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You are given marbles of diameter 10mm. ...

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.

Text Solution

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Area of square `= 40 xx 40 = 1600 mm^(2)`
To have maximum number of spheres, packing must be hcp. As shown in the figure, the maximum number of spheres of diameter 10 mm are = 18
Area = `1600 mm^2 = 16 cm^2`
`:.` No. of spheres per `cm^2`
`= 18/16 = 1.125`.
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