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I have a question about the origin of the odd proton-number elements in the periodic table, please.

As it is generally thought that the big bang produces hydrogen first, and then hydrogen combined to form helium. Helium combines into beryllium, and beryllium into carbon, etc... This means that all fusion atoms have even numbers of protons, does not not?

Then, if radioactive decay involving protons always result in a 2 protons decay, how then can we ever end up with atoms of odd number of protons, such as lithium, boron, nitrogen, etc?

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    $\begingroup$ This is question rather for nuclear physics and cosmology. Generally, they are created by the same processes as even-proton nuclei. BTW Li, Be and B are not produced by fusion. See also Nucleosynthesis. Search also for S-process, R-process and Spallation. $\endgroup$
    – Poutnik
    Jan 9, 2022 at 10:00
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    $\begingroup$ @Poutnik According to the Wikipedia article you link, Li-7 can be produced by the fusion of tritium and He-4; and Be-7 can be produced by the fusion of He-3 and He-4. $\endgroup$
    – theorist
    Jan 9, 2022 at 10:03
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    $\begingroup$ @theorist I should say naturally and in majority. You cannot fuse 2 4He to 8Be, unless there is the 3rd 4He to form 12C. 7Be would quickly decay to 7Li. $\endgroup$
    – Poutnik
    Jan 9, 2022 at 10:06
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    $\begingroup$ @Poutnik The article described these as the "chief nuclear reactions responsible for the relative abundances of light atomic nuclei observed throughout the universe", indicating these are the primary reactions that gave rise to these isotopes. Yes, the Be-7 would quickly decay (half-life of 52 days), but Li-7 is stable. I.e., it's saying the main origin of present-day Li is nuclear fusion. $\endgroup$
    – theorist
    Jan 9, 2022 at 10:11
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    $\begingroup$ More generally, it seems the asker may not be aware of beta decay (both minus and plus, but especially the former) as a major process capable of converting nuclei with an even number of protons into a nucleus with an odd number of protons. $\endgroup$
    – Nicolau Saker Neto
    Jan 9, 2022 at 10:41

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One of the most significant sources of an odd-numbered element is the CNO cycle that operates to a minor extent in our Sun and more prominently in more massive stars like Sirius. There are actually several CNO cycles, but they all involve carbon, nitrogen and oxygen interchanging through the absorption of protons and the emission of alpha and positron beta particles. The net result is the same as direct hydrogen-to-helium fusion: four protons absorbed into the nuclei during this cycle are converted into one alpha particle and two positrons that are emitted, plus the same energy that we see with the direct fusion. This mechanism is responsible for nitrogen being the second most abundant odd-numbered element in the Universe, behind hydrogen but beating lithium and boron despite the lower atomic numbers of the latter two elements.

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