Why is uranium fissionable and not, say, aluminum?
The short answer is "aluminum's not big enough." Here's why: The nuclear force saturates due to its short range, meaning that heavier nuclei have protons that don't attract each other via the nuclear force but still repel each other electrostatically. This is why heavier nuclei tend to have more neutrons in relation to the number of protons - the neutrons only attract. The binding energy per nucleon, a measure of how tightly a nucleus is bound, peaks at about 60 nucleons. (There's also a sharp peak at 4; the alpha particle, which is a He-4 nucleus, is very tightly bound) So light nuclei require energy to split apart and would release energy only if you can fuse them together. You might expect that anything heavier than 120 nucleons would fission, but these nuclei are still bound together, so the two parts you would get in fission aren't likely to fly apart. It's not until you get into the elements heavier than lead (all of which are radioactive) that you find nuclei whose binding energy per nucleon is low enough that the fission fragments could tunnel apart.
Tom Swanson, Ph.D., Physicist, US Naval Observatory
Check out this graph:
What this shows is that Iron is essentially the most stable element. Everything lighter than Iron can be fused and release some energy. Everything heavier than iron can be fissioned and release some energy.
See the answer is that you theoretically could split Aluminum up into lighter elements but it'd cost you a huge amount of energy to do so. Uranium can be split with a net energy gain.
Jason Fahrion, B.S., Lab Technician, Portland, Or.
If you were to weigh the protons and neutrons that make up an atomic nucleus individually, you would see that the nucleus weighs less than its individual components. For example, carbon 12 has a mass of exactly 12 amu, but it is made up of six protons (1.0073 amu each) and 6 neutrons (1.0087 amu each). This missing energy, called the binding energy for the carbon 12 nucleus, is released when the nucleus is formed. You can calculate how much energy is released using Einstein's e=mc2 to convert the missing mass (0.096 amu, where 1 amu = 1.66 x 10-27 kg) to energy (89 MeV, or 89 million electron volts). So, in order to break up a carbon 12 nucleus into individual protons and neutrons, it takes an infusion of 89 million electron volts of energy. For comparison, in order to break apart a hydrogen atom into a proton and an electron, it only takes 13.6 electron volts, so the nucleus is bound over a million times more strongly!
A plot of binding energy for a given atomic weight of the nucleus can be found at http://encarta.msn.com/media_461531006_761558960_-1_1/Nuclear_Binding_Energy.html.
In the case of carbon 12, each individual nucleon (proton or neutron) is bound by 89 MeV / 12, or around 7.45 MeV. As the mass number increases, the binding energy also increases, which means that light elements can release additional energy through fusion. The maximum binding energy per nucleon occurs for Iron 56, and for heavier elements the binding energy decreases as the mass number gets larger. Therefore, a very heavy nucleus such a uranium 238 nucleus can produce additional energy not through fusion, but rather through fission that divides it into two lighter and more tightly bound nuclei. So to answer your question, uranium can naturally undergo fission because fission produces energy, but aluminum is too light to undergo fission. However, at the center of some stars conditions are right for elements such as carbon, oxygen, silicon, etc. to undergo fusion and to continue to produce energy until iron is produced and no more energy can be produced through either fusion or fission.
Finally, I should mention that the binding energy curve is much steeper when increasing for light elements than when decreasing for heavy elements. As a result, while fission releases an immense amount of energy (as evidenced by power plants and atomic weaponry), fusion releases far more energy, which is why researchers are actively working on methods to harness that energy for power production.
Charles Steinhardt, B.A., Astronomy Grad Student, Harvard University
'The atomic bomb ... made the prospect of future war unendurable. It has led us up those last few steps to the mountain pass; and beyond there is different country.'