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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?

NTA AbhyasNTA Abhyas 2022

Solution:

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