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A metallic element crystallizes into a l...

A metallic element crystallizes into a lattice contained sequence of layers `ABABAB….` Any packing of sphere leaves out voilds in the lattice.The percentage by volume of this lattice as empty space is

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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 %
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