A little debate at work today. Does every element have a half life or only the radioactive ones? If they all do then why and if not then why?
thanks,
Pat
Elements without half-lives are known as stable elements. Digging around this site reveals various elements that are stable. Oxygen-16, -17, and -18 are examples. Hydrogen is usually stable as well (with some exceptions).
By definition, only radioactive isotopes can have half-lives. This is because radioactive decay is the only process by which an element can “disappear,” leaving another in its place. Most elements have one or two radioactive isotopes, but only the transuranic elements and a handful of others have only radioactive isotopes – these are the “radioactive elements.” Such an element has several isotopes, and thus has a combination of half-lives; usually the isotope with the longest half-life is the most common one, and that half-life is attributed to the element as a whole.
A half-life is not a property of an element. It is a property of an isotope. And not every isotope decays to a completely stable istope in a single step. As to whether any completely stable isotopes exist at all, I’m not entirely certain. Perhaps a Quantum Mechanic can share with us the answer to that question. It’s conceivable that the “stable” isotopes merely have half-lives that are so long that it’s easiest to just treat them as though they will never decay.
I believe that all elements have a half-life.
In fact, even protons are surmised to have a half-life (on the order of 10[sup]31[/sup] years).
Cite:
http://hyperphysics.phy-astr.gsu.edu/hbase/particles/proton.html
In a larger sense, one of my observations I have made in the physical sciences is that virtually all characteristics of the natural world consist of a spectrum. Examples include: the electromagnetic spectrum, solution solubility vs. insolubility, ionic vs. covalent bonding, etc.
In other words, just as there is no sharp dividing line between blue and green on the visual spectrum, there is no sharp dividing line between “radioactive” and “stable.”
Note that half-lives for elements characterized as “stable” may not have been determined. The longer the half-life, the harder it is to measure.
Eventually, protons and neutrons will decay. As they play an integral role in the structure of the isotope, I suppose every stable isotope has a half-life measured in the length of time it will take for half of its protons and neutrons to break down. But as that’s such a long, long time, it makes no real sense to speak of the half-lives of stable isotopes.
kaylasdad99 is on the money, of course. Please replace the term “elements” in my previous post with “isotopes.”
What if you meant by half life “the time it takes to change into another element”. In other words: does the decay of protons and neutrons in stable isotopes turn them into different elements?
Well, of course. Nuclear decay of any sort results in transmutation.
Just checking that the decay of protons in “stable” elements is the same as in “unstable” ones. So my chair radiates too, does it?
Or into something else entirely. A hydrogen nucleus, for instance, consists of a single proton (at least, in the simplest isotope). When that proton decays, it’ll most likely turn into a positron (the antiparticle of the electron), an unknown number of photons, and an unknown even number of neutrinos. The positron will then likely annihilate with the electron which was orbiting the proton, forming two more photons, and neither photons nor neutrinos are considered “elements”. Actually, there are many other combinations of particles a proton might conceivably decay to, but all of them can eventually get down to just photons and neutrinos.
Note, secondly, that the 10[sup]31[/sup] years that robby quoted is just a lower bound: Since we’ve never actually seen it occur, it could be much longer, and the fragments of a Grand Unified Theory which we have are only just enough to predict that it decays at all, without giving us any numbers we can be confident in.
Note, thirdly, that this is for a proton in isolation, and it’s quite possible that in combination with other protons and neutrons (like in an atomic nucleus), the lifetime of the proton might be longer yet. For comparison, a neutron all by itself has a half-life of about 15 minutes, but most things with neutrons in them last much longer than that.
Although everything chronos said is accurate (AFAIK), let me just add a few points. I think it would be fair to describe any decay involving protons as extraordinary. Proton decay has never been observed, but on that basis it has a half life of 10^31 years. Maybe much longer. Ordinary radioactive decay involves either the expulsion of a helium nucleus (alpha particle), which lowers the atomic mass by 4 and the atomic number by 2 so you get an element 2 lower on the periodic chart or the decay of a neutron and expulsion of an electron, which leaves the atomic mass unchanged and raises the atomic number by 1. For instance, the main reaction in a nuclear power reactor involves first the capture of a neutron by U-238, which turns it into U-239 (that’s not a decay reaction at all), followed quickly by a beta decay producing Np-239 and a second beta decay producing Pu-239, which, while not stable, has a long half life.
IIRC no element above bismuth has a stable isotope and there are two elements below (technetium is one and I don’t recall the other) that have no stable isotope either and have not been found in nature.
However, I have often wondered if something like O-16 might decay, but just with a half life so long that we have never noticed. The H-1 nucleus consists of a single proton and can decay only by proton decay.
It is thought that in the far future (say 10^120 years) all the protons and similar particles will have decayed, all the black holes will have evaporated and the only thing left will be a “soup” of photons and neutrinos.
And just as a particularly nitpicky correction, let me add that technically what we’re talking about is not necessarily isotopes but nuclides. Each element has one or more nuclides – what makes it an element, with the chemical and gross-physical properties of that element, is the number of protons; what makes a nuclide is the sum of protons and neutrons. Carbon has six protons and six, seven, or eight neutrons, the varieties with different neutrons being distinguished as C-12, C-13, and C-14 respectively. An Isotope is one of two or more nuclides of a given element. If you will allow that one of a set of quadruplets can refer to his same-age brother or sister as “his twin,” then “twin” becomes synonymous with “isotope” – in the sense that a person who was a single birth does not have a twin, but people who were parts of multiple births can have one or more twins.
Almost all elements (perhaps all) have radioactive nuclides; many are composed only of radioactive nuclides. In the case of Indium, interestingly, over 95% of the element is a radioactive nuclide with a half-life in the quadrillions of years; the stable isotope is less than 5% of indium.
Polycarp, I have always understood the terms “isotope” and “nuclide” to be synonymous. (And for what it’s worth, this comes from someone who is quite familiar with the Chart of the Nuclides). After reading your post twice, (and googling for “nuclide isotope”) I still fail to see the distinction, other than the fact that “nuclide” sounds cooler. 
The other element you’re thinking of is promethium. Both it and technetium were first created artificially. [sub]99[/sub]Tc has since been found in African pitchblende in very small quantities. And promethium has been identified in the spectrum of a star in the Andromeda galaxy.
The distinction as I learned it – and this may have gone the way of “shall” vs. “will” over the years – is quite simple.
A hypothetical element with only a single nuclide has no isotopes. An element with two or more nuclide has that number of isotopes – “isotope” presumes another isotope of that element to exist.
If Nobelium, for example, exists in only one nuclide, there are no Nobelium isotopes. Thorium exists in only one semi-stable nuclide; Uranium has two semi-stable isotopes.
Catch the distinction that way?
I believe the latest figure for the minimum length of proton decay (coming from an article in New Scientist IIRC) is 10[sup]36[/sup]. Just bought us a bunch more years that way. 
Thanks, I understand the explanation.
However, how can any element (hypothetical or not) have only one nuclide? Can one not always presuppose the existence of another nuclide with one more or one less neutron? Stable or not, this hypothetical nuclide is a different isotope with different properties (that may likely include that of an exceedingly short half-life).
To use your thorium example, while thorium indeed has only one naturally occurring isotope (Th-232), the entry for thorium in this nuclide table lists properties for an additional 28 isotopes, ranging from Th-210 to Th-238.
For that matter, why can I not consider the case of Th-209, Th-208, or even Th-200? Even though Th-200 has never been isolated, it surely has existed at one time, if only in a supernova, and likely not for long.
Radioactive elements have half-lives, but if they study hard and get a good education, they can lead very full lives.