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An atom’s atomic number is defined as the number of protons in the nucleus. This is done because it defines the number of electrons the atom has, which defines it’s chemical reactivity. The nucleus actually consists of both protons and neutrons. When a nucleus decays, one of the neutrons splits and becomes a beta particle and a proton. So, now the nucleus will have one less neutron (which wasn’t counted in the atomic number before) and becomes a proton which is counted.
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