Polonium metal crystallizes in a simple cubic structure. If the atomic radius of polonium is 160 pm, what is the volume of a unit cell?

Question

Quizplus · Accepted Answer

In a simple cubic structure, the edge length (a) of the unit cell is equal to two times the atomic radius. Therefore, $a = 2 \times 160\, \text{pm} = 320\, \text{pm}$. The volume ($V$) of the unit cell is $a^3$, so $V = (320\, \text{pm})^3 = 32,768,000\, \text{pm}^3 = 3.28 \times 10^{7}\, \text{pm}^3$. Converting to cubic centimeters ($\text{cm}^3$), since $1\, \text{pm} = 10^{-12}\, \text{cm}$, $V = 3.28 \times 10^{-23}\, \text{cm}^3$.

Polonium Metal Crystallizes in a Simple Cubic Structure