If the atomic radius of aluminum is 0.143 nm and aluminum crystallizes in a face-centered cubic (FCC) structure, what is the volume of its unit cell in cubic meters?

• A. 9.23 × 10^{-30} m^3
• B. 2.92 × 10^{-28} m^3
• C. 1.17 × 10^{-28} m^3
• D. 4.65 × 10^{-29} m^3

Answer: (D)

Verified step by step guidance

1. Recall that in a face-centered cubic (FCC) structure, the atoms touch along the face diagonal of the cube. The relationship between the atomic radius (r) and the edge length (a) of the unit cell is given by the formula: \(a = \frac{4r}{\sqrt{2}}\).
2. Substitute the given atomic radius of aluminum, \(r = 0.143\) nm, into the formula to calculate the edge length \(a\). Remember to convert the radius from nanometers to meters by multiplying by \$10^{-9}$.
3. Calculate the volume of the unit cell using the formula for the volume of a cube: \(V = a^3\), where \(a\) is the edge length in meters.
4. Perform the cube operation on the edge length to find the volume in cubic meters.
5. Compare your calculated volume with the given options to identify the correct volume of the aluminum FCC unit cell.