[Douglas100]

Hi,
I recently had a question to do with the trends of decreasing half life as the atomic number increased for the actinide group within the periodic table.
I answered by saying that the half life decreases due to the large size of the nuclei as the atomic number increases. This is due to the elements only being stable up until the atomic number of 81, thereafter the elements are less stable as the atomic number increases.
Could anybody tell me if this is correct and the scientific reason for this trend occurring.
Thank you in advance.

[Enthalpy]

More protons in a nucleus repel an other more strongly.

With details: more nucleons also attract an other more strongly, but this interaction occurs only at a short distance, so it increases slowly with the number of nucleons, while the repulsion increases more quickly at bigger nuclei.

This "water drop" model is not the whole picture, as for instance ²³⁸U and ²³²Th are more stable than lighter nuclei, so details about the numbers of protons and neutrons matter. Even numbers of protons and of neutrons tend to be more stable, suggesting spin pairing, but this explanation doesn't suffice. Other models have had a limited success too, including with shells as inspired by electrons in atoms, but none is good. As far as I know (and I ignore much) this is still an open topic.

[Enthalpy]

Thorium and uranium, or at least some natural isotopes, are abnormally stable, much more so than the nuclides between them and bismuth, so I believe a general trend shouldn't include these two.

I'm not even sure that a solid theory exists that explains the stability of Th and U.

[gippgig]

Thorium and uranium aren't abnormally stable; the elements from polonium-actinium are abnormally unstable, particularly the lighter ones, because they are just above the closed shell at lead. A good analogy is that the closer you are to a sinkhole the more likely you are to fall even tho someone a long way away may actually be higher up than you are. The elements from thorium-rutherfordium are about normal stability. From dubnium on elements are abnormally stable (as they approach the partially closed shell at hassium & closed shell somewhere in the 114-126 region).

[Enthalpy]

The shell theory has serious difficulties - pity, it was simple. For instance, the doubly magic ⁵⁶Ni is unstable while ⁵⁶Fe has the highest binding energy per nucleon.

One may also notice that (the stablest isotopes of) polonium is more stable than radon
https://www-nds.iaea.org/relnsd/vcharthtml/VChartHTML.html
https://en.wikipedia.org/wiki/Table_of_nuclides_%28complete%29
despite being nearer to lead (I take only even nuclides in the comparison).

[pcm81]

Half life is determined by the decay constant lambda via HL=ln(2)/lambda.

Lambda in turn is determined via quantum mechanics. You can think of a nucleus as a potential well that the particle is trying to escape (this is easier to imagine for alpha particles). This particle is bouncing off the walls of the potential well since the well is deeper than the energy of the particle. Eventually it will escape via quantum tunnelling. Large nucleus means particle takes longer to bounce back and fourth between the walls of this potential well, hence in a given period of time, say 1 second, it has fewer chances to escape.

[wildfyr]

pcm, this is a 3+ year old topic.

[Enthalpy]

[...] Large nucleus means particle takes longer to bounce back and fourth between the walls of this potential well, hence in a given period of time, say 1 second, it has fewer chances to escape.

Ouch. Alpha emission appears as nuclei get larger. And these are all stationary states, without movement in the nucleus.

[pcm81]

[...] Large nucleus means particle takes longer to bounce back and fourth between the walls of this potential well, hence in a given period of time, say 1 second, it has fewer chances to escape.

Ouch. Alpha emission appears as nuclei get larger. And these are all stationary states, without movement in the nucleus.

For more information it is easier to just direct the readers to a pdf...
https://www.colorado.edu/physics/phys2170/phys2170_sp07/downloads/alphadecay.pdf
equations 9-29 onward.

[Enthalpy]

This pdf is b*llocks.

[pcm81]

This pdf is b*llocks.

That PDF is consistent with what i was taught in undergraduate course of nuclear physics, for my major in nuclear engineering. I did not "find" this information in that pdf, i found that pdf to cite as a source and avoid having to type up the equations. You are wrong, I am right, let's move on with life.

Unlike gamma decay, where a nucleus in an excited state decays to a ground state and emits a gamma ray, and unlike beta decay where neutron decays into proton and an electron an alpha decay problem is a escape probability problem of an alpha particle from a potential well of a nucleus.

Read section III.2 on page 4 of this document for a similar explanation, but without "confusing" formulas.
http://web.mit.edu/8.13/www/JLExperiments/JLExp45.pdf
and if you cant believe a text from MIT... well i doubt i or anyone else can convince you otherwise.

[Enthalpy]

By believing a source rather than deciding by yourself what is correct, you take the wrong path. This is not science, it's religion.

If the model you promote wants faster alpha decay for lighter nuclei, despite alpha decay appears when nuclei are heavy enough, then the model is wrong. This is clear enough that you should be able to decide it by yourself. This is your job as a scientist, whether the source is MIT or anything else.

That alphas don't move within nuclei is less obvious, but it would be useful for you to understand. It's the same situation as for electrons in atoms: they would radiate light and lose energy, which doesn't happen, hence wrong model. QM says "stationary solution" as a solution. Any course that suggests that nucleons move in an unexcited nucleus gives a bad service to the students.

As for the speed of alpha decay, you might give a thought at the electrostatic repulsion among protons. Check the "liquid drop model", it's incomplete but at least it goes in the right direction.

[Corribus]

By believing a source rather than deciding by yourself what is correct, you take the wrong path. This is not science, it's religion.

I'm a healthy advocate of some degree of skepticism, but this is not an entirely fair or useful view either. At some point, we always have to take something as axiomatic and reap the consequences. That doesn't make it religion. Students especially don't have the experience to always "decide for yourself what is correct", and for that matter professionals don't always have the background in new scientific areas to make those determinations either. Which is why we use textbooks and reference materials and peer reviewed literature in the first place - even though there is the possibility they may be wrong or (more likely) over simplified.

[pcm81]

[...] Large nucleus means particle takes longer to bounce back and fourth between the walls of this potential well, hence in a given period of time, say 1 second, it has fewer chances to escape.

Ouch. Alpha emission appears as nuclei get larger. And these are all stationary states, without movement in the nucleus.

The point here is to be very careful in accurate statements and what we mean by "increasing size of the nucleus".
If we are talking about adding more protons etc then yes the nuclei become more unstable and half life goes down.
BUT we need to be careful about how else the statement about "larger" nucleus is interpreted. If by "larger someone understands a geometrical size, then the half life is expected to increase and probability of decay decease.

http://periodictable.com/Properties/A/HalfLife.html
from Francium to thorium you actually see an increase in half life. Point is: the increase in nucleon count (which correlates to increase is geometrical size of the nucleus) and increase in Z number, which also correlates to increased size of the nucleus both have an effect on the half life and just making a nucleus bigger, without increasing count of proton would actually increase half life as illustrated by alpha decay models i referenced above.

[Enthalpy]

You have derailed. Alpha emission appears at the most common isotopes of the elements as these get heavier than lead. It's a matter of repulsion and of barrier height. And too heavy elements don't exist because of alpha emission.

The detailed organisation of the nuclei, which is still a research topic, adds some fluctuations, so that simple models like the liquid drop are too coarse.

Don't try to save your misunderstandings by rhetoric. It won't help you correct them.