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Problem: Consider the body-centered cubic structure shown below: .What is the length of the line (labeled c) that runs from one corner of the cube diagonally through the center of the cube to the other corner in terms of r (the atomic radius)?

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  • For a BCC unit, this particular line c, passes thru half of the purple atom to one whole of the yellow and finally thru another half of the purple atom

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Problem Details

Consider the body-centered cubic structure shown below: 

A depiction of the unit cell of the body-centered cubic structure. A complete sphere is in the center of the cube with one eighth portions of spheres at each corner of the cube. The length of the edge is labeled as l. The diagonal of one of the faces of the cube is labeled as b. Line c starts at one corner of the cube, passes through the geometric center of the cube, and ends at the diametrically opposite corner of the cube. Line c is the only segment where the spheres are touching, with the center sphere touching the two eighth sphere portions at opposite corners of the cube. Line b is the hypotenuse of a right triangle with both edges of length l. Line c is the hypotenuse of another right triangle with side lengths of l and b..

What is the length of the line (labeled c) that runs from one corner of the cube diagonally through the center of the cube to the other corner in terms of r (the atomic radius)?

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