Determine the radius of an Al atom (in pm) if the density of aluminum is 2.71 g cm^-3. Aluminum crystallizes in a face-centred cubic structure with an edge length of $ 2 \sqrt{2} r $. A) 143 pm B) 227 pm C) 96 pm D) 172 pm E) 193 pm

Question

Quizplus · Accepted Answer

In a face-centered cubic (FCC) structure, the edge length $ a $ is related to the atomic radius $ r $ by $ a = 2\sqrt{2}r $. The volume of the unit cell is $ a^3 $. The FCC unit cell contains 4 atoms. Using the density formula $\text{density} = \frac{\text{mass}}{\text{volume}}$, and knowing the molar mass of Al is 26.98 g/mol, we can calculate the radius. Solving gives $ r \approx 143 $ pm.

Determine the Radius of an Al Atom (In Pm) If 22r 2 \sqrt{2} r 22​r

Determine the Radius of an Al Atom (In Pm) If $2 \sqrt{2} r$