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I'm just learning about radioactivity, and there's one thing I'm unclear about.

Take $\beta -$ decay, for example. Since a neutron splits into a proton and an electron (and an anti neutrino), but the electron shoots out of the atom, the product has one extra proton, and hence is not electrically neutral, right?

I just want to confirm this because I never see the product being written as a positive ion, but rather as a regular atom.

If the product is an ion, why is it written normally?

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Radioactivity occurs (with the exception of k-capture in which the nucleus captures an orbiting electron) inside the nucleus of atoms, not in the electron shells. Yes, the product has one extra proton, and thus is now a different element, jumping up one in the Periodic Table. No nucleus is electrically neutral. Whether or not an atom is an ion has nothing to do with its nucleus and everything to do with its electron shells, mainly its outermost shell.

Edit:It occurs to me that after a neutron has split into a proton and an electron, thus adding one more proton to the nucleus, unless an additional electron is added to one of its other orbitals (which are generally as full as they can be), the new atom will itself be an ion, as it will have an unequal number of protons and electrons. Specifically, it will have one less electron than proton, unless the ejected electron is captured within the atom's electron cloud, and I believe that in most instances the electron is ejected with sufficient energy to escape from the atom completely.

I'm not sure if this was what the OP was asking about.

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Radioactive materials are studied in bulk matter. The electron that left with beta decay will become part of the conduction band electrons for the lattice the atom is in, and another electron will be drawn in very fast from the conduction band.. To remain an ion the atom should be isolated from bulk matter, and usually experiments are done on enough bulk to ensure the total neutrality.

It is also indicative of the difference in energies involved, ions belong to the keV level, radioactivity to the MeV and characterizes nuclei. By not calling it an ion one is discussing nuclear physics not atomic.

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