Question #ee4f4

Question

Question #ee4f4

1 Answer

Impact of this question

3168 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-07-08T00:45:01

$0.407 nm$ $"0.407 nm"$

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 $a$ $a$ , and the radius of an atom of gold, which is usually labeled $r$ $r$ .

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

![https://classconnection.s3.amazonaws.com/38/flashcards/512038/png/fcc1316360426857png](useruploads.socratic.org)

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

$diagonal = side \times \sqrt{2}$ $"diagonal" = "side" xx sqrt(2)$

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

$diagonal = r + 2 r + r = 4 r$ $"diagonal" = r + 2r + r = 4r$

Here $r$ $r$ represents the radius of the two quarter of an atom that occupy the two corners of the face and $2 r$ $2r$ represents the diameter of the atom that occupies the middle of the face.

![www.chemteam.info)

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

$side = \frac{diagonal}{\sqrt{2}}$ $"side" = "diagonal"/sqrt(2)$

will be equal to

$a = \frac{4 r}{\sqrt{2}} = \frac{4 r \sqrt{2}}{2} = 2 \sqrt{2} \cdot r$ $a = (4r)/sqrt(2) = (4r sqrt(2))/2 = 2sqrt(2) * r$

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.

Science

Math

Humanities

... and beyond

Question #ee4f4

1 Answer

Explanation:

Related questions

Impact of this question