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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 layers of ABABAB ..... . Any packing of spheres leaves out voids in the lattice. What percentage by volume of this lattice is empty space?

Correct answer

26

Step-by-step solution

Packing fraction in hcp =6×43πr3Volume= \dfrac{6 \times \dfrac{4}{3}\pi{r}^{3}}{Volume}

=6×4πr33×Area×Height= \dfrac{6 \times 4\pi{r}^{3}}{3 \times Area \times Height}

Area (of base) of unit cell in hcp =63r2= 6\sqrt{3}{r}^{2} (follow text)

height of unit cell in hcp =4r×23= 4r \times \sqrt{\dfrac{2}{3}} (follow text)

So packing fraction =6×4πr33×63r2×4r×23= \dfrac{6 \times 4\pi{r}^{3}}{3 \times 6\sqrt{3}{r}^{2} \times 4r \times \sqrt{\dfrac{2}{3}}}

=π32=0.74= \dfrac{\pi}{3\sqrt{2}} = 0.74

or = 74%

Thus, empty space in hcp = 1 - 0.74 = 0.26

or = 26%.
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