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A metal crystallizes with a face-centered cubic lattice. The edge length of the unit cell is 408 pm. The diameter of the metal atom is:

1. 288 pm
2. 408 pm
3. 144 pm
4. 204 pm

Correct answer: 288 pm

Solution

In a face-centered cubic (FCC) lattice, the relation between the edge length (a) and the atomic radius (r) is given by: a = 2√2r. Substituting a = 408 pm, we get r = 144 pm. The diameter is 2r = 288 pm.

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