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An element crystallises in a face-centre...

An element crystallises in a face-centred cubic lattice. The distance between the nearest neighbours in the unit cell is 282.8pm. Calculate the edge length of the unit cell, and the radius of an atom of the element.

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The distance (d) between the nearest neighbours in a face-centred unit cell is related with the edge length (a) and radius ( r) of its particles as d = 2r = 0.707a.
As d = 282.8pm, 2r = 282.8pm or, r = 141.4pm
Therefore, the radius of an atom of the element = 141.4pm and edge length of the unit cell = `d/0.707=282.2/0.707`pm = 400pm
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