You are given marbles of diameter `10mm`. They are to be placed such that their centres are laying in a square bound by four lines each of length `40mm`. What will be the arrangements of marbles in a plane so that maximum number of marbles can be placed inside the area? Sketch the diagram and derive expression for the number of molecules per unit area.

Explanation

`CD = 10 sin 60 = 10(sqrt3)/(2)`
`= 5sqrt3 nm`
Area of squre having spherical marbles in it
`= 40 xx 10^(-1) xx 40 xx 10^(-1) cm^(2) = 16 cm^(2)`
The maximum number of sphere of `10 mm` diameter in `hcp` packing can be seen in the figure above.
Totol length covered by spheres `= 5 + 4xx CD`
`= 5 + 4 + 10 sin 60^(@)`
`= 5 + 4 xx 5sqrt3 = 40 mm`
Maximum number of sphere`(s) = underset((Fu ll))(14) + underset((Half)) 8 = 18`
`:.` Number of spheres per `cm^(2) = (18)/(16) = 1.125`