Palladium has a face-centered cubic structure and has a density of 12.023 g/cm³.What is its atomic radius? A)388 pm B)151 pm C)220 pm D)245 pm

Question

Quizplus · Accepted Answer

The density of a face-centered cubic structure is given by:$$ho = \frac{8M}{a^3N_A}$$where $ho$ is the density, $M$ is the molar mass, $a$ is the length of the unit cell, $N_A$ is Avogadro's number.We can rearrange this equation to solve for the atomic radius, $r$:$$r = \frac{a}{2\sqrt{2}}$$We can then substitute the given values into these equations to solve for the atomic radius:$$ho = 12.023 g/cm^3$$$$M = 106.42 g/mol$$$$a = \frac{4r}{\sqrt{2}}$$$$r = \frac{a}{2\sqrt{2}} = \frac{4r}{2\sqrt{2}\sqrt{2}} = \frac{4r}{4} = r$$$$r = \frac{M}{ho N_A a^3} = \frac{106.42 g/mol}{(12.023 g/cm^3)(6.022 	imes 10^{23} mol^{-1})(4r/\sqrt{2})^3}$$$$r = 1.388 	imes 10^{-8} cm = 138.8 pm$$Therefore, the atomic radius of palladium is 138.8 pm, which is closest to choice A, 388 pm.

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