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2.1- http://mbscientific.org/wiki/Creation_of_Nuclei

2.2- http://mbscientific.org/wiki/Creation_of_Orbitals

ch2- Creation of Atoms

Through a big bang event all of the permutations of possibilities of particles are formed. Of these, the stable proton-neutron-electron combinations go on to form atoms. Protons and electrons, having a positive and a negative charge attract one another in a one-to-one manner. For each proton in a nucleus, typically one neutron acts as a buffer, otherwise protons, by the virtue of having the same positive charge would repel each other. So the process of atom creation adds one electron, one proton and at least one neutron to the atom until the periodic table of elements is complete. Atoms have isotopes, that is the same number of electrons and protons but more neutrons.

The process for creation of atoms takes shape in two manners. First is the creation of nuclei and second is the formation of the electron orbitals.

Protons and neutrons, subjected to the strong nuclear forces, fuse together to create nuclei. The simplest element's nucleus, hydrogen, having a single proton (2 up and one down quarks), is formed in the cooling process of a big bang event. Once gravity takes hold, dense hydrogen clouds form proto-galaxies. Eventually, gravity collapses portions of the clouds into denser and denser balls until the gravitational squeeze forms a star and starts fusion reactions. In proton-proton fusion reaction, hydrogen nuclei are fused together at about 700000-1 million Kelvin (MK), forming helium nuclei in a 3 step cascade (isotopes are noted in parenthesis):

1- deuterium isotope formation: 2 protons ==> (proton/neutron) + positron + neutrino
2- light helium isotope formation from deuterium isotope: (proton/neutron) + proton ==> (proton/proton/neutron)
3- helium nuclei formation: 2(proton/proton/neutron) ==> (proton/proton/neutron/neutron)+ 2 protons.

Once enough helium nuclei are formed, the helium fusion cascade starts at about 100MK. It is a 3 step cascade as well (P= Proton, N= Neutron), called triple-alpha (helium nucleus) process:

1- helium to beryllium fusion: 2 P2N2 ==> P4N4

2- beryllium fuses to helium producing carbon:

P4N4 + P2N2 ==> P6N6

3- sometimes carbon fuses to helium producing oxygen:

P6N6+ P2N2 ==> P8N8

At about 600+ MK, carbon fusion proceeds. One reaction, demonstrated in a 4-step cyclical cascade, is called the carbon cycle:

1- carbon isotope formation: P6N6 + P ==> P6N7 + positron + neutrino

2- the isotope fuses with proton to form nitrogen: P6N7+ P ==> P7N7

3- nitrogen isotope step: P7N7 + P ==> P7N8 + positron + neutrino

4- completing carbon cycle P7N8 + P ==> P6N6 + P2N2 , expelling helium and rejoining the cycle

Stars that achieve fusion beyond carbon are much more massive than the sun and run at much higher temperatures. The list below summarizes some known fusion cascades:

Hydrogen - Helium - 1 Million K

Helium - Carbon (Oxygen) - 100 Million K

Carbon - Neon - 600 Million K

Neon - Oxygen - 1 Billion K

Oxygen - Silicon- 1.5 Billion K

Silicon - Iron - 3 Billion K

Larger nuclei require yet more temperature/pressures to be produced. That is achieved in super-nova explosions. In fact super-nova explosions recycle stars. That is the supernova clouds form stellar nurseries, which in turn condense the elements, including heavy elements, back into new stars. Much stronger, hyper-nova explosions, obliterate entire portions of galaxies, thereby creating all of the heavy elements and recycling them back into the newly modified galaxy.

Once nuclei are bubbled up to the stellar corona or are ejected (e.g. via supernova explosions) they can pick up electrons to complete the creation of atoms. Nuclei pick up electrons in a one-to-one manner proportional to the number of protons they contain. But these electrons can fill orbitals at discrete (quantized) energies. We have evidence to that fact because as elements such as hydrogen heat up and radiate, they emit light at given frequencies (energies). That is when hydrogen electron drops from one orbital to a lower energy orbital, and the difference of the energy of the electron from one orbital to the next is imparted to a photon. And therefore we observe the heated hydrogen at that specific energy, i.e. that specific frequency.

Electrons fill in allowable orbitals as defined by quantum numbers (n,L,ml,ms) within shells.

The first of these, n, is called the principal quantum number, defining the shell in which an electron can be placed.

The second quantum number, L, corresponds to a sub-shell and is called the orbital angular momentum. The relationship between n and L is:

L = 0, 1, 2, ..., (n-1), i.e. L can range between 0 and n-1. This means that if n = 1, then L = 0, and if n = 2, then L = 0 or 1

There is a third quantum number called the orbital magnetic quantum number, ml, and is related to L:

ml = -L, (-L-1), (-L-2), ..., -1, 0, 1, ..., (L-1), L; i.e. ml ranges from -L to +L. Therefore, if L = 1, ml can be -1, 0, or +1. For L=2, ml= -2,-1,0,1 or 2

The final quantum number is the spin magnetic quantum number, ms. It describes the direction of the electron spin and can have values of 1/2 or -1/2.

To fill the orbitals we also need the Pauli exclusion principle: no two electrons can have all four quantum numbers to be the same.

Armed with these tools we can build the periodic table of elements:

For the first shell, n = 1, L = 0, ml = 0, and ms = -1/2 or +1/2. This shell therefore can contain the maximum of two electrons corresponding to ms=-1/2 or +1/2. That would give us hydrogen, with one electron, and helium with two electrons.

For the second shell n = 2; so L = 0 or 1. For L = 0, we get ml = 0 and ms = +1/2 or -1/2; allowing for 2 additional electrons to be placed. In doing so we get lithium and beryllium. For L = 1, we get ml = -1, 0, or +1, and ms for each is +1/2 or -1/2, adding 6 electrons to be placed, producing boron, carbon, nitrogen, oxygen, iron and neon.

We can carry on with this process for the 3rd shell (n=3), adding another 18 electrons; for the 4th shell (n=4) adding another 32, etc. thus completely building the atomic table (source: http://www.chemicool.com/).

This is one of the rare occasions where the constructor for the entire process of filling the orbitals is elegantly modeled by what is called the Schrodinger equation. The solutions to the equation allows for the visualization of the orbitals. The outer layer orbitals define the shape of the atom. The shape of the atom defines the electrical field that is projected by the atom. The electrical field is what attracts atoms to one another, and once in contact bonds can be established between various atoms. That is how the morphological flow continues on to create molecules.

Chapter Key: Morphological Flows, entities going through functional constructs thereby creating more complex entities with more complex functionalities:

Stellar Nuclei == nuclear fusion (strong nuclear force) ==> more complex nuclei up to iron == super/hyper nova compression ==> yet more complex nuclei == atomic orbital constructors (Electro-Magnetism) ==> atoms in the periodic table of elements

Links

Schrodinger Equation: Concepts

Generalized Solutions to Schrodinger Equation for multi-electron atoms

Tons of stuff on Quantum Mechanics

Nice site on atomic orbitals

A nice molecular visualization software package