Palladium crystallizes in a face-centered cubic unit cell. Its density is 12.0 g/cm³ at 27^$\circ$C. Calculate the atomic radius of Pd. A) 154 pm B) 138 pm C) 1.95 * 10^-8 nm D) 0.109 nm E) 1.95 * 10^-8 cm

Question

Quizplus · Accepted Answer

In a face-centered cubic unit cell, there are 4 atoms per unit cell. We can use the formula for the density of a material to solve for the atomic radius:
density = (atomic mass * number of atoms per unit cell) / (volume of unit cell * Avogadro's number)
We know the density, and the atomic mass of Pd is 106.42 g/mol. Avogadro's number is 6.022 x 10^23 particles/mol. The volume of a face-centered cubic unit cell can be calculated using the formula:
volume = (4r/√2)^3
where r is the atomic radius.
Substituting in the values and solving for r, we get:
r = (3 * density * Avogadro's number / (4 * atomic mass * π))^1/3
Plugging in the values, we get r = 1.38 Å or 138 pm. Therefore, the correct answer is B.

Palladium Crystallizes in a Face-Centered Cubic Unit Cell ∘\circ∘ C Calculate the Atomic Radius of Pd

Palladium Crystallizes in a Face-Centered Cubic Unit Cell $\circ$ C Calculate the Atomic Radius of Pd