Quantum NumbersGeneral Rules of Electron Configuration
The electron configuration of an atomic species (neutral or ionic) allows us to understand the shape and energy of its electrons. Many general rules are taken into consideration when assigning the “location” of the electron to its prospective energy state, however these assignments are arbitrary and it is always uncertain as to which electron is being described. Knowing the electron configuration of a species gives us a better understanding of its bonding ability, magnetism and other y2kcenter.orgical properties.
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The electron configuration is the standard notation used to describe the electronic structure of an atom. Under the orbital approximation, we let each electron occupy an orbital, which can be solved by a single wavefunction. In doing so, we obtain three quantum numbers (n,l,ml), which are the same as the ones obtained from solving the Schrodinger”s equation for Bohr”s hydrogen atom. Hence, many of the rules that we use to describe the electron”s address in the hydrogen atom can also be used in systems involving multiple electrons. When assigning electrons to orbitals, we must follow a set of three rules: the Aufbau Principle, the Pauli-Exclusion Principle, and Hund”s Rule.
The wavefunction is the solution to the Schrödinger equation. By solving the Schrödinger equation for the hydrogen atom, we obtain three quantum numbers, namely the principal quantum number (n), the orbital angular momentum quantum number (l), and the magnetic quantum number (ml). There is a fourth quantum number, called the spin magnetic quantum number (ms), which is not obtained from solving the Schrödinger equation. Together, these four quantum numbers can be used to describe the location of an electron in Bohr”s hydrogen atom. These numbers can be thought of as an electron”s “address” in the atom.
To help describe the appropriate notation for electron configuration, it is best to do so through example. For this example, we will use the iodine atom. There are two ways in which electron configuration can be written:
In both of these types of notations, the order of the energy levels must be written by increased energy, showing the number of electrons in each subshell as an exponent. In the short notation, you place brackets around the preceding noble gas element followed by the valence shell electron configuration. The periodic table shows that kyrpton (Kr) is the previous noble gas listed before iodine. The noble gas configuration encompases the energy states lower than the valence shell electrons. Therefore, in this case
Principal Quantum Number (n)
The principal quantum number n indicates the shell or energy level in which the electron is found. The value of n can be set between 1 to n, where n is the value of the outermost shell containing an electron. This quantum number can only be positive, non-zero, and integer values. That is, n=1,2,3,4,..
For example, an Iodine atom has its outmost electrons in the 5p orbital. Therefore, the principle quantum number for Iodine is 5.
Orbital Angular Momentum Quantum Number (l)
The orbital angular momentum quantum number, l, indicates the subshell of the electron. You can also tell the shape of the atomic orbital with this quantum number. An s subshell corresponds to l=0, a p subshell = 1, a d subshell = 2, a f subshell = 3, and so forth. This quantum number can only be positive and integer values, although it can take on a zero value. In general, for every value of n, there are n values of l. Furthermore, the value of l ranges from 0 to n-1. For example, if n=3, l=0,1,2.
So in regards to the example used above, the l values of Iodine for n = 5 are l = 0, 1, 2, 3, 4.
Magnetic Quantum Number (ml)
The magnetic quantum number, ml, represents the orbitals of a given subshell. For a given l, ml can range from -l to +l. A p subshell (l=1), for instance, can have three orbitals corresponding to ml = -1, 0, +1. In other words, it defines the px, py and pzorbitals of the p subshell. (However, the ml numbers don”t necessarily correspond to a given orbital. The fact that there are three orbitals simply is indicative of the three orbitals of a p subshell.) In general, for a given l, there are 2l+1 possible values for ml; and in a n principal shell, there are n2 orbitals found in that energy level.
Continuing on from out example from above, the ml values of Iodine are ml = -4, -3, -2, -1, 0 1, 2, 3, 4. These arbitrarily correspond to the 5s, 5px, 5py, 5pz, 4dx2-y2, 4dz2, 4dxy, 4dxz, and 4dyz orbitals.
Spin Magnetic Quantum Number (ms)
The spin magnetic quantum number can only have a value of either +1/2 or -1/2. The value of 1/2 is the spin quantum number, s, which describes the electron”s spin. Due to the spinning of the electron, it generates a magnetic field. In general, an electron with a ms=+1/2 is called an alpha electron, and one with a ms=-1/2 is called a beta electron. No two paired electrons can have the same spin value.
Out of these four quantum numbers, however, Bohr postulated that only the principal quantum number, n, determines the energy of the electron. Therefore, the 3s orbital (l=0) has the same energy as the 3p (l=1) and 3d (l=2) orbitals, regardless of a difference in l values. This postulate, however, holds true only for Bohr”s hydrogen atom or other hydrogen-like atoms.
When dealing with multi-electron systems, we must consider the electron-electron interactions. Hence, the previously described postulate breaks down in that the energy of the electron is now determined by both the principal quantum number, n, and the orbital angular momentum quantum number, l. Although the Schrodinger equation for many-electron atoms is extremely difficult to solve mathematically, we can still describe their electronic structures via electron configurations.
General Rules of Electron Configuration
There are a set of general rules that are used to figure out the electron configuration of an atomic species: Aufbau Principle, Hund”s Rule and the Pauli-Exclusion Principle. Before continuing, it”s important to understand that each orbital can be occupied by two electrons of opposite spin (which will be further discussed later). The following table shows the possible number of electrons that can occupy each orbital in a given subshell.
|subshell||number of orbitals||total number of possible electrons in each orbital|
|p||3 (px, py, pz)||6|
|d||5 (dx2-y2, dz2, dxy, dxz, dyz)||10|
|f||7 (fz3, fxz2, fxyz, fx(x2-3y2), fyz2, fz(x2-y2), fy(3×2-y2)||
Using our example, iodine, again, we see on the periodic table that its atomic number is 53 (meaning it contains 53 electrons in its neutral state). Its complete electron configuration is 1s22s22p63s23p64s23d104p65s24d105p5. If you count up all of these electrons, you will see that it adds up to 53 electrons. Notice that each subshell can only contain the max amount of electrons as indicated in the table above.
The word “Aufbau” is German for “building up”. The Aufbau Principle, also called the building-up principle, states that electron”s occupy orbitals in order of increasing energy. The order of occupation is as follows: