# Calculate the density of Na metal.

1. Aug 30, 2009

### daviddee305

1. Calculate the density of Na metal. The length of the body-centered cubic unit cell is 4.24 Å.

2. Attempted solution:

[4 Na Atoms/unit cell] * [1 mol Na atoms/(6.022*10^23 atoms)] * [22.99g Na/1 mol Na] = 1.527 * 10-22 g/unit cell

(4.24 Å)3 = 7.6225 * 10-23 cm3/unit cell

[1.527 * 10-22 g/unit cell] / [7.6225 * 10-23 cm3/unit cell] = 2.00 g/cm3

The correct answer is 1.00 g/cm3... What went wrong in my calculations?

2. Aug 30, 2009

### tiny-tim

Hi daviddee305!

There are 9 atoms in a body-centered cubic cell (1 in the centre, and one at each vertex), but how many cells is each atom in (and why)?

3. Aug 30, 2009

### daviddee305

Each corner atom is shared by 8 unit cells, so only (1/8)th of each atom belongs to the body-centered cubic. Plus the one in the middle. Thank you.

That was a great follow-up question, exactly what I needed to see through these confusing diagrams in my text.

4. Aug 30, 2009

### tiny-tim

Yup … always go back to the definition.

(And now have a look at http://en.wikipedia.org/wiki/Body-centred_cubic. )