Orbital Rules
Leoma Cianchetti
The Bohr model was a one-dimensional model that used one quantum number to describe thedistribution of electrons in the atom. The only information that was important was the sizeof the orbit, which was described by the n quantum number. Schrdinger's modelallowed the electron to occupy three-dimensional space. It therefore required threecoordinates, or three quantum numbers, to describe the orbitals in which electronscan be found.
There is only one orbital in the n = 1 shell because there is only one way inwhich a sphere can be oriented in space. The only allowed combination of quantum numbersfor which n = 1 is the following.
Before we can use these orbitals we need to know the number of electrons that canoccupy an orbital and how they can be distinguished from one another. Experimentalevidence suggests that an orbital can hold no more than two electrons.
To distinguish between the two electrons in an orbital, we need a fourth quantumnumber. This is called the spin quantum number (s) because electrons behaveas if they were spinning in either a clockwise or counterclockwise fashion. One of theelectrons in an orbital is arbitrarily assigned an s quantum number of +1/2, theother is assigned an s quantum number of -1/2. Thus, it takes three quantum numbersto define an orbital but four quantum numbers to identify one of the electrons that canoccupy the orbital.
Because of the force of attraction between objects of opposite charge, the mostimportant factor influencing the energy of an orbital is its size and therefore the valueof the principal quantum number, n. For an atom that contains only one electron,there is no difference between the energies of the different subshells within a shell. The3s, 3p, and 3d orbitals, for example, have the same energy in ahydrogen atom. The Bohr model, which specified the energies of orbits in terms of nothingmore than the distance between the electron and the nucleus, therefore works for thisatom.
The hydrogen atom is unusual, however. As soon as an atom contains more than oneelectron, the different subshells no longer have the same energy. Within a given shell,the s orbitals always have the lowest energy. The energy of the subshells graduallybecomes larger as the value of the angular quantum number becomes larger.
A very simple device can be constructed to estimate the relativeenergies of atomic orbitals. The allowed combinations of the n and l quantumnumbers are organized in a table, as shown in the figure below and arrows are drawn at 45degree angles pointing toward the bottom left corner of the table.
The order of increasing energy of the orbitals is then read off by following thesearrows, starting at the top of the first line and then proceeding on to the second, third,fourth lines, and so on. This diagram predicts the following order of increasing energyfor atomic orbitals.
The electron configuration of an atom describes the orbitals occupied byelectrons on the atom. The basis of this prediction is a rule known as the aufbauprinciple, which assumes that electrons are added to an atom, one at a time, startingwith the lowest energy orbital, until all of the electrons have been placed in anappropriate orbital.
The next element has two electrons and the second electron fills the 1s orbitalbecause there are only two possible values for the spin quantum number used to distinguishbetween the electrons in an orbital.
To answer this, we need to understand the concept of degenerate orbitals. Bydefinition, orbitals are degenerate when they have the same energy. The energy ofan orbital depends on both its size and its shape because the electron spends more of itstime further from the nucleus of the atom as the orbital becomes larger or the shapebecomes more complex. In an isolated atom, however, the energy of an orbital doesn'tdepend on the direction in which it points in space. Orbitals that differ only in theirorientation in space, such as the 2px, 2py, and 2pzorbitals, are therefore degenerate.
Electrons fill degenerate orbitals according to rules first stated by Friedrich Hund. Hund'srules can be summarized as follows.
- One electron is added to each of the degenerate orbitals in a subshell before two electrons are added to any orbital in the subshell.
- Electrons are added to a subshell with the same value of the spin quantum number until each orbital in the subshell has at least one electron.
There is something unusually stable about atoms, such as He and Ne, that have electronconfigurations with filled shells of orbitals. By convention, we therefore writeabbreviated electron configurations in terms of the number of electrons beyond theprevious element with a filled-shell electron configuration. Electron configurations ofthe next two elements in the periodic table, for example, could be written as follows.
Click here to check your answer to Practice Problem 8 The aufbau process can be used to predict the electron configuration for an element.The actual configuration used by the element has to be determined experimentally. Theexperimentally determined electron configurations for the elements in the first four rowsof the periodic table are given in the table in the following section.
There are several patterns in the electron configurations listed in the table in theprevious section. One of the most striking is the remarkable level of agreement betweenthese configurations and the configurations we would predict. There are only twoexceptions among the first 40 elements: chromium and copper.
Once we get beyond atomic number 40, the difference between the energies of adjacentorbitals is small enough that it becomes much easier to transfer an electron from oneorbital to another. Most of the exceptions to the electron configuration predicted fromthe aufbau diagram shown earlier therefore occur among elementswith atomic numbers larger than 40. Although it is tempting to focus attention on thehandful of elements that have electron configurations that differ from those predictedwith the aufbau diagram, the amazing thing is that this simple diagram works for so manyelements.
When electron configuration data are arranged so that we can compare elements in one ofthe horizontal rows of the periodic table, we find that these rows typically correspond tothe filling of a shell of orbitals. The second row, for example, contains elements inwhich the orbitals in the n = 2 shell are filled.
There is an obvious pattern within the vertical columns, or groups, of the periodictable as well. The elements in a group have similar configurations for their outermostelectrons. This relationship can be seen by looking at the electron configurations ofelements in columns on either side of the periodic table.
The figure below shows the relationship between the periodic table and the orbitalsbeing filled during the aufbau process. The two columns on the left side of the periodictable correspond to the filling of an s orbital. The next 10 columns includeelements in which the five orbitals in a d subshell are filled. The six columns onthe right represent the filling of the three orbitals in a p subshell. Finally, the14 columns at the bottom of the table correspond to the filling of the seven orbitals inan f subshell.
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If left unchecked, the accumulation of orbital debris will increase the risk of collisions and clutter orbits used for human spaceflight and for satellites providing communications, weather and global positioning system services.
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