Are no chemical elements truly stable?

[jfizzix]

I recently learned that Bismuth is actually radioactive with its longest lived isotope having a half-life of about 20 quintillion years.
(For source, see: https://www.nature.com/articles/nature01541)

As a very basic question, what determines whether an element/isotope will be radioactive? Is there something special about certain isotopes that makes them stable? Are no elements truly stable, but just have half-lives too long to accurately measure?

 

[mfb]

As a very basic question, what determines whether an element/isotope will be radioactive?

If there is enough energy for a decay it will decay eventually.

It is unclear if protons (and neutrons) are stable or decay to other particles eventually. If they do (what is generally expected, but has never been measured) then all nuclei will decay eventually.
If we ignore that (or if they are stable) 90 nuclides are stable. As an example: You always have to put energy into a helium atom (both helium-3 and helium-4) to change it to something else. It cannot decay on its own.
56 additional nuclides cannot decay via the usual decay modes (alpha, beta, gamma) but could potentially decay via spontaneous fission. Their half-lives could be way beyond anything ever measurable.
107 additional nuclides can decay via one of the usual decay modes (typically alpha) but their half life is so long we have never observed a decay.
Wikipedia has a table and a list below.

 

[phyzguy]

If there is enough energy for a decay it will decay eventually.

It is unclear if protons (and neutrons) are stable or decay to other particles eventually. If they do (what is generally expected, but has never been measured) then all nuclei will decay eventually.
If we ignore that (or if they are stable) 90 nuclides are stable. As an example: You always have to put energy into a helium atom (both helium-3 and helium-4) to change it to something else. It cannot decay on its own.
56 additional nuclides cannot decay via the usual decay modes (alpha, beta, gamma) but could potentially decay via spontaneous fission. Their half-lives could be way beyond anything ever measurable.
107 additional nuclides can decay via one of the usual decay modes (typically alpha) but their half life is so long we have never observed a decay.
Wikipedia has a table and a list below.

I'm sure you know this, but your post implies that It's not known whether or not neutrons are stable. Of course free neutrons are unstable.

 

[mfb]

Free neutrons are unstable, sure, but neutrons in nuclei not necessarily. They are stable if and only if free protons are stable.

 

[Vanadium 50]

I recently learned that Bismuth is actually radioactive with its longest lived isotope having a half-life of about 20 quintillion years.

That is true. That's around 3x shorter than the prediction - i.e. a sample of bismuth is about 3x as radioactive as was predicted. This was discovered by a group that wanted to do precision measurements using BGO (bismuth germanium oxide) and discovering that the detector itself was more radioactive than they anticipated.

 

[king vitamin]

Free neutrons are unstable, sure, but neutrons in nuclei not necessarily. They are stable if and only if free protons are stable.

That's pretty interesting (specifically the second sentence), how does the argument for this go?

 

[mfb]

Every proposed proton decay goes to particles much lighter than a proton. So much lighter that you can add a pion to make a similar decay channel for neutrons, even if you don't find an easier decay for neutrons.

 

[lpetrich]

First, a note on proton decay. This usually refers to the decay of isolated protons, and such decays are predicted by most Grand Unified Theories. Neutrons will also decay by GUT mechanisms, and at similar rates, because of their similar quark content. I will ignore GUT decay in the rest of this discussion, with "stability" meaning stability in the absence of GUT decays.

Unstable nuclides are unstable because it is energetically favorable for them to decay into some other nuclides. If it is not, then they will not decay. Nuclear Binding Energy and Nuclear binding energy - Wikipedia have more. The most tightly bound nuclide is Ni-62, followed by Fe-58 and Fe-56. So nickel-62 won't decay into anything.

An alternative to individual-nucleus decay is quantum-tunneling fusion, usually followed by some decay reaction. Such "pycnonuclear reactions" are VERY slow in ordinary matter, slower than some calculated GUT decays.