Chemistry in 4d

[anderscolingustafson]

I have found that the number of electrons in the p subshell is the same as the number of sides to a cube, I have also found that the number of electrons in each subshell can be found by adding 4 to the number of electrons in the previous shell. In a 4d universe the number of electrons in the p subshell would be 8 the same as the number of sides to a 4d cube. Assuming the 1st shell would still have 2 electrons the way to find the number of electrons for each subshell would be to add 6 to the number of electrons in the previouse subshell. The the number of electrons for each subshell would be 2 for the 1st, 8 for the 2nd, 14 for the 3rd, 20 for the 4th, 26 for the 5th and so on. The number of electrons needed to get a full shell would be 2 for the 1st shell, 10 for the 2nd and 3rd shells, 24 for the 4th and 5th shells and so on. The chemical that would behave most like water and, which life would probably use as a solvent would be either H2Ne, or H3F. Life would probably use nitrogen in place of carbon as in four dimensions nitrogen would be most able to bond with itself and other elements and would probably behave like carbon does in our universe. Just as in our universe organisms use a strand of DNA, which is longer in 1 of the dimensions than in the others, 4d life might use a sheet of DNA anolog, which would be longer in 2 of the dimensions than in the others. In a 4d universe there could be more elements because atomic nuclei would be 4d rather 3d alowing them to gain more protons and nutrons before becoming unstable. There could also be more elements that could be created in the cores of stars because it would take more protons and nutrons to make the nucleous to dense to be fused into another nucleous.

[wendy]

I'd really wish you would discover paragraphs. It does lead to greater readability.

In any case, there are solutions to the potential quantum well, which sets the shells in N dimensions. Ye get s=1, p=N. Each state is occupied by an 'up' and a 'down' electron. The shells, going outwards are 1s 2s 2p 3s 3p 4s 3d 4p ... Element names follow the supposed chemestry, not the place in 3d. So Ne is still at the end of the second row, not 'element 10'. Ne here would be z=12.

Elements like 2, 4+2N, 6+4N, ... are the noble elements.

The carbon-like element is 3+N, representing a simplex-arrangement in the 2sp shell (eg tetrahedral or pentachoral). You would have CH5 for 'methane'. O is typically set at 2+2N, ie 2 before Ne. Because C is now with 5 open bonds, you could have things like HCO2, or C2O5 or even C2O6. Water might still be H20 or H30, depending on where one allocates O (as bivalent or trivalent). A trivalent O would allow things like O2 and O4 (the latter tetrahedral atoms).

[PWrong]

I remember these numbers from 1st year physics and chemistry. I don't remember what they were about, but remember wondering what the pattern was and how to calculate more. The sequence didn't go very far.

[wendy]

Electrons, being fermions, can not occupy a state that a second one already has. Since they are spin-half particles, with +1/2 and -1/2, there can be two electrons in each state (with opposite spin).

The states correspond to solutions of the quantum potential well for different energy levels. (Ionisation corresponds to the energy required to escape a layer). The first layer is simply a spherical solution, 1s.

The second layer has a 2s solution, and N 2p (notionally a pair of lobes at right angles, so that there is one in the x, y, and z directions.

The 2sp layers can merge to give (N+1) lobes, being quite short at one end, and long at the other. This corresponds to lobes pointing to the vertices of a simplex. In carbon, these are occupied by a single electron each.

The layers of the third shell correspond to three solutions, 3s, 3p and 3d. d corresponds to something like 10 levels in N=3, but does not occur until after 4s (and before 4p. ie, The rows of the periodic table go

Code: Select all

  1s                              (2 items)
   2s (2)    <---- gap --->  2p    [2N+2]
   3s (2)   <---- gap ---->  3p    [2N+2]
   4s (2)        3d  (?)     4p   
   5s (2)        4d  (?)     5p
   6s (2)  4f    5d          6p
   7s      5f    6d          7p


Atoms in 4f and 5f are usually shown below the main table (rare earth metals).

[quickfur]

Some time ago on this forum it was discovered that the Schrodinger equation for the 4D atom has no stable solutions - assuming that the electromagnetic force propagates via an inverse cube law, the potential curve for an electron bound to a nucleus has no local minima which might define an orbital. So the 4D atom simply can't exist at all. To do any 4D chemistry at all will require a completely new and different physics, since the physics we're familiar with only works in 3D.

But of course, that doesn't mean we can't pretend that we can generalize orbitals to 4D by suitably extrapolating the patterns we observe in 3D. :-)

[anderscolingustafson]

I have also noticed that the first element that cannot form in the cores of stars has an atomic number of 3³ and the last element that can form in the cores of stars has an atomic number of 3³-3 so in 4d the fist element that could not form in the cores of stars would probably have an atomic number of 3⁴ and the last element that could form in the cores of stars would probably have an atomic number of 3⁴-1. This would mean that the last 4d element that could form in the cores of stars would probably be 4d element number 80 and the first that could not form in the cores of stars would probably be element 81. So the last 4d element that could form in the cores of stars would probably have 6 electron shells and be the tenth element of its shell.

[quickfur]

I don't think you can generalize it that easily... the physics behind the stability of nuclei is a lot more complex than mere nuclear volume, so simply generalizing x³ to x⁴ doesn't really quite pan out.

[anderscolingustafson]

Also in the fourth dimension life would probably be based on "carbon" rings that would be arranged into dodecahedron's instead of hexagons like in 3d. It might also have "carbon" rings arranged into cubes since cubes have the same kind of corners as dodecahedron's just like how life in 3d not only has carbon rings arranged into hexagons but also into pentagons. I wander though if 4d amino acids would be made of linear chains like in 3d or plainer chains do to the extra dimension.

As the 4d element that would be the building block of life would need the same number of electrons to fill its outer shell as 3d boron it would probably have some similar properties to 3d boron. For instance it could probably have some of its electrons involved in multiple bonds allowing it to bond with more atoms than the number of atoms it would have just like 3d boron, which would also be necessary for it to form the dodecahedral rings necessary for life in 4d.