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Could we in theory change atoms on an atomic level (Think 5 protons, 5 neutrons -> 4 protons, 4 neutrons), and if so could we then use those protons, and neutrons to add to another atom? (3 protons, 3 neutrons -> 4 protons -> 4 neutrons)

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We can certainly change atomic structure.

  • With nuclear fusion we can add protons and neutrons to the nucleus. Humanity managed to do this since 1958 and nature does it in stellar interiors all over the Universe.
  • With nuclear fission we can subtract protons and neutrons from the nucleus. Humanity has done this intentionally in nuclear reactors since 1939. Nature does it everywhere in radioactive materials, and even our planet has done it in a controlled sustained reaction.
  • Neutron capture allows for an increase in the number of neutrons in the nucleus. This is totally possible in modern laboratories and is something that happens in stars also.
  • By inducing $\beta$-decay you can transform a neutron of the nucleus into a proton, and by electron capture you can do the reverse process.
  • You can change the internal energy levels of the atom (thus its structure) by exciting their electrons (ionization and other phenomena) or their nuclei (gamma ray bombardment). Nature also does this everywhere, from lightning to stellar atmospheres.
  • You can change the electron energy levels inside the atom by putting it in an electric field, or also in a magnetic field.

There are many many ways one can change the internal structure and energy levels of an atom (photodisintegration, photofission, n-p reactions, etc...). An answer to your question would inevitably be extremely broad. Atoms are no longer regarded as indivisible elementary entities since the beggining of the XX century. Atoms are complex multi-part objects that can be splitted, rearenged, joined and transformed in many ways. The answer to your question is basically all of nuclear physics and even some chemistry.

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