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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 correct Answer is:
0.261
In case of hcp unit cell, there are 6 atoms per unit cell. If the radius of metal atom is `r_(1)` ten volume occupied by the metallic atom
`=6xx(4)/(3)xxpir^(3)=6xx1.33xx(22)/(7)xxr^(3)=25.8r^(3)`
Geometrically it has been shown that the base area of hcp unit cell.
`=6xxsqrt(3)/(4)xx4xxr^(3)` and the height `=4rxxsqrt((2)/(3))`
Volume of unit cell =Area xx Height
`=6xxsqrt(3)/(4)xxr4r^(3)xx4rxxsqrt((2)/(3))=33.94r^(3)`
`therefore` Volume of the empty space of one unit cell
`=33.94r^(3)-25.08r^(3)=8.86r^(3)`
hence, percentage void `(8.86r^(3))/(33.94r^(3))xx100=26.10%`
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