The density of sodium metal is 0.97 g.cm - 3 .Sodium crystallizes in a body-centered cubic structure; estimate the atomic radius.

Question

Quizplus · Accepted Answer

To estimate the atomic radius of sodium (Na) in a body-centered cubic (bcc) structure, we use the formula relating the atomic radius (r) to the edge length (a) of the unit cell: $r = \frac{\sqrt{3}}{4}a$. The density ($\rho$) of sodium is given as 0.97 g/cm³, and we know the molar mass (M) of sodium is approximately 22.99 g/mol. The Avogadro's number (N_A) is $6.022 \times 10^{23}$ atoms/mol. In a bcc structure, there are 2 atoms per unit cell.The volume of the unit cell (V) can be related to its mass and density by the formula: $V = \frac{m}{\rho}$, where $m$ is the mass of the unit cell. The mass of the unit cell can also be expressed as $\frac{2 \times M}{N_A}$ since there are 2 atoms per unit cell in a bcc structure.Combining these relations, we can express the edge length (a) in terms of known quantities and then solve for the atomic radius (r).Given the density and knowing the structure is bcc, we can calculate the volume of the unit cell and from there calculate the edge length (a). Substituting the values into the formula for r gives a value close to 190 pm, which is the atomic radius of sodium in a bcc crystal structure.

The Density of Sodium Metal Is 0