The size of the largest atom that can fit within a face-centered cubic (FCC) unit cell can be determined by comparing the diameter of the atom to the diagonal of the unit cell.
In an FCC unit cell, the body diagonal is related to the edge length (a) by the equation:
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Answer:
The size of the largest atom that can fit within a face-centered cubic (FCC) unit cell can be determined by comparing the diameter of the atom to the diagonal of the unit cell.
In an FCC unit cell, the body diagonal is related to the edge length (a) by the equation:
\[ \text{Body diagonal} = \sqrt{3} \times \text{Edge length} \]
For the largest atom to fit, its diameter should be equal to the body diagonal:
\[ \text{Diameter of atom} = \sqrt{3} \times \text{Edge length} \]
Assuming the atom is a sphere, the diameter is twice the atomic radius:
\[ 2 \times \text{Atomic radius} = \sqrt{3} \times \text{Edge length} \]
Solving for the atomic radius:
\[ \text{Atomic radius} = \frac{\sqrt{3}}{2} \times \text{Edge length} \]
So, the size of the largest atom that can fit in an FCC unit cell is given by multiplying the edge length by \(\frac{\sqrt{3}}{2}\).
Explanation:
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