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In face - centred cubic (fcc) crystal l...

In face - centred cubic (fcc) crystal lattice, edge length is 400 pm. Find the diameter of the greatest sphere which can be fitted into the interstital void without distortion of the lattice.

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For fcc, radius of atom `( R) = a/ (2sqrt2) = 400/(2sqrt2) "pm" = 141.4` pm
As octahedral void is bigger in size than the tetrahedral void, the greastest sphere will fit into octahedral void.
Radius of octahedral void ( R) = 0.414 R = ` 0.414 xx 141.4 " pm" = 58.54 "pm" `
Diameter of the greatest sphere fitting into the void = ` 2xx 58.54` pm = 117. 08 pm.
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