NTA Abhyas 2020
- Exam
- NTA Abhyas
- Year
- 2020
- Subject
- Chemistry
- Chapter
- Solid State
NTA Abhyas 2020 · Chemistry · Solid State
A metallic element crystallizes into a lattice containing a...
A metallic element crystallizes into a lattice containing a sequence of hexagonal layers of ABABAB....... What percentage by volume of this lattice is empty space?
Options
- A26%
- B74%
- C50%
- D85%
Correct answer
A. 26%
Step-by-step solution
Number of atoms in hcp is 6 per unit cell.
Packing fraction = \dfrac{6 \times \dfrac{4}{3} {\text{\pi r}^{3}}{\text{Base area} \times \text{C}}
Base area = 6 \times \dfrac{\sqrt{3}}{4} \left(\text{4}{\text{r}^{2}\right)<br /><br /> C = = \left(1 - 0 . \text{74}\right) \times100 = \text{26}%
Packing fraction = \dfrac{6 \times \dfrac{4}{3} {\text{\pi r}^{3}}{\text{Base area} \times \text{C}}
Base area = 6 \times \dfrac{\sqrt{3}}{4} \left(\text{4}{\text{r}^{2}\right)<br /><br /> C = = \left(1 - 0 . \text{74}\right) \times100 = \text{26}%