(a) 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). entry field with correct answer 0.414 r

radius r is  0.414 R

Explanation:

Given data

FCC octahedral site

atomic radius R

to find out

radius r

solution

we know that at FCC octahedral

length of side = 2 R + 2r

and by pythagorean theorem

a = 2√2R

here a = 2R + 2r

so 2R + 2r = 2√2R

so r = ( √2R )- R

r = 0.414 R

so  radius r is  0.414 R

it's a b and

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