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A cubic unit cell contains one atom at e...

A cubic unit cell contains one atom at each of its corner and two atoms on each of its body diagonal. How many atoms does the unit cell contain?

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A crystalline unit cell contains 1 atom at each of its corner. There are eight corners in each cubic unit cell where each constituents in each corner is shared with 8 adjoining cubic unit cells. Therefore, number of corner-atom present per unit cell = `8xx1/8=1`.
There are 4 body diagonals in a cubic unit cell where each of it, 2 atoms are present . Therefore, number of atoms present in body diagonals per cubic unit cell = `4xx2=8`.
Therefore, the total number of atoms present per unit cell = 1 + 8 = 9.
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