- #1

- 3

- 0

- Thread starter cotyledon
- Start date

- #1

- 3

- 0

- #2

alxm

Science Advisor

- 1,842

- 9

IIRC, metallic sodium is a body-centered cubic (BCC) crystal. The unit cell looks like http://en.wikipedia.org/wiki/File:Lattice_body_centered_cubic.svg" [Broken], a cube with side a, with one atom in the middle and the neighboring atoms on the 8 corners.

So the diagonal is 4 radiii in length, so if the side of the unit cube is a you have [tex]4r = \sqrt{a^2+a^2+a^2} = \sqrt{3}a[/tex] and the radius is [tex]r = \frac{\sqrt{3}a}{4}[/tex].

There are two whole atoms in a unit cell (one in the middle and 1/8 in each corner), so the unit cell weighs [tex]\frac{2*M_{Na}}{N_A}[/tex] g. The density of sodium metal is 968 kg/m3.

Do the arithmetic and you get a radius of 1.86 Å. That's called the 'metallic radius'.

As you can see, the size of the unit cell depends on the type of unit cell, the type of bonding going on, etc. Pick up a book on crystallography and you'll see it can actually get rather complicated.

So the diagonal is 4 radiii in length, so if the side of the unit cube is a you have [tex]4r = \sqrt{a^2+a^2+a^2} = \sqrt{3}a[/tex] and the radius is [tex]r = \frac{\sqrt{3}a}{4}[/tex].

There are two whole atoms in a unit cell (one in the middle and 1/8 in each corner), so the unit cell weighs [tex]\frac{2*M_{Na}}{N_A}[/tex] g. The density of sodium metal is 968 kg/m3.

Do the arithmetic and you get a radius of 1.86 Å. That's called the 'metallic radius'.

As you can see, the size of the unit cell depends on the type of unit cell, the type of bonding going on, etc. Pick up a book on crystallography and you'll see it can actually get rather complicated.

Last edited by a moderator:

- Last Post

- Replies
- 1

- Views
- 3K

- Last Post

- Replies
- 1

- Views
- 699

- Replies
- 3

- Views
- 1K

- Replies
- 8

- Views
- 18K

- Replies
- 3

- Views
- 2K

- Replies
- 1

- Views
- 699

- Last Post

- Replies
- 1

- Views
- 6K

- Last Post

- Replies
- 1

- Views
- 3K

- Last Post

- Replies
- 18

- Views
- 4K

- Last Post

- Replies
- 4

- Views
- 1K