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From A Short History of Nearly Everything by Bill Bryson:

Atoms, however, go on practically forever. Nobody actually knows how long an atom can survive, but according to Martin Rees it is probably about 10^35 years

Can anybody explain this result to me?

I am told that the original atoms in the universe were likely Hydrogen, condensing out of primordial big bang stuff. Lighter atoms are said to come around as part of the fusion cycles that keep stars running, and heavier ones out fusions that occurs in energetic events like supernovae. We also have radioactive decay to consider. I'm fine with all of these things, but it sounds like Bryson is talking about something altogether different.

I see how you could make a statistical argument involving the likelihood of a given atom to be involved in future such events, but I don't think that is what's going on here as the result is twenty-five orders of magnitude older than the universe (as far as we know). Any ideas?

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This has to do with the probability that the proton would decay into lighter subatomic particles, such as a neutral pion and a positron, which is a calculable number depending on the theories existing at the moment. The limit in your quote is one order of magnitude higher than the latest experimental limit of proton decay up to now.

If a proton decays in the nucleus of an atom the nucleus disintegrates because it loses a baryon and the energy released within will destroy it, and then the atom dissolves.

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  • $\begingroup$ No one knows experimentally if the proton will ever decay, there is however an lower limit on its life time. it is predicted to decay by many GUT's. $\endgroup$
    – Prathyush
    Commented Oct 26, 2012 at 10:47
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    $\begingroup$ @Prathyush: There is also an upper limit from standard model instanton mediated decay, which is enormous. $\endgroup$
    – Ron Maimon
    Commented Oct 26, 2012 at 21:35
  • $\begingroup$ I did not know that thank you. can this instanton mediated decay be approximated by a Feynman vertex, after somehow calculating its contribution. I know what instantons are but their contribution to Feynman diagrams is very new to me. $\endgroup$
    – Prathyush
    Commented Oct 26, 2012 at 22:20
  • $\begingroup$ Well even if all the protons got destroyed there will still be neutrons. These neutrons can undergo beta decay and turn into protons. So the atom can still last longer than that. Of course you are right about proton decay(it is not experimentally proven of course). $\endgroup$
    – Roghan Arun
    Commented May 11, 2020 at 17:33
  • $\begingroup$ @RoghanArun atoms depend on electromagnetic interactions for their binding also. The nucleus will disintegrate once protons start decaying , first with nuclear decays and then when all protons are gone the neutrons will be free to decay. $\endgroup$
    – anna v
    Commented May 11, 2020 at 18:01

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