There is so much to be discovered just by noticing relatively simple patterns in numbers. Here is something else that I have found and at the bottom is a link to more.
There is something about how stars operate that I have never seen referred to but have long thought deserves attention. We would always like to know more about stars since we depend on one, the sun, for life on earth. But we can only ever study stars by the electromagnetic radiation that they release. It isn't possible to actually land a spacecraft on a star.
But there is a star that we can access, although it no longer exists as a star. It is what I refer to as "The Most Accessible Star". We know that our sun is a second-generation star, because it contains elements that are heavier than it's current stage in the successive fusion process. The star that preceded the sun exploded in a supernova and some the matter fell back together by gravity to form the sun and the planets. We know that this star was much larger than the sun because only the largest stars will explode in a supernova. Every atom on earth, including every atom in your body, was once part of this star that exploded.
The reason that a star shines is that the collective gravity of it's mass overcomes the electron repulsion that keeps atoms separate. Smaller atoms are continuously being crunched together into larger ones. The new, larger atom has less overall internal energy than the ones that were crunched together to form it. The excess energy is released as radiation, and this is why stars shine. This process is known as "fusion" because atoms are fused together by gravity.
The fusion process continues, with successively heavier elements being fused together. But, as this happens, more energy is being released per time. This upsets the equilibrium of the star, between the outward release of energy and the inward force of gravity. A star like the sun will eventually swell into a "red giant", but the largest stars will explode from the center as a supernova. The sun is now at the early stage of fusing four atoms of hydrogen into one atom of helium. It contains elements heavier than this because it is a second-generation star.
This ordinary fusion only goes as far as iron, element number 26. The elements up to iron tend to be formed by this process, known as the S-process, for "slow". This is why iron is so abundant in the inner Solar System and is the most common element in the earth, going by mass.
The elements that are heavier than iron are formed only by a supernova, during the brief time that the star is actually exploding, because an input of energy is required to force atoms together that would not be joined by the ordinary fusion process. This is known as the R-process, for "rapid".
This is why elements heavier than iron, including gold, silver and, uranium, are exponentially less common than the elements up to iron. Only a fraction of the elements up to iron are further fused into heavier elements. Some of these new heavy atoms are less-than-stable and gradually give off particles or radiation, in order to seek a more stable state. These emissions are known as radioactivity.
In terms of atoms, remember that "heavier" does not necessarily refer to mass but to the number of protons in the nucleus. Generally elements with more protons are indeed more massive. But there are exceptions. Iron has exceptional density and, although tin has more protons, iron is heavier than tin.
When the large star that preceded the sun exploded in a supernova it's matter was scattered across space, including the heavier elements formed by the energy of the explosion, as described above. Some of the matter fell back together by gravity to form the sun and Solar System. While the process of falling back together is mostly complete, it is actually still going on. That is why the earth may still be struck with meteorites and asteroids.
In a star the heavier elements, when it reaches that stage, tend to fall toward the center. This creates a rough layering, by mass, as shown in the following image from the Wikipedia article "Oxygen".
Remember that this does not include elements heavier than iron, because the star has not yet exploded in a supernova, and only the largest stars will end in a supernova.
What this tendency toward layering, by gravity, means is that atoms of the same element tend to be together when the matter is thrown across space by the supernova. This is why the deposits of metals on earth are of a certain specific metal, such as iron or copper or lead. The metal deposits that we mine are the result of asteroids, composed of that metal, striking the earth. This is why the arrangement of these deposits are unpredictable and do not follow a pattern. Which is why we cannot predict where a deposit of gold might be found.
Rare Earth elements have been in the news lately. These are metals that have useful applications in modern electronics. Rare Earths are elements 57-70, and also 21 and 39. They are not actually rare, they are just generally difficult to mine and often don't occur in concentrated deposits.
As successively heavier elements are fused together in a star, the heavier elements are formed from a kind of "factor tree" of lighter elements. What caught my attention is that there is a pattern in the atomic numbers of the Rare Earth elements. From 21 to 39 is 18, and from 39 to 57 is also 18. 18 is a very divisible number.
A very common fusion route in stars is the Triple Alpha Process, in which three helium atoms are fused together into a carbon atom. This is why carbon is so common. A helium nucleus is sometimes referred to as an Alpha Particle. A helium atom has two protons and a carbon atom has six. If we then put three carbon atoms together it would give us the 18.
Iron, atomic number 26, is so common because it is as far as the ordinary fusion process goes. If we put two iron and one carbon atom together we get cerium, with atomic number 58, which is the most common of the Rare Earth elements.
What I find to be so interesting is that the Rare Earth elements tend to be found together on earth. That is why we read about "Rare Earth mines", whereas other metals are found separately. I haven't seen it referred to but this has great astronomical significance, as it reveals what happens inside a star during a supernova. This is when the elements heavier than iron, which do not form by the ordinary fusion process, are able to form because of the input of energy caused by the explosion of the supernova.
The explosion of a supernova is not neat. There is not a sudden "bang" and then it's over. The energy released builds to a peak, and then decreases. The brilliant light released by the supernova of 1054 continued for about two years. The remnants of it are what we see today as the Crab Nebula.
What I have decided happens is that the elements from 6 to 10 get mixed together, by the initial force of the explosion, before some are fused together into heavier elements. These are carbon-6, nitrogen-7, oxygen-8, fluorine-9 and Neon-10. Iron is so common because it is the end result of the ordinary fusion process, so iron atoms may get mixed in too.
What do you notice about these five elements? They are all non-metals and are very common. We could call these the "Common Non-Metals". Most elements are metals. The difference between a metal and a non-metal is that a large number of neighboring atoms in a metal, known as a crystal, share their outermost electrons. This is why metals have different properties than non-metals.
This is the Periodic Table of the Elements. Image from the Wikipedia article "Periodic Table". A Periodic Table is structured like a calendar. Each successive element has one more proton in it's nucleus than the one before, which is the definition of the element.
There is a maximum of eight electrons in the outer shell of an atom, and the number determines the chemical behavior of the atom. Columns in the Periodic Table have elements with the same number of electrons in the outer shell, and thus with similar chemical behavior. This is like the days of the week in a column of a calendar.
But remember that none of this has anything to do with ordinary chemistry, which is determined by the number of electrons in the atom's outermost shell and has nothing to do with the nucleus. This is about fusing atomic nuclei together into heavier elements.
The non-metals, other than hydrogen, are concentrated in the upper right of the Periodic Table.
This is the same image with the five Common Non-Metals indicated by the red dots. They are in a row in the upper right.
These Common Non-Metals are mixed together in the initial stages of the supernova explosion. They are mixed together, before being fused together into the Rare Earth Elements as the energy from the supernova becomes greater, because they are non-metals and so the initial energy of the supernova doesn't go into forming metallic bonds between the atoms.
With the layers of elements that are heavier and lighter than this, some of the energy applied by the supernova explosion goes into forming structural bonds between the atoms that have already been fused together from lighter elements. But with these elements, from 6 (carbon) to 10 (neon), the energy from the supernova explosion first goes to mix the atoms together before they are then fused together into the Rare Earth elements. This is why the Rare Earth elements, lacking the structural bonds of other elements, are difficult to mine because they do not occur in masses.
This is what forms the Rare Earth elements and explains why they tend to be found together on earth. These lighter elements got mixed together by the force of the explosion, before some were fused together into heavier elements. Since the star was in the process of exploding, the new heavy elements didn't have as much chance to settle into layers by mass as during the ordinary fusion process. The elements above and below the Rare Earths came from a different factor tree and had more chance to settle into layers, which is why other metals tend to not be found with other metals.
The heaviest Rare Earth is 70. That could have formed by ten nitrogens or seven neons, without iron, or one or two iron atoms might be included.
Since element 21 is included in the Rare Earths, that must mean that elements lighter than iron may also form by the R-process. Three nitrogen-7 atoms together would form it, and then adding three carbon-6 would form element 39.
Here is a link to a posting about discoveries made by noticing patterns in numbers. I noticed this pattern in the formation of Rare Earth elements because 21 to 39 is 18, and then 39 to 57 is also 18.
www.markmeeksideas.blogspot.com/2024/05/the-special-numbers.html?m=0
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