Does the number of electrons in an atom determine the element?
No, the number of electrons does not determine the element. For example, atoms of iron and the iron ions in ferrous sulfate and ferric nitrate, for example (FeSO4 and Fe(NO3)3, respectively) have different numbers of electrons, but the same number of protons. What happens in beta decay is that a neutron decays, forming a proton and an electron. Due to the high energy level, the electron is emitted as a beta particle. However, because of the proton formed, the element changes. Beta decay always forms the next element up in the periodic table. Technetium would form ruthenium, for example. Hope that helps a little!