Question

question 4 if the atomic radius of a metal that has the body - centered cubic crystal structure is 0.139 nm, calculate the volume of its unit cell. select < nm³ 1 pts

Explanation:

Step1: Recall relationship for BCC unit - cell edge length and atomic radius

For a body - centered cubic (BCC) unit cell, the relationship between the edge length $a$ and the atomic radius $r$ is $a=\frac{4r}{\sqrt{3}}$.

Step2: Substitute the given atomic radius value

Given $r = 0.139$ nm, then $a=\frac{4\times0.139}{\sqrt{3}}$ nm.
\[a=\frac{0.556}{\sqrt{3}}\text{ nm}\approx\frac{0.556}{1.732}\text{ nm}\approx0.321\text{ nm}\]

Step3: Calculate the volume of the unit cell

The volume of a cubic unit cell $V=a^{3}$.
\[V=(0.321)^{3}\text{ nm}^{3}\approx0.033\text{ nm}^{3}\]

Answer:

$0.033$