationship: a = 4r / sqrt(3).
- The volume of the unit cell is given by V = a^3 = 64r^3 / 3.
- Each bcc unit cell contains 2 atoms, so the volume occupied by atoms is 2 * (4/3) * π * r^3.
- The packing fraction is then calculated as: (2 * (4/3) * π * r^3) / (64r^3 / 3) = π / (6 * sqrt(2)) ≈ 0.68 or 68%.

Coordination number of fee structure is 8:
- The coordination number of a face-centered cubic (fcc) structure is 12, not 8.
- In an fcc structure, each atom is located at the center of a face and is surrounded by 4 nearest neighboring atoms in the same plane and 8 neighboring atoms in the adjacent planes.
- This results in a coordination number of 12, as each atom is in contact with 12 neighboring atoms.

Packing fraction for simple cubic structure is 52%:
- The packing fraction for a simple cubic structure is given by π / 6 ≈ 0.52 or 52%.
- In a simple cubic structure, each atom is located at the corner of a cube and is only in contact with 1 neighboring atom.
- The volume occupied by an atom is (4/3) * π * r^3, and the volume of the unit cell is a^3, where a is the edge length of the cube.
- The packing fraction is then calculated as: [(4/3) * π * r^3] / a^3 = π / 6 ≈ 0.52 or 52%.

Therefore, the correct statements are:
a) Coordination number of simple Cubic structure is 6.
b) Packing fraction of bcc structure is 68%.
d) Packing fraction for simple cubic structure is 52%.
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Which of the following statements are Correct:-a)Coordination number of simple Cubic structure is 6b)Packing fraction of bcc structure is 68%c)Coordination number of fee structure is 8d)Packing fraction for simple cubic structure is 52%Correct answer is option 'A,B,D'. Can you explain this answer?
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