Join Date: Jul 2004
Location: Surrey, UK
Posts: 92
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Hydrogen on one side, Helium on the other, and nothing in between ?
It may seem like my question should be in another board on periodic tables but I need answers from here. I'm hoping for vigorous criticism on a couple of deliberately annoying questions;

1) Why do the inner shells have a specific electron capacity - and the outer ones all the same ?

2) Is there any chance that helium and hydrogen fit as well into other columns in the periodic table ? (I'm not saying they do - just hoping for an explanation in terms of physics rather than chemistry)

3) Could there be atomic orbital shells, or sections of those shells, that we cannot detect ?

4) Whilst chemists like to flatten out the orbital shells, is there any room for physicists to envision multi dimensional electron shells ?

5) Could it be that on the chemists flattened out electron shell model (okay I admit they don't really use them ), that dark matter is in fact atoms with electrons in inner shells before we even see the Hydrogen shell ?

I think its best I stop there - but I would really appreciate any comments or criticism. Any details about why my comments are stupid would be welcomed immensely.

Many thanks

Simon

I'm not even sure exactly what the questions you are asking mean? Perhaps I could give an elementary description of what electron orbital (shells) are and then get the questions rephrased with this in mind. Schrodinger set up wave function for the possible potential energy levels of an electron in a hydrogen atom V=-er (e electronic charge, r distance from the nucleus, as a point, and the electron). Solving the equation, Schrodinger found that the electron could be described by three quantum numbers, which are now called n,l, and m. These quantum numbers establish the state of the electron, fixing both its energy and the wave function. n is the principal quantum number, and the principal determinant of the potential energy, it can have the values 1,2,3,--n(but not zero). In an atom, electrons having the same value of n are said to be in the same level or shell. As the quantum number increeases the energy of the average distance of the electron cloud from the nucleus also increases.
Each level of electrons in an atom includes one or more sublevels or subshells. These sublevels are characterized by the l quantum number (the angular momentum quantum number). The l quantum number determines the general geometric contour of the electron. For a given value of n, l is limited to the values l=0,1,2..(n-1).
The third quantum number, m(magnetic orbital quantum number) is associated with the orientation of the electron cloud with respect to a given direction usually one that is imposed on the atom by a strong magnetic fiels. for a given value of l, m can have any integral value between l and -l. Electrons having the same values of n,l, and m are said to be in the same orbital. Within a given sublevel of quantum number l there will be 2l+1 orbitals.
There is a fourth quantum number (the spin quantum number) it can have two values +1/2 or -1/2. electrons are said to be paired if one is +1/2 and the other is -1/2 in the same orbital. The Pauli exclusion principle states that no two electrons in the same atom can have the same set of four quantum numbers.
Using these rules one can determine the orbital filling sequence of all the elements.

Remembering that psi^2 (the wave function square) gives the probability of finding an electron within a particular volume of space-- one can calculate the size and 3-dimensional shape of the various orbitals corresponding to the various n,l,m quantum numbers. The pictures and plots that are given in the literature and textbooks correspond to the volumes that would have a 90% probability of containg the electron. The energies (obtained from spectroscopy) and the shape (from x-ray measurements) found experimentally correspond to those calculated theoretically.
see:
. Report *New York Times* 9/9/99 page D-1. Study in *Nature* by J. Spence et al. of the sharpest direct images ever made of electronic bond orbitals. “The shapes revealed by these images- doughnutlike rings, dumbbell shaped lobes and arrays suggestive of butterfly wings- confirmed theoretical predictions of what these bonds should look like in the molecule under study. “Orbitals have generally ben considered more as useful mathematical representations than as physical reality., but Dr. Spence and his colleagues have shown that orbitals can actually be imagined. “I want to emphasize,” he said in an interview,” that these pictures are not computer simulations. They are photographs: true images of real objects.” [paper] J.M Zuo, M. Kim, M. O’Keefe, and J.C.H. Spence.1999. “Direct Observation of d-Orbital Holes and Cu-Cu bonding in Cu2O” Nature 401:49-52. [comment] Colin J. Humphreys. 1999. “Electrons seen in Orbit” Nature 401: 21-22. “Whereas in an isolated hydrogen atom all the 3d states have the same energy; this degeneracy is removed in transition elements if they are in an environment which is not symmetrical, as is the case in many crystals....The paper by Zuo, et al, is remarkable because the quality of their charge-density maps allows, for the first time, a direct experimental ‘picture’ to be taken of the complex shape of the dz2 orbital... The correspondence between the experimental charge-density map of Zuo et al (see fig. 3d, p. 50) and the textbook dz2 orbital is striking.”

Bernard