Island of Stability: Answers to Questions

[Lazernugget]

Okay, so even though I really don't need to, I do a LOT of research on astronomy, physics, math, etc. I was doing research on the extended periodic table, and super heavy unstable elements. I was quickly turned to the Island of Stability, and I get the theory but have a few questions.

1. Element 126 supposedly if it had 126 of each nucleon particle, (protons and neutrons) would mean it would be stable, but why is element 126 supposed to be super special, because it would be heavy+stable or what?

2. (This is a bit off topic) What does the number left of an element mean? (I'm only 11, so this may seem like a stupid question) for example what's the 234 in ²³⁴U ?

3. Could someone explain why The Bohr Model shows difficulty for existence (In elements) Beyond 137?

Thanks,

Lazernugget :D

 

[mathman]

Q1. - A nucleus that large would need a lot more neutrons than protons to have any hope of stability. For example, element 110 isotopes range from 267 to 273 nucleons (157 to 163 neutrons).
Q2. - 234 is total number of nucleons (92 protons + 142 neutrons).

 

[Bill_K]

Lazernugget, A very successful model for the nucleus is the single particle shell model in which each nucleon is considered to move independently within a background field produced by all the others. It predicts that nuceons as they are added to the nucleus will occupy well-defined orbitals until a closed shell is completed, very much like the way that electrons fill orbital shells in an atom. The shell model further predicts that a nucleus with exactly the right number of protons or neutrons to complete a shell will be exceptionally stable. The number of nucleons required for this are called magic numbers and have the values 20, 50, 82, 126, etc.

A nucleus with 126 protons is beyond what we've observed to date, but would be more stable than its neighbors, provided it had a suitable number of neutrons as well. For heavy nuclei, the required ratio of neutrons to protons is about two to one.

In answer to the third question, the Coulomb field that surrounds the nucleus is predicted to become strong enough at Z ≈ 137 to cause pair production, and therefore nuclei this heavy would likely decay by capturing virtual positrons from the pairs.

 

[Lazernugget]

Thanks, these are great answers, but again, Element 126 supposedly if it had 126 of each nucleon particle, (protons and neutrons) would mean it would be stable, but why is element 126 supposed to be super special, because it would be heavy+stable or what?

 

[eXorikos]

The Coulomb repulsion between the protons inside the nucleus makes it impossible to have a nucleus with 126 protons and only 126 neutrons.

Those magic numbers are predicted and explained by the Shell Model as posted before. It makes that all nucleons are paired and all quantum mechanical shells are closed. The binding energy between the nucleons is then sufficient to keep all of them together. The mass has nothing to do with being stable or unstable.

I don't know why it's an island of stability and the nuclei before the island are so unstable.

 

[mathman]

For heavy nuclei, the required ratio of neutrons to protons is about two to one.

It looks more like 3 to 2.

 

[Drakkith]

The Coulomb repulsion between the protons inside the nucleus makes it impossible to have a nucleus with 126 protons and only 126 neutrons.

Those magic numbers are predicted and explained by the Shell Model as posted before. It makes that all nucleons are paired and all quantum mechanical shells are closed. The binding energy between the nucleons is then sufficient to keep all of them together. The mass has nothing to do with being stable or unstable.

I don't know why it's an island of stability and the nuclei before the island are so unstable.

I think "stability" in this case means that it doesn't decay quite as fast as it would otherwise, right?
At least that's what wikipedia says here: http://en.wikipedia.org/wiki/Island_of_stability

 

[eXorikos]

Lifetimes in the order of seconds I thought. But it's still an anomaly which I can't explain, but my first guess is deformation. I could ask one of my professors after my exams.

 

[Drakkith]

Lifetimes in the order of seconds I thought. But it's still an anomaly which I can't explain, but my first guess is deformation. I could ask one of my professors after my exams.

What are you saying here exactly? Your first guess for what is deformation?

 

[eXorikos]

What are you saying here exactly? Your first guess for what is deformation?

Such very exotic nuclei are probably very deformed and that's why the nuclei surrounding the island of stability are very unstable.

 

[Nik_2213]

IIRC, there's some indication that those 'magic numbers' may not apply as strictly to 115+ region, as the many nucleons can arrange themselves non-spherically...

A bit like transition elements' electrons shuffle into unexpected configurations...

 

[eXorikos]

These numbers shift and this can be calculated using advanced Hartree-Fock methods. The results are shown in a Nilsson diagram like http://ns.ph.liv.ac.uk/~esp/nuclear/WS/Nilsson.gif The beta stand for the ratio between major and minor axis or the other way around.