Question

The crystal structure of sodium is based on the body-centered cubic unit cell. What is the mass of one unit cell of Na?

Short answer

Mass of one unit cell of Na is $46\mathrm{g}/\mathrm{mol}$.

Step-by-step solution

Definition of crystal structure

In a crystal, the constituent particles form a structure by repeating a symmetric pattern along three dimensions. This symmetric structure of the particles in a crystal is named as crystal structure.

Calculation of mass of one unit cell

$\begin{array}{rcl}\mathrm{Mass}\mathrm{of}\mathrm{a}\mathrm{unit}\mathrm{cell}& =& \mathrm{Number}\mathrm{of}\mathrm{ions}\mathrm{in}\mathrm{the}\mathrm{unit}\mathrm{cell}\\ & & \times \mathrm{mass}\mathrm{of}\mathrm{an}\mathrm{atom}\mathrm{in}\mathrm{the}\mathrm{unit}\mathrm{cell}\mathrm{Number}\mathrm{of}\mathrm{ions}\mathrm{in}\mathrm{body}\\ & & -\mathrm{centered}\mathrm{cubic}\mathrm{unit}\mathrm{cell}\\ & =& \left(\frac{1}{8}\times 8\right)+1\\ & =& 2\end{array}$

Mass of one Na atom$=23\mathrm{g}/\mathrm{mol}$.

Therefore, the mass of the unit cell of Nais$2\times 23\mathrm{g}/\mathrm{mol}=46\mathrm{g}/\mathrm{mol}$.