Thread: Sphere Packing Problem and Chemistry

Physcists and chemists alike know that an element is determined by the number of protons in its nucleus. For example, a hydrogen atom can be defined as an atom with a single proton in its nucleus, a helium atom can be defined as an atom with two protons in its nucleus, and so on and so forth.

However, what if we looked at the nucleus of an atom as a sphere, and we considered protons as spheres as well. Therefore, finding the maximum number of protons that can fit into the nucleus of an atom would be tantamount to solving a sphere packing problem. In doing so, we could find all of the derivable elements in the universe, both artificial and natural.

An initial problem that comes to mind is that neutrons are also found in the nucleus of an atom, but perhaps we could determine the minimum number of neutrons and from that derive the maximum number of protons. Any thoughts on this or?

Originally Posted by ellatha

However, what if we looked at the nucleus of an atom as a sphere, and we considered protons as spheres as well. Therefore, finding the maximum number of protons that can fit into the nucleus of an atom would be tantamount to solving a sphere packing problem.

Apart from the fact that you're using the vastly simplified (and not-quite-correct) Bohr model the other problem is that the packing problem doesn't enter into it.
Unless there's a maximum allowable "space" for those "spheres" to be fitted into then there isn't a "maximum number" of protons to a nucleus. You can always just bung another wherever it'll go, as it were.

Originally Posted by Dywyddyr

Apart from the fact that you're using the vastly simplified (and not-quite-correct) Bohr model the other problem is that the packing problem doesn't enter into it.
Unless there's a maximum allowable "space" for those "spheres" to be fitted into then there isn't a "maximum number" of protons to a nucleus. You can always just bung another wherever it'll go, as it were.

I see what you're saying, but than why don't we see atoms with an atomic mass of 3,495,898,434 amu? Clearly the nuclei seem to possess a maximum achievable volume.

Good question.
I have no idea.
Stability?

Ah possibly: Scientists will continue to try to create larger atoms -- even though they will decay nearly instantly. Is there an upper limit to how large these atoms can get? We do not know. Right now the technical hurdles are preventing us from making infinitely larger atoms.
http://www.newton.dep.anl.gov/askasci/phy05/phy05174.htm

Yes, it's got a lot to do with stability.

I find the OP question a bit vague and confusing. So here's a good starting point:

Any nuclear structure will be based on the radioactive half lives, to explain why this particular isotope has a half-life of this length.

Originally Posted by PhDemon

Wrong way around, the half life is a consequence of the (in)stability of the nucleus, nuclear stability is not a consequence of half life...

Oh, that's not what I meant.

what I meant was, any nuclear structure theory that scientists come up with will first be based on all the half-lives we've measured.

Originally Posted by ellatha

However, what if we looked at the nucleus of an atom as a sphere, and we considered protons as spheres as well.

The structure of the nucleus is a major problem in physics.

It is important to note that nucleons (protons and neutrons) are not really little solid spheres and so sphere packing doe not really apply. There are also other issues such as the positive charges of protons cause them to repel one another (and hence the need for increasing proportion of neutrons as atomic number increases). And also the fact that re fermions and so the Pauli exclusion principle applies (no two protons can have the same quantum sate)

However, the shell model, which is one of the most successful approaches, is not too far from what you suggest:
Nuclear shell model - Wikipedia, the free encyclopedia

Originally Posted by ostkef

what I meant was, any nuclear structure theory that scientists come up with will first be based on all the half-lives we've measured.

Or bottom-up, based on QCD (but most likely a mixture of observation and theory).

Originally Posted by ellatha

I see what you're saying, but than why don't we see atoms with an atomic mass of 3,495,898,434 amu? Clearly the nuclei seem to possess a maximum achievable volume.

Larger nuclei become increasingly unstable. But there is thought to be an "island of stability" where some very large nuclei will be stable.
Island of stability - Wikipedia, the free encyclopedia