# If every radioisotope atom in your body decayed at once, would you explode? What are the odds of it happening spontaneously? [closed]

The title pretty much sums it all.

• Ask a question like that and get an answer like ... see below. – Oscar Lanzi Apr 26 at 22:38
• An atomic bomb explodes in about 1 microsecond which is $3.2\times 10^{-14}$ of a year. – MaxW Apr 26 at 23:40
• 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. – Poutnik Apr 27 at 4:23

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:
$$0.000176^{7.4×10^{14}} \approx 10^{-2.78×10^{15}}$$