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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new discovery

Two of the chief problems here are 1) that mathematical patterns can be extracted from almost any array given enough ingenuity and 2) such mathematical patterns are merely mathematical, not chemical which is what the periodic chart is supposed to be; helium stands in the group with neon because it is also an inert gas; calcium is an alkaline earth metal similar in properties to magnesium and strontium; all three will accumulate in your bones if you ingest them; you can eat and breathe all the helium you want and none of it will form phosphate compounds in your bones.

On another level the mathematics is significant. quantum level 1 has one level and contains 2 positions Thus, the first period of the periodic chart has 2 elements H and He; quantum level 2 has two sublevels 2s and 2p. The s sublevel accomodate 2x1 electrons; the p sublevels 2x3 electrons; thus the second period has 8 elements Li, Be, B, C, O, N, F, and Ne. The third level has 3 sublevels 3s, 3p, and 3d with 2x1, 2x3, and 2x10 electrons; Period three contains 8 elements (Na, Mg, Al, Si, P, S, Cl, and Ar) because the 3d level is of such energy that the 4s level (K and Ca) are filled before the 3d orbital gets filled thus the ten transition metals of the d-block (Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, and Zn) and the 4p elements Ga, Ge, As, Se, Br, and Kr) are the 18 elements of period 4. The 4f orbital is of such high energy that its 14 elements don't appear until La and the rare earths.

The importance here is not merely that a mathematical order can be created but as Mendeleev first proposed, the periods predict recurring chemical properties. A key point is that in order for Mendeleev's scheme to work out, he was forced to leave blank spots in the table for elements not yet known, Thus, he had knew of no tetravalent metalloid before As, but needed one, so he predicted ekasilicon with properties much like those discovered in Germanium. Thus the chart's value is not merely that it presents the data in a tidy fashion, but that it predicted phenomena.
In modern nuclear chemistry, it is harder to confirm predictions because the transuranic elements are of such minimal durations, but element 118 should be an inert gas, 119 should be an alkali metal and 121 should inaugurate a g-block of 18 "super-rare" earths.

This is obviously a creative & intelligent individual

Keep on thinking creatively. Your theorum shows evidence that you are a true scientist. I ask of you "Is Hydrogen the start of the periodic table of elements?" Just like "When did time begin?" Infinity. Well done.

I have the extra elements through 153 up at my site. Here is a direct link: http://www.chemicalforums.com/index.php?page=periodictable

Nice web-site Mitch!!!

However, under Arsenic I think it is spelled sublimation not suplimation; also, are you sure of the melting and boiling temperatures for I? I think those are under pressure and that I otherwise sublimes.

True, Iodine does sublime readily, I didn't think about that. However, the data at my site is consistent with what webelements has within .1C, so I'm assuming its correct.

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

[quote="Exterminance"]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?[/quote]

There IS NO 8th SHELLS OR MORE!!! TOday known shells is only 7 and 8th shells is unlikely to happen because it's gonna be the whole artificial shell, (The 7th shells were natural happening, for ex- uranium's configuration:2,8,18,32,21,9,2)which means that 7th shell were already created, 8th shell(or larger) will be too hard to make because it need more force to move electrons into the orbit.
And the Shells can't have more than 32 electrons, Those shells don't has enough energy to held those electrons, that's why after shell 6 the electron it held is decreasing~ too much energy to hold that much elecron in far outer shell!
The following is the List of the Subshells of each shell
1. s(2 electrons)
Total 2 electrons
2. s(2 electrons)
p(6 electrons)
Total 8 electrons
3. s(2 electrons)
p(6 electrons)
d(10 electrons)
Total 18 electrons
4. s(2 electrons)
p(6 electrons)
d(10 electrons)
f(14 electrons)
Total 32 electrons
5. s(2 electrons)
p(6 electrons)
d(10 electrons)
f(14 electrons)
Total 32 electrons
6. s(2 electrons)
p(6 electrons)
d(10 electrons)
Total 18 electrons
7. s(2 electrons)
p(6 electrons)
Total 8 electrons
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.

the number of the electrons per shell is predicted by quantum mechanics -
it's all to do with the degeneracy of the quantum numbers in the various shells etc etc (it's years since i looked at this stuff, so please excuse the vagueness....)

If you wanted to do the sums (and I don't doubt somebody somewhere already did), you could find the wavefunctions for the next orbitals beyond 7f or whatever..... they'd probably be lovely shapes, even wierder than f.
(would they be called g orbitals? "f" stands for fine...... "g" could be "gah!" .......)

Thanks for all your feedback, folks.

Since the website hosting the image of my periodic table crashed, here is the same pic on Geocities [url=http://ca.geocities.com/exterminance/periodictable.html](link)[/url].

[b]kevinanrt[/b] - the 8th shell may be unlikely, but it's still possible - who knows what might be discovered in the future?

And of course, most elements above Uranium don't occur in nature due to their instability. I would conjecture that, if it were possible to continue making atoms without any upward restriction on the number of subatomic particles, that their structures might follow the pattern that I outlined; but, due to the inherent instability of the bulkier atoms, I guess we may never know...

Unless somebody invents, say, some sort of force field in which supersized atoms are stabilized... who knows where science and discovery may take us?

Exterminance,
I really think it's best to try and think of all this in terms of
what "physically" is going on, rather than in terms of just pure maths.

the number of electron levels in each quantum shell are
predicted by quantum mechanics - now, of course, one could argue
that quantum mechanics is just mathematical voodoo and number
games at their worst ;-)
but it's not too bad an analogy to think of it like this
the electrons are vibrating 'standing waves' of resonating negative
charge around the nucleus.
Just like the real harmonics you get in nature when a piano string or
a drum skin vibrate (different "modes" of vibration - various
different ways a complete wave can fit onto that confined
string or skin),
similarly, there's only a finite number of ways (or resonant harmonic modes) that electrons could be wibbling around a nucleus -
so this, "physically", is where these numbers in the "shells" of electrons come from.

The reason that successive shells can hold more electrons is...
...um, well my quantum mechanics is a bit rusty ;-)
but in effect, each shell has more 'quantum numbers' to play with
(you could think of these as analogous to "dimensions" - such as
vertical, horizontal..... in actual fact, they correspond to
properties like spin and angular moment and stuff)

Another thing I completely forgot -

also bear in mind that all atoms have *all* the orbitals there, available -
it's just that they're vacant.

Even a hyrgoen nucleus (a single proton) has, in principle, a nice set of 5f oribtals sitting there around it -) .... in fact, it probably has "g" orbitals there as well.

If electrons get "excited" (bless them, they are such excitable little fellows), they can grab hold of a passing photon and jump up some levels
(thus creating an absorption spectrum),
and when they get tired and want to come home for their tea,
they can emit a photon and jump back down to lower levels (producing the lines of emission spectra)

what these vacant orbitals "are" is in effect, the number of unique ways in which an electron can wibble around a nucleus (analogous to the modes of vibration of a string).

WebElements: the periodic table on the WWW [http://www.webelements.com/]

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