The Development of Wave Mechanics
Using the hypothesis of Louis de Broglie, who suggested that the electron could have wave properties, the German mathematician, Erwin Schrödinger, devised a type of mathematics called wave mechanics. The basic idea is that both the position and the velocity of a body as small as an electron cannot be measured at the same time. The best that can be done is to calculate the probability of an electron being in a certain place at any given time. This led to the development of the present model of the atom, which is known as the Quantum Mechanical Model of the Atom or the Wave Mechanical Model of the Atom.
The Quantum Mechanical Model of the Atom
This model of the atom describes the position of the electrons in terms of probability of locating electrons at any theoretical position in space around the nucleus. This model does not tell us how an electron moves from one point to another. How electrons move or their trajectory is not known. The German scientist, Werner Heisenberg, formulated a generally accepted principle (Heisenberg's Uncertainty Principle) that states that “the exact position of an electron will never be known.”
The Orbitals
Quantum Mechanics mathematically describes regions in space around the nucleus of an atom where the electrons are most likely to be found (wave functions). The regions in space around the nucleus where there is a high probability of locating the electrons are called orbitals. These orbitals are given specific names such as s or sharp orbitals, p or principal orbitals, d or diffuse orbitals or f or fundamental orbitals. The orbitals all have characteristic shapes (for instance, the s orbitals are spherical in shape). This means that if we look for the electron somewhere on the surface of a sphere, having the nucleus at the centre, the probability of finding it at any one point is the same as finding the electron at any other point on the surface of the sphere. The orbitals are all distributed in the energy levels, which were a part of Neils Bohr’s model of the atom. An orbital may be empty or may contain one or two electrons. Pauli’s Exclusion Principle states that “no orbital can contain more than two electrons.” When two electrons fill any one orbital they spin in opposite directions, one spins clockwise and the other spins counter clockwise relative to an external magnetic field.
Using the wave functions, physicists have created three dimensional electron probability density plots (electron clouds) for the orbitals. The s, p and d orbitals are seen below; the drawings for the f orbitals are quite complicated. These orbitals are superimposed on top of one another to build a multi-electron atom.
The Energy Levels and Orbitals
Each main energy level around the nucleus is given a value n, which is the Principle Quantum Number. In the main energy level, n=1 and so the Principle Quantum Number is 1. In the second energy level, n=2 and the Principle Quantum Number is 2 and so on (n = 1, 2, 3 … ∞). In each main energy level, there are n types of orbitals, n2 orbitals and 2n2 electrons. For instance, in the third main energy level, there is one s type orbital called the 3s orbital, three p type orbitals called the 3p orbitals (3px, 3py, 3pz) and 5 d type orbitals called the 3d orbitals (3dz2, 3dxy, 3dxz, 3dyz, 3dx2-y2), for a total of 9 orbitals. Each separate orbital (3s, 3px, 3py, 3pz, 3dz2, 3dxy, 3dxz, 3dyz, 3dx2-y2) may contain up to two electrons, for a total of 18 electrons.
|
n |
|
|
|
|
Number of Electrons |
|
1 |
s → 1s |
|
|
|
2 |
|
2 |
s → 2s |
p → 2px, 2py, 2pz |
|
|
2 + 6 = 8 |
|
3 |
s → 3s |
p → 3px, 3py, 3pz |
d → 3d1, 3d2, 3d3, 3d4, 3d5 |
|
2 + 6+ 10 = 18 |
|
4 |
s → 4s |
p → 4px, 4py, 4pz |
d → 4d1, 4d2, 4d3, 4d4, 4d5 |
f → 4f1, 4f2, 4f3, 4f4, 4f5, 4f6, 4f7 |
2 + 6+ 10 + 14 = 32 |
Electron Configurations
Electron configurations simply represent the distribution of the electrons among the various orbitals in an atom. Electrons enter the lowest energy orbital of the lowest energy level first. When all the electrons in an atom are in the lowest energy orbitals available to them, they are said to be in the ground state. Atoms with electrons in higher energy orbitals with lower energy orbitals vacant or partially filled are said to be in the excited state. This building up of electron structures of the elements in the ground state is called the Aufbau Process. In this process, the filling of orbitals in a given set is governed by Hund’s Rule, which states that “no electron pairing takes place until each orbital in a given set contains one electron.”
The order of filling electrons into the orbitals is shown above. The lowest energy orbital is 1s, followed by 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f etc. Notice that the 4s orbital fills up before the 3d orbitals. This is because the 4s orbital is at a lower energy than the five 3d orbitals. This is called Energy Level Overlap and it occurs when certain orbitals in higher main energy levels fill up with electrons before all the orbitals in some lower main energy level do. The reason for this phenomenon goes beyond the scope of this course. Electron configurations are shown below as orbital box diagrams (energy level diagrams), in spectroscopic notation (full electron configuration) and in noble gas configuration (shorthand configuration).
Need more help? Check out this video that I made.
I made another video too! I'm on fire! (I'm not going to lie - I forgot I made the first video. I made the second video. I didn't want to waste it. So...)
Homework: # 1-10 (minus any work already assigned)
Remember the homework can be found here.
Student questions:
1. Can you go over the electron configuration for calcium?
Please be aware that I have cut and pasted the answer I gave from Edsby (which doesn't allow for subscripts.
