Question

an element crystallizes into lattice containing a sequence of layers ABAB...
percentage of empty space is
​

Answer 1

Answer: 26%

Explanation:

As we know that the lattice containing ABAB.. type layer packing is present in HEXAGONAL CLOSED PACKING i.e HCP packing. The packing fraction is 0.74 in the packing thus the void fraction becomes 0.26 and so the percent of void fraction becomes 26%

Answer 2

An element crystallizes into a lattice containing a sequence of layers ABAB percentage of empty space is $26$ %

Explanation:

• ABAB pattern implies mainly in hexagonal closed packed structure.

• In the packing fraction of hexagonal closed packed structure $6$× $\frac{4\pi r^{3} }{3}$/volume

• Area of unit cell in hexagonal closed structure is $6\sqrt{3}r^{2}$
• Height of unit cell in hexagonal closed packed structure = $4r$×$\frac{\sqrt{2} }{3}$

• Packing fraction will be $\frac{\pi }{3\sqrt{2} }$ on calculating we will get it as $0.74$

• Empty space in hexagonal packed structure is $1 - 0.74=0.26$or $26$ %

• The percentage of empty space in the given ABAB is  $26$ %