Chapter 12, Problem 12.1P

Calcium metal crystallizes in a cubic closest-packed arrangement. Calcium has an atomic radius of 197 pm. What is the edge length of a unit cell in pm?

Interpretation Introduction

Interpretation:

The edge length of unit cell in $\text{pm}$ is to be calculated.

Concept introduction:

The relationship between edge length (d) and radius of cubic closest-packing is as follows:

$2d^2={\left(4r\right)}^2$

Where

• $d$ is edge length of unit cell.
• $r$ is radius of atom.

Rearrange above equation to calculate the edge length as follows:

$d=\sqrt{\frac{{\left(4r\right)}^2}{2}}$

Answer to Problem 12.1P

The edge length of unit cell in $\text{pm}$ is $278.6\text{ pm}$.

Explanation of Solution

Given information:

Calcium crystallizes in cubic closest packed arrangement. The radius of calcium is $197\text{ pm}$.

The expression to calculate the edge length is as follows:

$d=\sqrt{\frac{{\left(4r\right)}^2}{2}}$

Where

• $d$ is edge length of unit cell.
• $r$ is radius of atom.

The radius of calcium is $197\text{ pm}$.

Substitute values in above equation.

$\begin{array}{c}d=\sqrt{\frac{{\left(4\left(197\text{ pm}\right)\right)}^2}{2}}\\ =278.6\text{ pm}\end{array}$

Conclusion

The edge length of unit cell in $\text{pm}$ is $278.6\text{ pm}$.