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I heard that even a banana generates a minute quantity of antimatter. Does any know radioactive nuclear reaction produce antimatter along with alpha, beta and gamma radiation?

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Bananas are notorious for having high levels of potassium, though a quick Google will find plenty of other potassium rich foods. Anyhow, one of the common radioactive isotopes of potassium is potassium-40. This mostly decays by emission of an electron and anti-neutrino but rarely it can decay by emission of a positron i.e. anti-matter. So it is true that bananas emit minute quantities of anti-matter.

But ...

Bananas don't emit a net amount of antimatter because the electron is always paired with an anti-neutrino and the positron is always paired with a (not anti) neutrino. The number of particles emitted is always equal to the number of anti-particles emitted. This always true and is the result of conservation of lepton number.

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    $\begingroup$ It might be fun to quantify your "rarely". I was surprised to learn from your potassium-40 Wikipedia link that K-40 decays an estimated 4,900 times per second in the human body. So how much anti-matter does a banana produce per second? $\endgroup$ – Aaron Novstrup Sep 20 '16 at 18:44
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    $\begingroup$ Ah, right, it's all there. A banana produces ~12 positrons a day, if I'm not mistaken. ;) $\endgroup$ – Aaron Novstrup Sep 20 '16 at 20:19
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    $\begingroup$ @Crowley: $\beta^+$ (a positron) is antimatter, if that's what you're asking. $\endgroup$ – Charles Sep 21 '16 at 0:29
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    $\begingroup$ so to power that antimatter drive all we need is about one moon sized pile of bananas? $\endgroup$ – jwenting Sep 21 '16 at 14:16
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    $\begingroup$ @jwenting And the ability to break the law of conservation. $\endgroup$ – TylerH Sep 21 '16 at 15:28
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This is the chart of nuclides, i.e. the isotopes of all atoms.

nuclides

The green color shows that most nuclei have isotopes decaying with beta+ decay, i.e. positrons. If you go to the link there is interactive information.

From this it is seen that everyday items which will always have a tiny percentage of the long lived isotopes will be decaying into positrons, the antiparticle of an electron.

Nuclides that have too many protons will decay with beta+

alpha, beta and gamma radiation

The "beta" in your question is both a beta+ and beta- , and yes the statement is correct.

The beta+ decay frees a positron into the environment of the nuclide.

$^\mathtt{A}_\mathtt{Z}X \rightarrow ^\mathtt{\hphantom{Z-}A}_\mathtt{Z-1}X' + e^+ + ν_e$

This decay is used in positron emission tomography, because the positron meeting an electron in the environment will annihilate into two photons and give medical information:

Positron emission tomography (PET)1 is a nuclear medicine, functional imaging technique that is used to observe metabolic processes in the body. The system detects pairs of gamma rays emitted indirectly by a positron-emitting radionuclide (tracer), which is introduced into the body on a biologically active molecule.

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