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What's the antimatter content of a banana?

2008-10-21 11:06:37

Antimatter is strange, exotic stuff, right? Only produced in dangerous physics experiments? Leads to complete annihilation with ordinary matter?

Sort of. It's a question of quantity.

Consider the element potassium. Potassium, like sodium, is an alkali metal; potassium ions in solution play an important role in several different biochemical processes. You have to eat potassium or you'll die, but this is true for lots of different plants and animals, so potassium deficiencies aren't common in well-fed people. Natural potassium is made of three different isotopes. About 117 parts per million natural potassium is potassium-40, 40K, which is unstable with a lifetime 1.25 billion years. This radioactive potassium is left over from the formation of the solar system; in the 4.5 billion years since the earth coalesced, 97% of the the original 40K has decayed.

A "medium" banana (whatever that means) has about half a gram of potassium, or 7.7×1021 atoms. Of these, 9.0×1017 (about sixy micrograms) are 40K. If you picked just one of these nuclei, you'd have to wait a billion years (on average) to see it decay; in our banana we have lots of atoms we can watch all at once, so there will be about 23 decays per second. Of these decays, 89% are β- decays to calcium, and 11% are electron capture decays to argon. Only one decay in 105 actually emits an antielectron. So an ordinary banana contains an antielectron for a brief instant about once every 75 minutes.

Of course, all the β- and electron capture decays are accompanied by an electron antineutrino, which leaves the banana at the speed of light. Which is a bigger contribution to the antimatter number density in a banana: an antielectron that stops and annihilates, or an antineutrino that instantly escapes?

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