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Total volume of atoms present in a face-centre cubic unit cell of a metal is (r is atomic radius)

1. 20/3 πr³
2. 24/3 πr³
3. 13/2 πr³
4. 16/3 πr³

Correct answer: 16/3 πr³

Solution

In a face-centered cubic (FCC) unit cell, there are 4 atoms per unit cell, and the volume of a single atom can be calculated using the formula for the volume of a sphere, which is (4/3)πr³. Therefore, the total volume of atoms in the unit cell is 4 times this volume, resulting in 16/3 πr³.

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