A metal crystallises in a face centred cubic structure. if the edge length of its unit cell is ‘a', the closest approach between two atoms in metallic crystal will be
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(a* radical 2)/2
-because if you look at face-centered cubic structures, there is an atom in the center of each outer cube surface (search google for picture)
-the distance from this atom to an atom on a vertex of the same surface would be half the length of the diagonal of the square surface
-using pythagoras theorem a^2+b^2=c^2, taking a and b as side length a, and finding length of the diagonal as c, diagonal is equal to radical 2a^2, which is equal to a*radical 2
-as closest approach is half the diagonal length, divide above result by 2, and that gives (a*radical 2)/2
-note: just write a*radical 2 as a, then radical 2 written after it
-because if you look at face-centered cubic structures, there is an atom in the center of each outer cube surface (search google for picture)
-the distance from this atom to an atom on a vertex of the same surface would be half the length of the diagonal of the square surface
-using pythagoras theorem a^2+b^2=c^2, taking a and b as side length a, and finding length of the diagonal as c, diagonal is equal to radical 2a^2, which is equal to a*radical 2
-as closest approach is half the diagonal length, divide above result by 2, and that gives (a*radical 2)/2
-note: just write a*radical 2 as a, then radical 2 written after it
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Answer:
2/root 2a
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