# Number of atoms that fill fit into 1cm^3

1. Sep 6, 2006

### paulhunn

I have been given a set of questions as a pre-course task for my physics AS level and i would be very grateful if somone could check my working and tell me if i'm on the right track.
One of the questions is how many atoms (with a given diameter of 0.0000001mm) can you fit into a 1cm^3 space. To work this out i began by calculating the volume of a single atom using the formula 4/3 pi r^3.
The answer for this came to 5.235987756*10^-25. Following this i calculated that with 100% efficiency 1.90985932 × 10^24 atoms would fit into the space. Then using the Kepler conjecture which says that you can pack spheres into a cube with a maximum efficency of 74% took 74% of the previous value which came to 1.41329589 × 10^24 atoms.

Paul

2. Sep 6, 2006

### rcgldr

How tightly can you pack spheres? Is it possible to pack them more tightly than cubes with sides equal to the diameter of the spheres? The outside shape of the container should only affect the spheres on the perimeter.

3. Sep 6, 2006

### paulhunn

What do you mean pack them more tightly than cubes? The question is how many will fit into a 1cm^3 space which is a cube so i don't see how else i could do it. I'm probably wrong though so i would appreciate some clarification

4. Sep 6, 2006

### rcgldr

I mis-understood your post. I thought you meant packing spheres in a cube formation, but I think you mean cubic packing, which is the 74% packing density you stated. At the boundaries of the actual cube, the cubic patterns may not be complete, unless the cube size was an exact multiple of the cubes formed by the cubic patterns (two pyramid shapes placed back to back), but this would only affect the total by a very small amount.

5. Sep 6, 2006

### Gokul43201

Staff Emeritus
Correct all the way.

6. Sep 7, 2006

### paulhunn

Ok thanks Jeff and Gokul43201!