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The edge length of a face centred unit cubic cell is 508 pm. If the radius of the cation is 100 pm, the radius of the anion is

1. 288 pm
2. 398 pm
3. 154 pm
4. 618 pm

Correct answer: 288 pm

Solution

In a face-centred cubic (FCC) unit cell, the relation between edge length (a) and the radii of cation (r+) and anion (r-) is given by: a = 2√2(r+ + r-). Substituting a = 508 pm and r+ = 100 pm, we solve for r-: 508 = 2√2(100 + r-), leading to r- = 288 pm.

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