I'm studying isotopes in high school and I don't understand how it works.
From my understanding, when neutrons are added or removed, an isotope is created.
To calculate the number of neutrons, the atomic number is subtracted from the atomic mass and then rounded to the nearest number.
What is the reason why neutrons would be removed? What could cause neutrons to be removed from the nucleus of an atom?
Many elements are found in nature with differing number of neutrons. For example, hydrogen may be found with no neutron (1H, AKA protium, where the atomic mass is ~1, just a proton and a lightweight electron), with one neutron (2H, AKA deuterium, where the atomic mass is ~2, a proton, a neutron and a lightweight electron), and so forth.
All of them are called isotopes. Isotope just means that the number of neutrons is specified in the atomic mass, as in 1H and 2H. As naturally found in nature, though, most elements contain a mix of isotopes. For example, on Earth, hydrogen in the oceans contains about one atom of 2H for every 6420 atoms of 1H. However, that is just an average, and the isotopes of hydrogen can be separated comparatively easily (because of the comparatively large mass differences of its isotopes) by natural processes, such as evaporation, or by the Girdler sulfide process.
There are some monoisotopic elements, such as fluorine, that have only one stable isotope. $\ce{UF6}$ is used for separating isotopes of uranium, because of this, avoiding the hassle of also having to separate the isotopes of the element with which uranium is combined.
As for changing the number of neutrons, that is not done through most chemical processes (though one could argue that a chemical explosion can trigger a thermonuclear explosion directly). The number of neutrons may change if the element is intrinsically radioactive, as when 226Ra emits an alpha particle (2 neutrons and 2 protons), changing it to 222Rn, or when a a substance is bombarded by neutrons, as in a star or nuclear reactor.
The chemistry of an atom is determined by the behaviour of the electrons, which in turn is dictated by the number of protons in nuclei. The so the thing which defines the element is the number of the protons.
Unless we consider kinetic effects then the number of neutrons has no effect on the chemistry of an element. If I was to do an experiment with Cs133, Cs134, Cs135, Cs136 or Cs137 then the cesium will behave in the same way in all the experiments. The only stable isotope of cesium is Cs133 but the others will behave the same way.
The number of neutrons in nuceli can be changed by either radioactive decay or by reactions induced by things which strike the nuclei.
Alpha decay causes the loss of two neutrons and at the same time two protons.
Beta - decay causes a neutron to turn into a proton
Electron capture or beta + decay causes a proton to turn into a neutron.
If nuclei are struck by thermal neutrons it is possible for them to capture neutrons and thus increase their neutron number by one for each neutron which hits them. Consider for a moment if I was to put Cs133 in a thermal nuclear reactor, some of the neutrons would be captured by the Cs133 nuclei to form Cs134.
If you use faster neutrons then other reactions start to become important such as reactions where a neutron is caputred and a proton is ejected from the nucelous. For example C-14 is formed from N-14 by this reaction.
With faster and faster neutrons more bits can be spallated out of the nuceli, it is possible to have reactions where nuclei are hit by a neutron and then things like helium nuclei, tritons, deutrons and other stuff comes out. What happens is that the energy of the incoming neutron causes the product nuclei to have an energy above the ground state.
For example Pu239 if it captures a neutron it forms Pu240, the higher the energy of the Pu240 product the more likely it is to split (fission) to form two nuclei. With lower neutron energies the fraction of Pu240 nuclei that manage to relax down into the ground state by emitting gamma rays increases.
Another option is photonuclear reactions, beryllium has a very low threshold energy for such reactions. If you expose beryllium to gamma photons which are a few MeV in energy then the Be9 nuclei eject a neutron and form Be8. Be8 is very unstable and quickly undergoes an alpha decay to two helium atoms.
You are being confused by linguistics; an attempt to explain, that has failed. Elements are defined by the number of protons in the nucleus. In the neutral atom there are an equal number of electrons in their appropriate energy levels [orbitals]. The electron arrangement is responsible for Chemical reactions and varies with the element. You will learn all about that in chemistry, college and graduate school so be patient.
The nucleus of hydrogen, Protium, H, has one [1] proton. There is also another stable isotope [nuclide] of hydrogen with one proton and one neutron, Deuterium [D]. There is another "natural" isotope of hydrogen, Tritium [T] that contains, again, one proton, and 2 neutrons This isotope [or nuclide] happens to be radioactive or unstable. Other isotopes of H have been made in nuclear reactors. This is true of most elements: there are several stable isotopes, sometimes natural radioactive isotopes, and many others have been made in nuclear reactors. The artificial isotopes are usually of little concern in most chemistry unless inserted specifically into molecules as tracers. In Chemistry we are usually talking about the natural mix of isotopes unless specifically stated or sometimes strongly implied.
Isotopes were formed in the nuclear reactors of stars, and we get to work with those that are stable enough to form into planets. An elemental symbol in chemistry almost always refers to the natural mix of isotopes the only ambiguous one is H. H can stand for the natural mix or for protium, the H isotope with one proton and No neutron. Isotopes of an element have very similar but NOT identical chemical and physical properties. This means that chemical reactions carried to completion or equilibrium will maintain the isotopic balance. Other reactions will show isotope effects. The differences are most pronounced for hydrogen H, D, and T.
Tritium, T, gives us a hint to what is going on in nuclei. It has an extra neutron and is unstable. Neutrons are needed to prevent the positive protons from repelling each other but too many neutrons are unstable in themselves. There are optimal neutron numbers for each element, usually close to the number of protons in each direction. Too many or too few neutrons and the nuclide is unstable, radioactive. It is fascinating to lookup a table of nuclides to see which are stable and the various nuclear reactions of unstable nuclei to become stable. A nuclide with too many neutrons loses negative charge; a nuclide with too few neutrons loses positive charge; there are several ways of doing each. This is nuclear chemistry!
The mass of a proton and a neutron are almost identical; the mass of an electron is much smaller so the mass of a proton+electron is again almost the same as that of a neutron. Each nuclide [isotope] consists of a number of proton-electron couples and a number of neutrons. These can be counted, and the count is the Atomic Mass Number. The total number is measured by comparing the mass of the nuclide to the mass of a defined nuclide and relating it to Carbon-12. The atomic mass unit, amu, is 1/12 the mass of a carbon-12 atom. [this is not strictly true because the definition is slightly different based on a defined value of Avogadro's number]. The number of proton-electrons and neutrons is measured by the relative mass; the number of protons is measured from Xray spectra; the difference is the number of neutrons. in the isotope. Tha actual relative mass in atomic mass units must be measured and is very close to a whole number because the mass of a proton-electron and neutron are almost the same and the binding energy holding the nucleus together, while huge, requires a small change in mass.
Isotopes exist and chemists usually use them as they are in the natural mix. There are specific applications where specific isotopes are involved. Chemists are not commonly involved in manufacturing isotopes. That is done by nuclear chemists and physicists using nuclear reactors, colliders etc. It is going on in the Sun and stars, a little bit in our upper atmosphere from cosmic ray interaction with matter, and the decay of radioactive nuclides that are still around, as we watch.
