A metallic crystal cystallizes into a lattice containing a sequence of layers `ABABAB…`. Any packing of spheres leaves out voids in the lattice. What percentage by volume of this lattice is empty spece?

Explanation

The given arrangement: ABABAB ……… represents hexagonal close-packed unit cell in which there are six atoms per unit cell.
Also volume of unit cell `24sqrt(2) r^(3)`
`rArr ` Packing fraction = `("Volume occupied by atom s")/("volume of unit cell ")`
` = 6 xx (4)/(3) pi r^(4) xx (1)/(24 sqrt(2)r^(3)) = 0.74`
`rArr` Percent empty space = 100 (1 - 0.74) = 26 %