Re: How big can an atom get?

Hi Isaac,

The forces that hold nuclei together are rather complicated. Protons and neutrons (both "nucleons") are held together by the "strong force", which tries to hold nucleons together whenever they are closer than about 10^-15 meters apart (0.000000000000001 meters). If any two protons and neutrons are further apart than this, they "can't see one another" with the short-range ties of the strong force. This is one of the things that limits the size of nuclei.

Also, notice that a nucleus with protons in it is positively charged. Since "like charges repel" electrically, any nucleus with protons in it will be trying to push itself apart via electrical forces.

Ultimately, it's the balance of these two forces that determines the allowed sizes of nuclei. The strong force is attractive and the electric force repulsive - there's only a limited range in which the strong force wins and can hold things together.

A nucleus with lots of protons has lots of electric repulsion, so sometimes adding another proton just doesn't work - the electric force is stronger than the strong force, and the proton can just fall out. The region where this occurs is called the proton drip line. Adding lots of extra neutrons to a nucleus doesn't affect the electric charge, but it does affect the size - and as things stretch beyond the range of the strong force, the nucleus can fall apart. Also, don't forget that a neutron by itself is unstable - it decays to a proton, an electron, and a neutrino. Neutrons that are tightly bound inside nuclei are stabilized by being deep inside a nucleus, but some of the neutrons in a really neutron-rich nucleus will want to decay into protons.

Of course, nucleons aren't floating around in the nucleus like marbles in a bag. They have a complicated shell structure, similar to the shell structure of atomic electrons, and certain numbers of particles are more stable than others. These are called "magic numbers" - any nucleus with a magic number of either protons or neutrons will be very stable (and especially so if both p and n are magic). The magic numbers are: 2,8,20,28,50,82,126. Check out a periodic table and figure out what possible nuclei might have these numbers. We haven't found anything with 126 protons yet, but it may turn out to be stable - that'd be the largest, and maybe the largest possible, nucleus.

Here's an interesting chart of all the known nuclei (click on areas for details). The horizontal axis is the number of neutrons, and the vertical is the number of protons. (Thus the usual elements - the common, stable isotopes - lie along a diagonal line, with P=N for light elements and 1.2*P=N for heavier elements) The black dots are natural (generally stable) nuclei, the red are very unstable, the other colors are long-lived but radioactive. The upper boundary of the red area is the proton dripline, and the lower boundary - rather less well understood - is the neutron sea. And of course, the heaviest nuclei are shooting off the upper right. Notice that the heaviest stable nucleus is the fairly lightweight Bismuth 209. Most everything above Nobelium 260 has a lifetime measured in minutes or seconds. So, beyond the possible "island of stability" associated with Z=126, nobody expects there to be any heavier nuclei and larger atoms - element 126 will have 126 protons, 126 electrons, probably something like 200 neutrons, and will barely hold itself together on the short strings of the strong nuclear force. Physicists are indeed trying to make this and nearby nuclei, but it has been a slow and incremental business so far. We're adding to the edges of the unstable red patch, one isotope at a time - and there's nothing but instability and short lifetimes as far as the eye can see.

Trying to make very-far-from-stability nuclei doesn't work at all. A large nucleus to which you "add" a proton can eject it in 10^-20 seconds - basically as fast as possible, limited only by the speed of light.

I haven't mentioned the electrons yet - for the most part, electrons do not participate in the stability of atoms. There is no theoretical limit to the number of electrons that could orbit an imaginary ultra-charged nucleus. It's just that the effects I talked about above place limits on the number of protons, and thus the charge, of a nucleus.

Also, if you want to push the definition of the word "nucleus", we can mention neutron stars - essentially huge, mostly-neutron "nuclei" held together by gravity. They can get very large - up to about three times the mass of the sun - and their structure is governed by the familiar strong force.

There are lots of good nuclear physics textbooks available - try one by Wong, or by Das & Ferbel, which you can find at a university library. In particular, you can calculate some stability limits yourself by solving the Bethe-Weizsacker formula (AKA the Weizsacker Semi-Empirical Mass Formula) for zero binding energy.

Hope this helps,

-Ben Monreal