Creation of Orbitals
From Mbscientific_wiki
Creation of Electron Orbitals- completing the creation of atoms and the Periodic Table of Elements
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 (see note below).
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/). (better yet interactively visualize the first 4 rows of the periodic table - Animation)
Why don't we leave it here for the sake of (over)simplicity, with the exception of a note . While the order of the quantum number iterations (above) is the case, electrons orbitals are filled in the order of energy ascendancy. That, we will leave to detailed topics linked below.
This is one of the rare occasions where the constructor for the entire process of filling the orbitals is elegantly modeled. The solutions to these mathematical models 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
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
Courses
Courses from Massachusetts Institute of Technology (MIT) OpenCourseWare:
http://ocw.mit.edu/OcwWeb/Physics/8-04Spring-2006/CourseHome/index.htm - MIT - 8.04 Quantum Physics I
http://ocw.mit.edu/OcwWeb/Chemistry/5-73Introductory-Quantum-Mechanics-IFall2002/CourseHome/ - MIT - 5.73 Introductory Quantum Mechanics I
http://ocw.mit.edu/OcwWeb/Chemistry/5-74Spring-2007/CourseHome/ - MIT - 5.74 Introductory Quantum Mechanics II
Links
http://www.pbs.org/wgbh/aso/tryit/atom/ - Atom builder, really cool toy.. thanks PBS
http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/schrcn.html - Schrodinger Equation: Concepts
http://cmm.info.nih.gov/modeling/guide_documents/quantum_mechanics_document.html - Generalized Solutions to Schrodinger Equation for multi-electron atoms
http://www.psigate.ac.uk/ROADS/subject-listing/physics/530.12.html - Tons of stuff on Quantum Mechanics
http://www.orbitals.com/orb/ - Nice site on atomic orbitals
http://departments.oxy.edu/chemistry/wreef/Intro_Modeling.html - A nice molecular visualization software package
http://en.wikipedia.org/wiki/Atomic_orbital - wikipedia atomic orbital page
http://www.colorado.edu/physics/2000/applets/a2.html - a neat orbital visualization tool
http://hyperphysics.phy-astr.gsu.edu/HBASE/Chemical/eleorb.html - yet another cool visualization site
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