Palladium crystallizes with a face-centered cubic structure. It has a density of 12.0 g/cm³, a radius of 138 pm, and a molar mass of 106.42 g/mol. Use these data to calculate Avogadro's number.

Verified step by step guidance

1. Identify the type of crystal structure: Palladium has a face-centered cubic (FCC) structure.
2. Calculate the volume of the unit cell: In an FCC structure, the edge length (a) of the unit cell is related to the atomic radius (r) by the formula: $a = \frac{4r}{\sqrt{2}}$. Convert the radius from picometers to centimeters before using it in the formula.
3. Determine the mass of the unit cell: Use the density formula $\text{Density} = \frac{\text{Mass}}{\text{Volume}}$ to find the mass of the unit cell. Rearrange the formula to solve for mass: $\text{Mass} = \text{Density} \times \text{Volume}$. Use the given density and the calculated volume of the unit cell.
4. Calculate the number of atoms per unit cell: In an FCC structure, there are 4 atoms per unit cell.
5. Calculate Avogadro's number: Use the formula $\text{Avogadro's number} = \frac{\text{Molar mass} \times \text{Number of atoms per unit cell}}{\text{Mass of the unit cell}}$. Use the molar mass of palladium and the mass of the unit cell calculated in the previous steps.