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The volume of the unit cell is 2.67 x 10⁻²⁸ m³.
In a body-centered cubic unit cell, the volume occupied by the particles of the substance is about 68% of the total unit cell.
Assuming that a single atomic a sphere, the volume is:
Volume(atom) = 4/3 x π x r³
Volume(atom) = 4/3 x π x (169 x 10⁻¹²)³
Volume(atom) = 2.02 x 10⁻²⁹ m³
There are a total of 9 atoms in a body-centered unit cell, so the total volume occupied by atoms is:
2.02 x 10⁻²⁹ x 9
= 1.82 x 10⁻²⁸ m³
Volume of cell = (1.15 x 10⁻²⁸ ) / 0.68
Volume of cell = 2.67 x 10⁻²⁸ m³
Therefore, the volume of the unit cell is 2.67 x 10⁻²⁸ m³.
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