The elements of the periodic table are defined by the number of protons in the nucleus of the atom. If there is a different number of protons, then it must necessarily be a different element. There is no such thing as the same element, but with a different number of protons in the nucleus.
There are also neutrons within atomic nuclei, and it is possible to have atoms of the same element but with varying numbers of neutrons. These are known as isotopes, and I would like to explain the formation of isotopes in my own way.
One of the first elements that we usually think of when we hear of isotopes is uranium. This element has 92 protons in it's nucleus. Most uranium atoms, the vast majority, are of the isotope known as Uranium-238, this means that there is a total of 238 nucleons, protons plus neutrons, in the nucleus. There is another isotope of uranium with fewer neutrons, Uranium-235. This is significant because U-235 can undergo nuclear fission, while U-238 cannot. Enriching is the extremely painstaking process of separating out the few percent of U-235 atoms from the rest.
Another commonly noted isotope is that of carbon. Most carbon is Carbon-12, with six protons and six neutrons in the nucleus. But there is also Carbon-14, with two extra neutrons, which undergoes radioactive decay. Since the so-called half-life of Carbon-14 is very precisely known, when half of the C-14 will have decayed into another isotope, it is of great use in archeological dating since all living things and former living things, such as wood and textiles, contain carbon.
Hydrogen, the lightest element with only one proton, actually has three isotopes. There can be either no neutrons, one neutron forming the isotope known as deuterium, or two neutrons in the nucleus forming tritium. The heavier isotopes of hydrogen are useful in that they can be combined with oxygen to form "heavy water", this is water, H2O, in which the hydrogen atom have neutrons so that it is heavier. This makes it useful as a nuclear moderator. Ordinary water cannot be used as a moderator because it absorbs neutrons, but if the hydrogen atoms in the water molecule already have neutrons it will slow down the neutrons without absorbing them.
In the centers of stars, lighter atoms are crunched together into heavier elements. Stars shine because there is some leftover nuclear binding energy when this takes place that is released. The first atoms created by the Big Bang, which began the universe, were mostly hydrogen and far lesser amounts of helium, lithium and beryllium. The vast majority of the atoms in the universe are still hydrogen.
The number of neutrons in the nucleus of a given atom is the result of the "addition route" that it took to get where it is by smaller atoms being crunched together into larger atoms. My thought is that a nucleus put together from more smaller atoms, rather than a few larger atoms, will tend to have fewer neutrons even as it has the same number of protons as like atoms. But, on the other hand, it would seem to make sense that unions formed of fewer atoms would be more likely to occur even if it may be easier to crunch smaller atoms together than larger ones and smaller atoms are naturally much more abundant. Some atoms are first formed as heavier ones and then, through radioactive decay, turn into lighter atoms.
Basically, the route through the "factor tree" of small atoms being crunched together into larger ones that the atom of the given element takes to arrive at being that element determines which isotope of that element it will be,
Another question is where neutrons originate from. We know that a neutron left outside a nucleus will decay into a proton and an electron in a relatively short period of time. This implies that neutrons are actually protons and electrons crunched together so that they are neutral particles with no charge, with the electron changing one of the component quarks to another. The neutron requires the nucleus to hold it together even as it holds the nucleus together. The larger the atom, by far the greater the number of neutrons relative to protons.
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