An hcp and a ccp structure for a given element would be expected to have
(a)The same co-ordinational number
(b)the same density
(c)the same packing fraction
(d)all of the above

Options

A. The same co-ordinational number
B. the same density
C. the same packing fraction
D. all of the above

Answer

To solve the question regarding the comparison between hexagonal close-packed (HCP) and cubic close-packed (CCP) structures, let's analyze each option step by step.

### Step 1: Coordination Number
- **HCP Structure**: In an HCP arrangement, the coordination number is calculated based on how many atoms surround a central atom. In HCP, each atom is surrounded by 12 other atoms (6 in the same plane and 6 in the adjacent planes).
- **CCP Structure**: Similarly, in a CCP arrangement, each atom is also surrounded by 12 other atoms (the arrangement is different, but the number of surrounding atoms remains the same).
- **Conclusion**: Both HCP and CCP structures have the same coordination number of 12.

### Step 2: Density
- **Density Calculation**: Density is defined as mass per unit volume. The density of a crystal structure depends on the number of atoms per unit cell and the volume of the unit cell.
- **HCP Structure**: The HCP structure has 6 atoms per unit cell.
- **CCP Structure**: The CCP structure has 4 atoms per unit cell.
- **Conclusion**: Since HCP and CCP have different numbers of atoms per unit cell, they will have different densities. Therefore, this option is incorrect.

### Step 3: Packing Fraction
- **Packing Fraction Definition**: Packing fraction (or packing efficiency) is the fraction of volume in a crystal structure that is occupied by the constituent particles (atoms).
- **HCP and CCP Packing Fraction**: Both HCP and CCP structures have a packing fraction of approximately 74% (or 0.74). This means that in both structures, 74% of the volume is occupied by atoms.
- **Conclusion**: Both structures have the same packing fraction.

### Final Conclusion
- From the analysis:
- (a) The same coordination number: **True**
- (b) The same density: **False**
- (c) The same packing fraction: **True**
- Therefore, the correct answer is **(a) and (c)**.

### Answer:
The correct options are (a) The same coordination number and (c) The same packing fraction.

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