# 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.

• An atomic bomb explodes in about 1 microsecond which is $3.2\times 10^{-14}$ of a year.
– MaxW
Apr 26, 2020 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. Apr 27, 2020 at 4:23

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.

• Oscar, I'm sorry for the delay in marking this answer as accepted, I completely forgot. Jul 31, 2022 at 14:39