Is there a formula that can be used to find the half life of an atom?
If so, what is it?
half life of an atom?!?!?
you mean half life of a nucleus right?
and the formula depends on what you are given....
Yeah half life of a nucleus.
I mean, say if you had radon nuclei, neptunium nuclei, and ununbium nuclei, etc. what is the pattern, or how can it (for example) calculate the half life of a unbihexium nucleus?
that is very very complicated. I am specalizing in Nuclear structure physics, and calculate half life from just theory is very complicated.
The pattern is how ever that the further away you are from the valley of stability, the shorter half-life.
Atomic nuclei are many body quantum systems with approx 240 particles (these nucleis you stated), so it is very complicated. So if you want to calculate this, you need a good reference on theoretical nuclear structure physics.
Also you must specify what ISOTOPE you are considering.
But things in nature always have a reason for being there, a physical principal.
Why are the valley of instability and the sea of instability in those spots?
Nuclei tends to go towards the most bounded state, which then is the most stable.
See for example this picture, showing you beta decay sequences for mass number A = 76.
The most bounded nuclei with A = 76 is Se-76, and you see two parabolas. The upper one is odd odd (i.e odd Z and odd N), the lower is even-even. The parabolas is the mass of the nucleis, the less mass, the more bound it is (remember the concept of binding energy).
Now the general idea is that depending on who many protons and neutrons you have, you get different potentinal wells, which gives you the number of stable/bound states and HOW stable they are etc. And this is a very complicated thing as I said.. The principle is to minimize the mass, physical systems always tends to go the lowest state physical possible.
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