Question

Help please...
Estimate the number of atoms in 1 cm3 of a solid. (Note
that the diameter of an atom is about 10 ^-10 m

Answer 1

It really depends on the way that the atoms are packed. Does the problem give any other indication to the structure of the unit cell?

Answer 2

no :(

Answer 3

Ok. We will assume that is is packed in a cubic manner, which is basically, like this in all 3 dimensions:

Answer 4

It certainly depends on how they are packed but since it's just an *estimate* I'd go with something like this:
\[\large V_{sphere}=\frac{4}{3}\pi r^3=\frac{4}{3}\pi*(\frac{10^{-10}}{2}m)^3=5.24 x 10 ^{-31}m^3\]\[\large 1cm^3=1x10^-6m^3\]Dividing the volume of a single atom into the available volume you'd get:
\[\large \frac{1x10^{-6}m^3}{5.24 x 10 ^{-31}m^3}=1.91x10^{24}atoms\]

Answer 5

I took a different route to estimation, and it still ended up being within a factor of 2, so that just shows you how much the answer may vary based on what packing method you choose.

Answer 6

My method is wrong, however, because I assumed that the atoms were cubic not spherical :P. Shane_B's approximation is closer.

Answer 7

With that many atoms....what's a factor of 2 really :) If the teacher doesn't like your estimate, tell her to count them :P

Answer 8

Exactly :P.

Answer 9

Thank you! I really appreciate the help. Wish my teacher was like you two...

Answer 10

you're welcome :)