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13. An element crystallizes in the body-centered tetragonal (BCT) unit cell. (A tetragonal unit cell is a x ax b, and all the internal angles are 90°.) Element Z has

a BCT unit cell with a = 2 r and b = 2.83 r, where r is the radius of a Z atom. The unit cell of Z has one atom at each corner of the tetragon and one atom at the center of the tetragon. (a) Sketch and label the unit cell. (b) Find n, the number of atoms in the unit cell. (c) Find the packing factor of this unit cell. (d) The BCT unit cell of Z is equivalent to one of the unit cells we studied in class (simple cubic, BCC, FCC,or HCP). Which one of these is it equivalent to? Show your work.

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