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The correct statement about, CCP structu...

The correct statement about, CCP structure is

A

Packing fraction = 26%

B

Coordination number = 6

C

Unit cell is face centred cubic

D

AB - AB type of packing

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The correct Answer is:
To determine the correct statement about the CCP (Cubic Close Packing) structure, let's analyze the information step-by-step. ### Step-by-Step Solution: 1. **Understanding Packing Fraction**: - The packing fraction is defined as the ratio of the volume occupied by the spheres (atoms) in the unit cell to the total volume of the unit cell. - For CCP, the formula for packing fraction is: \[ \text{Packing Fraction} = \left( \frac{\text{Volume occupied by spheres}}{\text{Total volume of unit cell}} \right) \times 100 \] 2. **Volume of Spheres in CCP**: - In a CCP structure, there are 4 effective atoms per unit cell. - The volume of one sphere (atom) is given by: \[ V_{\text{sphere}} = \frac{4}{3} \pi r^3 \] - Therefore, the total volume occupied by 4 spheres is: \[ V_{\text{occupied}} = 4 \times \frac{4}{3} \pi r^3 = \frac{16}{3} \pi r^3 \] 3. **Volume of the Unit Cell**: - The unit cell in CCP is a cube with edge length \( a \). - The volume of the cube is: \[ V_{\text{cell}} = a^3 \] 4. **Relationship between Edge Length and Radius**: - The relationship between the edge length \( a \) and the radius \( r \) in CCP is: \[ a = 2\sqrt{2}r \] - Thus, the volume of the unit cell can be expressed as: \[ V_{\text{cell}} = (2\sqrt{2}r)^3 = 16\sqrt{2}r^3 \] 5. **Calculating the Packing Fraction**: - Now substituting the volumes into the packing fraction formula: \[ \text{Packing Fraction} = \left( \frac{\frac{16}{3} \pi r^3}{16\sqrt{2}r^3} \right) \times 100 \] - Simplifying this gives: \[ \text{Packing Fraction} = \left( \frac{16\pi}{48\sqrt{2}} \right) \times 100 = \frac{\pi}{3\sqrt{2}} \times 100 \] - Approximating this value results in approximately 74%. 6. **Coordination Number**: - The coordination number in a CCP structure is the number of nearest neighbor atoms surrounding a central atom. - In CCP, the coordination number is 12, as each atom is in contact with 12 others. 7. **Unit Cell Type**: - The CCP structure is also known as a face-centered cubic (FCC) structure. 8. **Packing Type**: - The packing in CCP is ABCABC type, not ABAB type. ### Conclusion: From the analysis, we can conclude that: - The correct statement about CCP structure is that it is a face-centered cubic structure with a packing fraction of approximately 74% and a coordination number of 12.
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  10. In a BCC unit cell, if half of the atoms per unit cell are removed, th...

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