Question

PLEASE ANSWER VERY SOON I AM STUCK!


Crystalline silicon has a cubic structure. The unit cell edge length is 543
pm. The density of the solid is 2.33 g/cm3. Calculate the number of Si
atoms in one unit cell.

Answer 1

Here is how I would approach the problem.
543 nm = 5.43 x 10^-8 cm
V = a^3 = (5.43 x 10^-8)^3
Then mass of the unit cell = v x density.

(# atoms in unit cell x 28.0855)/(6.022 x01^23) = mass unit cell

Solve for # atoms. When I worked the problem, I ended up with 7.999 which rounds to 8 and we know that can't be right. The reason is that Si is a face centered cubic (# atoms to unit cell = 4) with two interpenetrating face centered cubic cells; therefore, we divide the 8 by 2 to obtain the 4 as an answer. If you wish to read more about this go to http://hyperphysics.phy-astr.gsu.edu/hbase/solids/sili2.html
Hope this helps.

Answer 2

OMG I CAN'T FIGURE IT OUT EITHER!!!!