# Question #ee4f4

##### 1 Answer

#### Explanation:

The idea here is that you need to use the configuration of a **face-centered cubic unit cell** to find a relationship between the *length of the cell*, which is usually labeled *radius* of an atom of gold, which is usually labeled

So, a face-centered cubic unit cell looks like this

Now, you should know that the **diagonal** of a square is equal to

#"diagonal" = "side" xx sqrt(2)#

In this case, the diagonal of a face has a length of

#"diagonal" = r + 2r + r = 4r#

Here **quarter of an atom** that occupy the two corners of the face and **diameter** of the atom that occupies the middle of the face.

This means that the length of the side of the unit cell

#"side" = "diagonal"/sqrt(2)#

will be equal to

#a = (4r)/sqrt(2) = (4r sqrt(2))/2 = 2sqrt(2) * r#

Plug in your value to find

#a = 2 sqrt(2) * "0.144 nm" = color(darkgreen)(ul(color(black)("0.407 nm")))#

The answer is rounded to three **sig figs**.