Wednesday, November 7, 2012

Nuclide Chart

One sunday morning in October, I woke up early to go to the Hopper exhibition in the Grand Palais, Paris with a friend. I wanted to see his paintings, some of them famous, even to those who do not know who he is. I like the contrast between the reassuring gentleness of the overview, and the crudeness (sometimes cruelty) of the details.


But the waiting time in the line was several hours, even though we arrived at the first hour ! So instead, we ended up in the Palais de La Découverte, next door. There it was blissfully empty, at this hour. This place is welcoming and designed for children, I think, even though many adults would learn a thing or two, or more, strolling along the corridors and reading the description panels, and watching the funny experiments on display. The good old planetarium is also very nice... But there is something peculiar about the atmosphere, something difficult to describe, an impression I rarely get..  It felt that I had traveled back in time. The inside of the Museum could have been exactly the same at any point in time from 40 years back to yesterday. I felt in a time warp !

Admittedly that is rather a good sign for a Museum, but I suspect I tend to identify sciences and technology, quite naturally in my view. In the latter field however, every concept, every item carries a very clear time stamp. In the Palais de La Découverte, on the contrary, it is late 19th - early 20th century science all over the place. This period in history is arguably one of most fertile in terms of scientific progress. It was breakthrough after breakthrough, in many disciplines. The human mind was furiously mapping Nature. And science was held in very high esteem, an unequivocal source of good. As the 20th century painfully rolled out, opinions gradually changed..

So I could not help thinking that the Museum would benefit from an upgrade and a strengthening of the connection between fundamental sciences and its applications. I would also use the vast real estate more efficiently, cram more presentations/experiments, systematically put the material on line too, and direct the visitor to related web sites, display the text in several languages (at the very least English), maybe even sublet a part of the Museum to technological/scientific companies/student bodies, if only to introduce some uncontrolled element in the place.

Now, I must be unfair to some of sections of the Museum. Surely they have some exhibitions in tune with the current zeitgeist  For example, there must be a section about climate change, a relatively new concern. There are some touch screens, but very few. Alternatively, one could defend the position that this dated atmosphere is completely intended, and must be carefully maintained. One could also point out that my suggestions are utopian, and that the Museum does very well with the budget. I would still think there is room for improvement.

In spite of all the remarks above, I enjoyed it very much. Especially the 'Atomic section'. I came across an enlightening short movie introducing the Nuclide Chart, the Valley of Stability, and basic radioactivity concepts, in no more than 5mn, and it was astonishingly clear !

I had never heard of the Nuclide Chart, as a way to sort and present all the elements in the Universe, only of the more famous the Mendeleev's Periodic Table. Well the Nuclide Chart is a lot better !!! It conveys the key concepts of nucleus stability and radioactivity so easily. I vaguely understand that the Periodic Table has more to do with chemical properties and the Nuclide Chart atomic properties. Maybe. But I don't explain the relative notoriety of both tables...

It was a very pleasant discovery for a Sunday morning !
I will briefly describe what I understood of it.

The Nuclide Chart is a 2D representation of all atomic nuclei, ordered by their number of neutrons on the X-axis, and protons on the X-axis. The number of protons (+1 electric charge) is usually called Atomic Number and denominated Z. The number of neutrons (0 electric charge) is denominated N. Usually Z+N is called the Mass Number and denominated A, as the mass of a proton is about the same as that of a neutron.

Z ranges from 1 (Hydrogen) to 118. For each Z, the number of possible N varies from 1 to 40 with average ~27.
There are typically more neutrons than protons. Very approximately, for each Z, the minimum N is ~1.5Z. The greatest N is 176 reached for Z = 115, 116.

Below is the Nuclide Chart with the stable nuclei in black, while the rest is light blue. My two observations are: Few nuclei are stable, only 256 out of a total of 3181 i.e. ~8%. The heaviest nuclei are all unstable. The heaviest stable nucleus is well known Lead-208 (Z=82, N=126).

The stability of a nucleus is by and large an increasing function of its binding energy. The higher the binding energy, the more energy is needed to break it one way or another, so the more stable it is.
Below is the Nuclide Chart showin the binding energy of the nuclei. The color code is rainbow, with the red en of the spectrum meaning higher energy, and blue/violet meaning lower energy.
The most stable nucleus is Nickel-62 (Z=28, N=34) (the small square in the red area).

Below is the list of all stable nuclei.

Now, the unstable nuclei are subject to several decay modes, which in the long run, turn them into stable nuclei. The decay modes are the different types of radioactivity. Schematically, the radioactive decays can be represented in terms of terms of mass and electric charge conservation, if one assumes that the mass of an electron/positron is very small relative to that a of proton/neutron.

  1. Alpha: A nucleus {Z, N} emits an alpha particule, i.e. 2 protons and 2 neutrons, i.e. an Helium-4 nucleus, and consequently turns into a new nucleus {Z-2, N-2}. In the Nuclide Chart the nucleus moves 2 ticks left, and 2 ticks down.
  2. Beta Minus: In a nucleus {Z, N} a neutron turns into a proton, and an electron is emitted, so the new nucleus is {Z+1, N-1}. In the Nuclide Chart the nucleus moves 1 tick left, and 1 tick up.
  3. Beta Plus: In a nucleus {Z, N} a proton turns into a neutron, either by electron capture or positron emission, so the new nucleus is {Z-1, N+1}. In the Nuclide Chart the nucleus moves 1 tick right, and 1 tick down.
  4. Proton Emission: A nucleus {Z, N} spontaneously emits a proton and turns into {Z-1, N}. In the Nuclide Chart the nucleus moves 1 tick down.
  5. Neutron Emission: A nucleus {Z, N} spontaneously emits a proton and turns into {Z, N-1}. In the Nuclide Chart the nucleus moves 1 tick left.
  6. Spontaneous Fission: A nucleus {Z, N} spontaneously breaks into 2 or more smaller nuclei. Then the nucleus becomes 2 nuclei, both of which move many ticks left and down on the Nuclide Chart.
What is enlightening is that these complex transformations, can be summarized by simple moves in the Nuclide Chart. The decay mode affecting an unstable nucleus depends essentially on its position in the Nuclide Chart, as is revealed by the the graph below.

Now in order to visualize the unforgettable concept of the Valley of Stability,  here is a 3D view of the Nuclide Chart (actually a fraction of it, Z<=45, N<=77, to make it clearer) relative to 'stability', being defined (personal definition) as the opposite of the binding energy of a nucleus. Note that the few lightest nuclei, say up to Z~10 and Z~10 have much lower binding energy, than the rest of the pack.
The short film they play at the Palais de La Découverte is really good, much better of course, but unfortunately I could not find it on the Internet...

One word about spontaneous fission. Once a nucleus has broken up and become nuclei of smaller sizes, the decay continues and it can take many step (and a considerable amount of time) for the resulting nuclei to decay all the way down to a stable element.
As an example, here is the decay graph of Uranium-235.

For reference the complete Nuclide Chart is on Wikipedia.
The Mathematica notebook to create the graphs and the animation is in this github repo.