Is this an original discovery, or is it known already?

Several years ago as I was perusing the periodic table of elements, I noticed a pattern in the structure of the atom which seemed to correlate with the pattern of the periodic table itself. My discovery started when I noticed that the innermost layer of electrons in an atom was limited to two, and from lithium on up, any larger atom required extra layers for additional electrons. Each successive layer has a specific limit, beyond which another layer becomes necessary.

The pattern among established elements runs thus:

Layer | Electron limit
Innermost layer - 2
Second layer - 8
Third layer - 18
Fourth layer - 32

Now, I toyed around with mathematical patterns from time to time. I noticed the prescence of 2, 8, and 32, and thought, 'Well, if the other number were 16 instead of 18, it'd be a lot more symmetrical.'

Or would it?

As I fiddled with the numbers, I saw a symmetrical enough pattern emerge:

Each number is first added to itself, and then multiplied by itself.

Thus:

[color=blue][b]0 + 0 x 0 = 0
1 + 1 x 1 = 2
2 + 2 x 2 = 8
3 + 3 x 3 = 18
4 + 4 x 4 = 32[/b][/color]
[color=red][b]5 + 5 x 5 = 50
6 + 6 x 6 = 72
7 + 7 x 7 = 98
8 + 8 x 8 = 128
9 + 9 x 9 = 162
10 + 10 x 10 = 200[/b][/color]

(blue are the electron limits of currently known elements; red are projected limits of thus-far undiscovered elements).

Now, when I arrange a periodic table, I do it a little differently than the versions you show on this website. I base mine upon mathematical patterns rather than chemical properties. For example, I place helium in the magnesium-calcium group of elements, rather than with the inert gases:
[img]http://members.odinsrage.com/exterminance/Periodictable-2.jpg[/img]
Note how, in this arrangement, every second left/right row claims a number of elements that corresponds to the numerical pattern based upon the limit of electrons in each successive layer:

First row - 2 elements
Second row - 2 elements
Third row - 8 elements
Fourth row - 8 elements
Fifth row - 18 elements
Sixth row - 18 elements
Seventh row - 32 elements
Eighth row - 32 elements

Thus, I would predict that if many elements were discovered past element 120 (unlikely enough, granted the inherent instability of artificial elements), they would extend into families even greater than those of the lanthanides and actinides, and that the subsequent rows of elements would appear in successive steps at these lengths:

Ninth row - 50 elements
Tenth row - 50 elements
Eleventh row - 72 elements
Twelfth row - 72 elements
Thirteenth row - 98 elements

... and so on.

It was a few years ago that I discovered this mathematical pattern, and I have never seen mention of it in any scientific books, so I am just curious as to whether anyone has discovered it before me?

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Re: Is this an original discovery, or is it known already?

[quote="kevinanrt"]That's made up to total 118 electrons when all of these shells were filled, so the element 119 would be very impossible because there is no 7d subshell and fill in that 1 extra electron.[/quote]

actually what your saying is not that 119 would be imposible it would just be impossible for 119 to hold onto its electrons. remember an atom is still an atom no matter how many electrons you knock off it. so 119 can probably only exist as an ion. ie Uun+ etc hmmm n = nil and nova how they get around that in the internation system of temporary names.....

Actually, the argument is fallacious; it is the intellectual equivalent of saying that there is no planet past Saturn because there were only seven orbits known to Aristotle or that there is no continent between Africa and Asia because all of the continents are known. There is no limit to the number of electron orbitals possible, and they are a function of quantum numbers which are infinite. In theory, the lone hydrogen electron can occupy any orbital at all and presumably the light from the sun comes from hyrdogen electrons bouncing from all sorts higher orbitals to lower states.

That higher orbitals exist is clear from the fact that the 3d and 3f suborbitals possess a higher energy state than the 4s which accounts for the odd blocking of the periodic chart. Since there is a 5s orbital, quantum theory predicts four additional suborbitals: 5p, 5d, 5f, & 5g.

For a neutral atom, the number of electrons is equivalent to the number of protons and there may be an upper limit because the forces of repulsion within the nucleus may ultimately become too great for any other forces to overcome, even momentarily, so that any limit to the number of elements would be constrained by nuclear forces not by electron orbitals.

And also, by this formulae
2n^2, where n is the number of shells
We can know the maximum number of electrons which can be put in the shell(n).

Also there may be three components

In all periodic table it is visible that any whole part - a row, the period, group, a subgroup - can be divided on two components. The same principle you can see in the structure of atom.
Fragment of structure of family consisting of two components
see on www.genevo.org/Z1.htm

The whole rule was very simple. For each new subshell, the number of electrons go up by 4.

Therefore, s:2, p:6, d:10, f:14

However, electrons always tend to go to the shell with lower energy. The pattern comes with 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p etc. As the inner shells are really inner, they can hold lesser electrons.

I hope to include the formula later.

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