Question

The radius of a single atom of a generic element X is 169 picometers (pm) and a crystal of X has a unit cell that is body-centered cubic. Calculate the volume of the unit cell.

Answer 1

The volume of the unit cell is 2.67 x 10⁻²⁸ m³.

What is the volume of a unit cell of a body-centered cubic crystal?

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.

Learn more volume of unit cells at: brainly.com/question/1594030

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