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I was not able to find an answer for this question...

Some radioactive elements have half-life measured in thousands of years and some others even in millions, but over 4.5 billion years all the radioactive material that was part of the initial material that formed the planet earth should have decayed by now?

However, there is still radioactive material with short half-life to be found in nature. How is this possible and if the answer is that the new radioactive material is constantly being generated somehow, can you explain the mechanism of how this happens?

Thanks.

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    $\begingroup$ Half-life is defined as the time for half the material to decay. If you constantly half something, it will keep getting smaller at a lower rate, but never quit reach 0, although when you are talking about atoms, eventually it will reach a point when there is 1 atom left, and after that there will be none left. $\endgroup$
    – AttackingHobo
    Commented Mar 18, 2011 at 20:01
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    $\begingroup$ @AttackingHobo Of course, it's entirely probabilistic (there's a 1/infinity chance that your material will never decay entirely). :) $\endgroup$
    – Mateen Ulhaq
    Commented Mar 19, 2011 at 5:03

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The half-life of Uranium 238 is about the age of the Earth, so only about half of the original supply should have decayed by now. Also, there are some radioactive nuclei that get created by interactions with cosmic rays in the upper atmosphere (carbon-14) or decay from more stable nuclei (all of the daughter nuclei between U-238 and lead, for example).

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  • $\begingroup$ I thought that half-life of U238 is measured in millions of years, if it is about the age of the Earth, that, in combination with some shorter half-life radioactive elements being the products of the decay of other radioactive elements, explains everything. Thanks. $\endgroup$
    – Dean Kuga
    Commented Mar 18, 2011 at 16:23
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    $\begingroup$ U238 is about 4.5Bn years (almost exactly the age of earth) U235 is about 700Myr $\endgroup$
    – Martin Beckett
    Commented Mar 18, 2011 at 18:27
  • $\begingroup$ @kzen: Useful link if you know what isotopes you are interested in: ie.lbl.gov/education/isotopes.htm $\endgroup$
    – dmckee --- ex-moderator kitten
    Commented Mar 18, 2011 at 18:56
  • $\begingroup$ And 700 Myr still means that you're going to be left with about 1% of the original material after 4.5 billion years - "tiny part", but for billions of tons of material, it still means you're left with tens of millions of tons, quite easy to notice. $\endgroup$
    – Luaan
    Commented Apr 30, 2015 at 11:08
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It's because the half life time is also incredibly long.

The half-life of Uranium-238 is $4.5*10^9$ (=4.5 billion) years. Thorium-232 has $1.4*10^{10}$. Potassium-40 has $1.2*10^9$. These are all examples of primordial nuclides. Such half lives are of the order of the age of the universe.

There's also the effect of having a decay chain, since decay products themself can also be radioactive. Although if you look at the tables you'll find that only a few decay products have a significant lifetime -- most are either stable or negligble short. It does explain why you will always find materials with short half lives.

One noteworthy mentioning is ofcourse carbon-14, which is used in radiocarbon dating (i.e. estimating the life of certain soils or the remains of plants and animals). Here stable nitrogen-14 is turned into a radioactive carbon-14 by a collission with a cosmic neutron (which replaces one proton). The carbon is then absorbed from the atmosphere by plants or oceans. Carbon-14 has a half-life of roughly 6000 years, which is considrably shorter than the earths lifetime.

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  • $\begingroup$ Question n-14 +1n would yield an atomic mass of 15, something must be missing. $\endgroup$
    – Omega Centauri
    Commented Mar 18, 2011 at 16:55
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    $\begingroup$ @Omega Centauri : a proton is emitted in the process. So N-14 +1n -> C14 + 1p. $\endgroup$
    – Olaf
    Commented Mar 18, 2011 at 17:02
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Some elements with short half-lifes, are just decay products of those with long half-lifes.

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The short half-life elements ocuring in nature come from the decay of long-half life elements. You can see examples of decay chains on this wikipedia page. For example, ²²⁴Ra (3.6 days half life) is produced by the decay of ²³²Th (14 billion years decay).

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Since the universe has not yet run out of hydrogen, new stars are forming. When those stars reach end of life and nova they produce the heavy elements beyond iron.

So until there are no more stars (large enough to create the heaviest elements such as uranium) and is no more hydrogen to form further stars, there will be a constant creation of further heavy elements.

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    $\begingroup$ Yes, but the creation of heavy elements in stars doesn't significantly affect the abundance of such elements on Earth. $\endgroup$
    – Keith Thompson
    Commented Sep 23, 2012 at 0:37
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Since radioactive materials are made in the intense power of super novas, radioactive materials can be created all the time since there are always supernovas going off and spreading this material around.

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Generally after 6 to 10 half lives radioactivity reduces very significantly. 133-In has half life of 180 milli secs (ms), so its radioactivity falls significantly after a few minutes. In comparison, 137-Cs with half life of 30.07 years show significantly low activity levels after 180 years or more.

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