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

Uttarkhand PMTUttarkhand PMT 2008

Solution:

There are four body diagonals. Atoms on the body diagonals are not shared by any other unit cell.
Contribution by atoms on comers $ =8\times \frac{1}{8}=1 $
and Contribution by atoms on body diagonal $ =2\times 4=8 $
$\therefore $ Total number of atoms $ = 1 + 8 = 9$