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Compute the radius r of an impurity atom that will just fit into an FCC octahedral site in terms of the atomic radius R of the host atom (without introducing lattice strains)

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Answer:

The Diameter of an atom that fits into the FCC is 2r,

Which leads to the final steps of 0414R

Explanation:

The diameter of an atom that  will fit into the FCC  site is  (2r) which differentiates  length edge unit cell for  the radii of two atoms that are seen on both side of the site (R); which is 2r = a – 2R

The  FCC is also a part of  R, therefore a=2R √2

Solving for R, the equation is,  r =a-2R/2 =2R√2-2R/2 =0414R

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