A **body-centered cubic (BCC) unit cell** is composed of a cube with one atom at each of its corners and one atom at the center of the cube.

Recall that the **edge length (a)** of** **a BCC unit cell can be calculated using the equation:

$\overline{){\mathbf{a}}{\mathbf{=}}\frac{\mathbf{4}\mathbf{r}}{\sqrt{\mathbf{3}}}}$

**Step 1: Calculate the volume of 1 unit cell using density**

- molar mass Ba = 137.33 g/mol
- 1 mole = 6.022x10
^{23}entities (Avogadro' number)*entities = atoms, ions, molecules, formula units*

*recall the # of atoms present **per 1 BCC unit cell*: *corner atoms contribute 1/8 and the center atom contribute 1*

$\mathbf{\#}\mathbf{}\mathbf{of}\mathbf{}\mathbf{atoms}\mathbf{=}\left(\mathbf{8}\mathbf{\times}\frac{\mathbf{1}}{\mathbf{8}}\right)\mathbf{+}\mathbf{1}$

**# of atoms = 2 per 1 unit cell**

• Solving **volume of 1 unit cell:**

$\mathbf{volume}\mathbf{=}\frac{\mathbf{137}\mathbf{.}\mathbf{33}\mathbf{}\overline{)\mathbf{g}\mathbf{}\mathbf{Ba}}}{\mathbf{1}\mathbf{}\overline{)\mathbf{mol}\mathbf{}\mathbf{Ba}}}\mathbf{\times}\frac{\mathbf{1}\mathbf{}\overline{)\mathbf{mol}\mathbf{}\mathbf{Ba}}}{(6.022\times {10}^{23})\mathbf{}\overline{)\mathbf{Ba}\mathbf{}\mathbf{atoms}}}\mathbf{\times}\frac{\mathbf{2}\mathbf{}\overline{)\mathbf{Ba}\mathbf{}\mathbf{atoms}}}{\mathbf{1}\mathbf{}\mathbf{unit}\mathbf{}\mathbf{cell}}\mathbf{}\mathbf{\times}\frac{\mathbf{1}\mathbf{}{\mathbf{cm}}^{\mathbf{3}}}{\mathbf{3}\mathbf{.}\mathbf{59}\mathbf{}\overline{)\mathbf{g}\mathbf{}\mathbf{Ba}}}$

**volume =1.27x10 ^{-22} cm^{3}/1 unit cell**

Barium has a density of 3.59 g/cm^{3} and crystallizes with a body-centered cubic unit cell. Calculate the radius of a barium atom.

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Unit Cell concept. You can view video lessons to learn Unit Cell. Or if you need more Unit Cell practice, you can also practice Unit Cell practice problems.

What professor is this problem relevant for?

Based on our data, we think this problem is relevant for Professor N/A's class at Ryerson University.