fredag 5 november 2010

The curve of binding energy.

Credit: User fastfission on wikipedia, image is in public domain.

Now, what is so remarkable about this graph that tells you how tightly bound different elements are? It makes sense of a great many interesting things about the Universe that we live in.

The strong nuclear force that binds nuclei together is very strong, but it is also very short range. In small nuclei every additional nucleon you add is attracted with the strong force to every other nucleon, but in big nuclei it only interacts strongly with the nucleons in its vicinity at any given moment. In contrast, the electric force is a much longer range force, it falls off only as the inverse square of distance between the charges. Each additional proton you add repels all other protons in the nucleus. This is a gross simplification, but it gives an intuitive feel for why there is an optimum size of nuclei that is most tightly bound.

Amongst other things you can see that merging toghether light elements is energetically favourable all the way up to iron and nickel. This process is known as fusion and is what powers stars.

It is apparent that helium-4 is a remarkably stable nuclei for such a light element. Elements with electrons arranged into complete shells are very unreactive; they're known as noble gases. Like the shell model that you learned about in chemistry class, there is a corresponding model for nuclides. Nuclides with a certain number of either protons or neutrons are especially stable because they have a complete outer shell. The numbers 2, 8, 20, 28, 50, 82 or 126 are called "magic numbers"; atoms with this many neutrons or protons are called "magic" and they are extra stable. Helium-4 has 2 neutrons and 2 protons; it is "double magic".

The slope of the binding curve gradually flattens before reaching its peak at nickel-62. In less massive stars like the sun the fusion process stops at carbon and oxygen; slightly heavier stars can fuse carbon and the process stops at oxygen, neon and magnesium. Massive stars can fuse everything up to iron.

Harnessing fusion power on Earth is difficult to achieve because it involves smashing toghether two positively charged particles that strongly repel each other. Only if they get very close can the strong nuclear force overpower the coulomb repulsion.

It is also energetically favourable for heavy elements to be split appart into smaller nuclei. The most common way for heavy elements to do this is to eject a helium-4 nucleus, which repelled by the coulomb repulsion will have a very large amount of kinetic energy. This is known as alpha decay. The curious stability of helium-4 is why alpha decay involves the tossing out of a helium-4 nuclei and not a proton, deuteron or lithium-7 nucleus.

The heaviest nuclide that is completely stable as far as anyone is aware is lead-208; a "double magic" nuclide(82 protons, 126 neutrons). Bismuth-209 was believed to be stable until recently, when it was discovered that Bismuth-209 has a half-life of 19 ×1018 years.

The heaviest elements that exist in measurable abundance in nature are actinides(IUPAC: actinoids); named after actinium, the first element in the actinide series. These elements can perform a new trick, they can split apart into bigger chunks than helium-4.

Uranium-235 in particular can be induced to split by pelting it with neutrons. If one of these neutrons get close enough it can be captured by the uranium nucleus, forming an excited nucleus of uranium-236. ~82% of the time this excited nucleus will split apart into two unequal halves, known as fission products. The rest of the ~18% of the time the excited nucleus returns to ground state by emitting a gamma ray. When this nucleus fissions, it releases more neutrons that can be used to continue the process.

However not all of these neutrons are released promptly; a small fraction are released by the decay of fission products, known as delayed neutrons. This is why both nuclear bombs and nuclear reactors are practical. There are enough prompt neutrons to create a very fast, run-away reaction under the right conditions; a bomb.

There are also enough delayed neutrons that it is possible to create a reactor that is not self-sustaining on prompt neutrons alone('prompt critical'). The delayed neutrons are thereby necessary to sustain the reaction, and since it takes time for them to emerge the power output of the reactor can be made to increase very slowly and controlably; slowly enough for self-regulation to occur. There are many mechanisms that can do this kind of self-regulation as the reactor heats up, such as thermal expansion and resonance broadening of the neutron capture resonance in U-238. Therefor, if the reactor operator injects only a little bit of positive reactivity into a properly designed reactor, the power level will rise a bit, the temperature will increase and then stabilize at a new, higher level.

Some reactors can handle even a huge insertion of reactivity with ease. Below is an example of such a reactor; a small research reactor at Penn State. What you see here is a control rod being rapidly ejected from a TRIGA core using compressed gas. The power-outout increase rapidly and peaks at about a gigawatt thermal. As the core heats up the reactivity drops to such an extent that it becomes negative and the reaction slows; the power goes down and eventually homes in towards some level where reactivity approaches 0(i.e. no change in power output).

Essentially all elements except hydrogen, helium and lithium that we see around us were once made in a star. But if stars can't fuse iron, why are there heavier elements than iron around? While there is some argument about the relative importances of the different processes, it is generally agreed that they are produced by the s-process, p-process and r-process. The s-process is the slow process of successive capture of neutrons that may occur in some heavy stars(believed to be mostly occuring in asymptotic giant branch). The r-process is the rapid process of neutron capture that occurs during a super nova. The p-process is photodisintegration, which can strip a neutron or an alpha particle from a heavy nuclide; this is responsible for producing some heavy, proton rich elements.

To a romantic, we are made of star-dust; risen from the ashes of a dying star. A cynic would point out that another word for "star-dust" is nuclear waste from a giant reactor exploded so violently that it surely must have killed everything within light-years, if there was anything there to kill.

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