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  4. How many number of atoms are there in a cube based unit cell having one atom on each comer and two atoms on each body diagonal of cube?

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Q. How many number of atoms are there in a cube based unit cell having one atom on each comer and two atoms on each body diagonal of cube?

AMUAMU 2008

Solution:

There are four body diagonals. Atoms on the body diagonals are not shared by any other unit cell.
Contribution by atoms on corners
$ =8\times \frac{1}{8}=1 $ and
Contribution by atoms on body diagonal
$ =2\times 4=8 $
Hence, total atoms in the cube based unit cell $= 8 + 1 = 9$