cosmology - Is there no radioactive decay between nuclear fusion and solid material formation?

I'm aware my question might be considered a duplicate of this one: Radio-dating and the age of the earth

I read that one and I looked everywhere and I still can't find my piece of mind. I would really like to understand the following points:

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  does one uranium nucleus start the radioactive decaying process the instant it is born inside a supernova ? (I understand that for a single nucleus the chance of decaying which is an instantaneous event, grows from 0% to 100% in the time from the beginning to the half-life)

  
  


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  while talking about a collection of atoms, Wikipedia states here that "This predictability allows the relative abundances of related nuclides to be used as a clock to measure the time from the incorporation of the original nuclides into a material to the present."

  
  



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  @JohnRennie helped me understand that chemically speaking zircon and lead do not mix whereas zircon and uranium do. So basically macroscopic contamination via accretion with flying lead is an event too rare to take into consideration right ? Also... I understand that the uranium-lead decay series has very short half-lives for every nuclide except for the beginning and the end (uranium and lead) and so, from a cosmological perspective it's quite improbable that zircon would mix with anything other than uranium, should a chemical compatibility exist with another nuclide.

  
  

Please bare with me and excuse my "highly scientific" vocabulary.

I have an experiment I would like to imagine in order to discover what I'm doing wrong:

1. A star goes supernova


2. We concentrate our attention on one uranium nucleus which is fused together during the violent event


3. The uranium nucleus travels for millenia towards the an accretion cloud surrounding a newborn star



4. The nucleus collides with brand new molten zircon crystal and becomes part of it.

Let's say that event 4. was happening after 0.99 uranium half-lives and the uranium nucleus still hadn't decayed. Isn't it imminent that the nucleus will decay pretty soon after event 4. ?

I mean, I understand that if the nucleus would've become thorium or protactirium or lead it wouldn't've gotten stuck in the crystal for chemical reasons, but if it was still uranium what does that say about the internal clock of the nucleus which had been ticking for 99% of the half-life ?

Is that clock reset because of external electromagnetic reasons the moment the nucleus becomes part of the crystal ?

Thank you for your indulgence

Answer

Here's the key point:

If [the nucleus] was still uranium what does that say about the internal clock of the nucleus which had been ticking for 99% of the half-life ?

The answer is "nothing," because a single nucleus doesn't have an internal clock.

Here's a better model for what's happening in an unstable nucleus. Think of it as an enclosed container with a small hole, or a tunnel, somewhere near the top.

Somewhere down in the bottom of the container is a rubber ball. That's the alpha particle. But the whole thing isn't just sitting there, static, because oscillators in quantum mechanics don't sit still even in their lowest energy states. The container is jumping and jiggling around, like it's on a paint shaker, and the ball is constantly bouncing off the bottom and off the walls. Importantly, the hole in the container always stays up near the top.

What happens to this system over the long term? Most of the time the ball only bounces partway up the walls of the container and falls back down. Sometimes it goes higher than the opening — but because the opening is small, the ball usually misses and falls back to the floor again. Eventually, by chance, the ball will find just the right trajectory so that it hops right out the tiny exit hole and leaves the container for ever. But the vibrations that take the ball near the hole are chaotic, and there's no way for you know whether the ball is "about" to come out or how long it's been bouncing around. Every time the ball hits the bottom, it gets a new random trajectory. The dice roll again.

If you have an unstable system, there's 50% chance it'll still be intact after one half-life. If you check on it later, and it's still there, there's still a 50% chance that it'll be intact after another half-life. But there's no memory, and no "almost decayed," for a single nucleus.