There’s some accuracy to that, but one also has to consider the amount of radioactive material available, too. After shutdown on a nuclear plant, for example, the isotope of major concern (outside the core) is Co-60. Not only does it have a relatively short half-life (a bit over five years, IIRC) but the beta decay of the isotope releases a very high energy gamma ray, just at the point in the energy curves where most traditional shielding schemes are weakest.
The amount of a radioactive material available is measured in units of Curies. A Curie is defined as that amount (or mass, if you prefer) of a given isotope that produces a disintegration rate of 3.7 x 10[sup]10[/sup] events per second. Like the mole, there is an astronomical number of atoms in each Curie. Now, remember, moles are 6.023 x 10[sup]23[/sup] atoms. One can get a large number of curies in a very small absolute mass of some isotopes. I shudder to think how many curies a mole of Co-60 would have…
However, cobalt is in the reactor plant in strictly limited numbers - it’s used in some alloys of steel that will be exposed to greater than normal erosive forces. In the core there are kilograms of fissile materials. Which more than makes up for the much longer half-life the fissile isotopes have.
Radon and it’s decay daughters are a common decay chain to use to illustrate this phenomenon. (Here’s a brief description of the decay chain, on Wiki.)
Thanks, all, for the helpful information. Let me push the discussion elsewhere. In reading Atom by Lawrence Krauss, he talks about how the elements came into being after the Big Bang, and that some hydrogen atoms, for instance, that we have today may be the very ones created early on. My question is: are atoms forever? Do their component electrons ever get “tired” form all that movement. Is a hydrogen atom that was created during the BB identical to one that may be created today? Is attraction and dance between the electron and proton as active?
Is the answer the same regarding molecules? Is a water molecule ten billion years old identical one made today? Do the bonds ever deteriorate? Does the net energy in the molecule dissipate over time.
By the way, thanks to all for keepiing the answers intelligible for the non-chemist.
Every element has unstable isotopes. In fact, every element has an infinite number of unstable isotopes. There’s no reason you couldn’t put one proton together with 10,000 neutrons, and make the hydrogen isotope [sub]10001[/sub][sup]1[/sup]H. I wouldn’t count on those 10,000 neutrons staying together very long, of course (back of the envelope, I estimate about 10[sup]-28[/sup] seconds), but isn’t that the whole point of something being unstable?
And the question about whether long or short half-lives are more dangerous is a bit complicated. On the one hand, it doesn’t matter how much rubidium 87 you’re exposed to; you’re not going to get a dangerous exposure from it. On the other hand, if something has a half-life of fifteen seconds, you can probably keep it well-protected for the few minutes it takes to become harmless. The most worrisome things are those with half-lives of, say, a few thousand years: That’s quick enough that exposure to them can be dangerous, but on the other hand, how confident that nobody’s going to ever break into your containment site in the next few millenia?
“Infinite” might be pushing it a bit. At some point, you’ll have enough neutrons that gravitation will overtake the other forces and your homemade atom will turn into an artificial neutron star or even a black hole. I suppose for all practical purposes, “infinite” is close enough, though.
And of course I forgot to refresh after coming back from lunch. Essentially all hydrogen nuclei (that is to say, individual protons) in existance today date all the way back to The Beginning, as well as a significant amount of the helium and lithium nuclei now in existance. However, the same nuclei were not associated with the same electrons for all of that time. Most elements (and especially hydrogen) just love sharing their electrons around in various ways. All chemical reactions involve electrons being shuffled around from one atom to another, so any atom which has ever participated in any chemical reaction almost certainly has different electrons than it started with. However, it doesn’t make any difference: Even though they don’t have the actual same electrons, all electrons are exactly identical, and all protons are exactly identical. If I made some protons, neutrons, and electrons in a particle accelerator, then combined them into atoms of hydrogen and oxygen, and then combined those atoms into molecules of water, there would be no difference whatsoever between those brand-new water molecules and water molecules which have been together for ten billion years.
This is also true for radioactive atoms, by the way. If I have a single atom of an isotope with a half-life of ten years, and through incredible luck that atom happens to have survived for a thousand years, that thousand-year old atom will be identical to any other atom of the same isotope that’s only a minute old. It doesn’t “remember” in any way that it’s old, nor is it “due” to decay, nor does it get “tired”. It’ll have a 50-50 chance to decay within the next 10 years, just like any other atom of that isotope.
I have to add: no experiment can rule out the absence of proton decay. At best, the lower bound can be increased.
Really? What about the protons generated by neutron decay? Unless you’re saying that these are only a tiny fraction of all protons (which they may be).
This is actually how the heavier elements (more massy that iron) form; in the wavefront of an supermassive exploding star, stellar nucleosynthesis occurs. While the p-process just binds free protons to existing nuclei to form new elements, the r-process and the s-process involve neutron capture plus beta decay (or inverse beta decay) to convert a neutron to a proton or vice versa in order to transmute elements. So protons can be “created”, or more properly, converted from neutrons.
Highly unstable atoms (those with more neutrons than protons, or for heavier elements, those out of the “Valley of Stability”) won’t exist for more than a fraction of a second, and then only under extremely high temperature and pressure conditions which may, in fact, be primordial or quagma-like conditions, so it’s hard to talk about the stabliity of these atoms; it’s sort of like trying to make a pig back out of a sausage.
Careful, you’re getting close to debunking homeopathy.
Going a bit beyond the scope of the OP’s original question and follow-ups, here. But isn’t that a bit oversimplifying things?
AIUI, there is no way to predict how a specific atom of any given isotope will behave, but there are some questions about whether or not individual nuclear geometries or other “deep” nuclear structure may affect how quickly a specific nucleus decays. We can describe what happens with radioactive decay, but the reasons for it are still poorly understood. (Primarily on the lines of comments like those that Stranger on a Train made about the "valley of stability.) In some ways it reminds me of the problems that organic chemistry had before the idea that the structure of the various complex organic molecules could affect how they behaved.
I certainly don’t want to give the impression that I believe that there is some way to make unstable isotopes stable. Just saying that we may not yet know all the things that should be being measured. (Though I’ll admit it’s quite possible, we couldn’t measure them all even if they are found to exist, thanks to Heisenbergian-style exclusions.)
One more question: Isn’t it theorhetorically possible for high energy pair production to produce protons and anti-protons?
Pair production only produces elementary particles (and their complementary anti-particles, of course). Protons are composite particles (hadrons) made from one down and two up quarks. I suppose the requisite quarks (and anti-quarks) could be produced and condense into a proton and its evil twin, but since free quarks don’t exist under normal conditions[sup]*[/sup] owing to the principle of confinement this is unlikely. Hadronization–the condensation of quarks into normal baryonic matter (stable protons and neutrons)–only occurs under free quark conditions, such as the early, pre-expansion phase of the universe or (hypothetically) in the quark-muon plasma center of a massive star.
Stranger
*With the exception of the supermassive top quark, which decays rapidly.
There is a finite amount in the universe, correct? (This is only somewhat rhetorical) Thus, although this really isn’t an issue for atoms, an element can have a finite number of isotopes.
OtakuLoki: Yes, high energy interactions can produce proton/antiproton pairs (although, often with other random junk produced alongside.) Behold: FNAL’s antiproton source. Chronosdid say “essentially” all protons. Proton production much after the initial burst is peanuts compared to what we started with.
