The title pretty much sums it all.
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2$\begingroup$ An atomic bomb explodes in about 1 microsecond which is $3.2\times 10^{-14}$ of a year. $\endgroup$– MaxWApr 26, 2020 at 23:40
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1$\begingroup$ Question titles should be like book titles. They distinguish the book from other books, give a hint about content, but do not tell the full story of the book. The content then should elaborate the topic to full depth the author is able to do. $\endgroup$– PoutnikApr 27, 2020 at 4:23
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1 Answer
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Let's look at just the carbon-14 atoms.
Assune 18.5% of your body mass is carbon and you weigh 80 kg. One carbon atom in a trillion is carbon-14. Working out the resulting mass of carbon-14 atoms in grams, dividing by 12.01 g/mol and multiplying by Avogadro's Number leads to roughly $7.4×10^{14}$ atoms.
Carbon-14 has a half-life of about 5730 years. Dividing $\ln 2$ by that figure you find that the probability of a specific atom of carbon-14 decaying in a year is 0.000176. For all the carbon-14 atoms to do it within one year you're looking at roughly:
$0.000176^{7.4×10^{14}} \approx 10^{-2.78×10^{15}}$
And that's just the carbon-14.
Did I mention that only one carbon atom in a trillion has this potency? Assuming the above scenario comes to pass with that proportion of atoms over the course of a year is going to make for a pretty wimpy explosion.
answered Apr 26, 2020 at 22:37
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1$\begingroup$ Oscar, I'm sorry for the delay in marking this answer as accepted, I completely forgot. $\endgroup$– ksousaJul 31, 2022 at 14:39