Aluminum has a face-centered cubic structure and has a density of 2.70 g/cm³.What is its atomic radius? A)143 pm B)286 pm C)405 pm D)1150 pm

Question

Quizplus · Accepted Answer

The atomic radius of aluminum in a face-centered cubic (FCC) structure can be calculated using the formula for the volume of the unit cell and the density. In an FCC structure, the relationship between the atomic radius (r) and the edge length of the unit cell (a) is $a = 2\sqrt{2}r$. The volume of the unit cell is $a^3$, and since there are 4 atoms per unit cell in an FCC structure, we can relate the mass of these atoms to the density and the volume of the unit cell. Given the density ($\rho$) is 2.70 g/cm³ and the atomic mass of aluminum (Al) is approximately 26.98 g/mol, and using Avogadro's number ($6.022 \times 10^{23}$ atoms/mol), we can solve for $r$. The calculation leads to an atomic radius close to 143 pm.

Aluminum Has a Face-Centered Cubic Structure and Has a Density