Q48 / 77 · NTA Abhyas (JEE Main) 2020 · Chemistry · Solid State

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

Solution

Packing fraction in hcp =6×43πr3Volume

=6×4πr33×Area×Height

Area (of base) of unit cell in hcp =63r2 (follow text)

height of unit cell in hcp =4r×23 (follow text)

So packing fraction =6×4πr33×63r2×4r×23

=π32=0.74

or = 74%

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

or = 26%.

Hence, the correct answer is 26.

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