1.

Packing efficiency by arrangement of atoms in two dimensional hexagonal close packing is

Answer»

60.43
65.78
59.78
68.76

Solution :
let radius of the sphere=r
AREA occupied by sphere in hexagonal close packing
`pir^(2)+6XX((1)/(6)xxpir^(2))=2pir^(2)`
Area of hexagonal`=6xx[(SQRT(sqrt(3))/(4)xx(2r)^(2)]`
`=6xx(sqrt(3))/(4)xx4r^(2)`
`=6sqrt(3)xxr^(2)`
% occupied by `=(2pir^(2))/(6xxsqrt(3)xxr^(2))xx100`
`=(2xx3.14)/(6xxsqrt(3))xx100=60.43%`


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