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Calculate the void space in closest pack...

Calculate the void space in closest packing of `n` spheres of radius 1 unit, `n` spheres of radiys `0.414` units, and `2n` spheres of radius `0.225` units.

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To calculate the void space in the closest packing of the given spheres, we will follow these steps: ### Step 1: Identify the Structure and Parameters Given that the spheres are in closest packing, we can assume they form a face-centered cubic (FCC) structure. In FCC, the effective number of atoms per unit cell (Z) is 4. ### Step 2: Calculate the Edge Length (a) for Radius 1 Unit For FCC, the relationship between the radius (r) and the edge length (a) is given by: \[ 4r^2 = 2a^2 \] ...
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