Quantum Mechanics & Electron Configuration

The First Quantum Number

Quantum numbers represent different electron energy states. They are sometimes referred to as "shells" and are the quantum theory equivalent of the Bohr model. The first or principal quantum number, n, refers to the energy levels 1 – 7 (corresponding to the row numbers on the periodic table). As n increases, the distance of the main energy levels from the nucleus increases and their energy increases. You will recall that the maximum number of electrons found at each of these levels is: 2, 8, 18, 32, 50, 98. An easy way to remember this is 2(n)2 where n stands for the energy level.

The Second Quantum Number (l)
The "azimuthal quantum number" (l) defines the shape of the orbital and is generally designated by the letters s,p,d, and f. It has been shown that an energy level is actually made of many energy states closely grouped together. We call these states sublevels. An electron effectively occupies all the space around a nucleus by occupying a series of energy sublevels within an energy level. The second quantum number, l, identifies the energy sublevel.
The number of sublevels in each energy level is equal to the value of the principal quantum number. Within the 2nd energy level there are two sublevels (s &p), three in the 3rd (s, p, & d), 4 in the fourth (s, p, d, & f) and so on. The maximum number of electrons in the sublevels, s, p, d, and f, are 2, 6, 10, and 14. The numerical values for each sublevel are:
s, l = 0
p, l = 1
d, l = 2
f, l = 3

Electron Configuration

We have learned that electrons fill the energy levels beginning with the lowest energy states first. Electron configuration is a method of labeling where the electrons are at the ground state. For example the two electrons of helium will choose the sublevel of the first energy level, 1s. A superscript of 2 is used to indicate the number of electrons found in the sublevel. The total electrons of an energy levels sublevels cannot exceed the maximum for that energy level.

EXAMPLE: Write the configuration for beryllium 4Be
1s2,2s2

EXAMPLE: Write the configuration for phosphorus 15P
1s2,2s2,2p6,3s2,3p3

Overlapping Sublevels
With all these levels and sublevels some overlapping does occur. This happens when we reach the third and the fourth levels. There is even more over lapping when we reach the fifth, sixth and seventh.
Example: write the electron configuration for 28Ni
1s2 2s2 2p6 3s2 3p6 4s2 3d8
*note the 4s sublevel is filled before the 3d due to lower energy and greater stability.


The periodic Table and Configurations
The periodic table was originally constructed by placing elements with similar properties in a column. We now know that an atom's chemical properties are determined by its electron configuration. By reversing the procedure in which the table was constructed, the table may be used to "read" the configuration of an element. The written configuration of any element in Group IA will end in s1. The outer energy level is easily found from the table because the number of the period indicates the energy level. For example potassium's configuration would end with 4s1. The same procedure can be used for Groups IIA through VIIIA. There the endings, instead of s1, are s2, p1, through p6. For Groups IIIB through IIB, the ending are d1 through d10. The energy level is always one less than the period. For the lanthanides and actinides, the endings are f1 through f14. The energy level is always two less than the period. There are a number of exceptions to this arrangement.

The Octet Rule
One of the most basic rules in chemistry is that an atom with eight electrons in its outer level is particularly stable. Atoms react chemically in order to obtain this stable configuration. Atoms gain and lose electrons to become "isoelectronic" with a noble gas. For example we have learned that sodium, with eleven electrons, will lose one electron for a total of ten giving it the same electron configuration as neon (1s2, 2s2, 2p6). The noble gases do not react chemically due to the fact that they already have a full outer level. Although the helium atom has only two electrons in its outer level, it, too, is one of these stable elements. Its outer level is the first level and can hold only two electrons. Thus, it has a full outer level. For the transition and innertransition elements in the d and f blocks a pseudo-octet rule applies. These elements cannot obtain eight electrons in the outer most energy level, here a full or half full sublevel is particularly stable. An abbreviated configuration can be written using the stable noble gases. This notation uses the previous noble gas plus the additional electrons of the specified atom.
Example: Write the Nobel gas abbreviated notation for oxygen
O: [He] 2s2 2p4
Example: Write the Nobel gas abbreviated notation for magnesium
Mg: [Ne] 3s2
4. Write the complete electron configuration, noble gas abbreviated configuration and then assign quantum numbers n, and l for each of the electrons of lithium.
5. Predict the oxidation numbers of the following elements: Ar, P, Te, Cd, V, Sr, Cs, Cu.
6. Manganese has four oxidation states. Predict at least two of the four.Orbitals
The sum of all electron clouds in any sublevel (or energy level) is a spherical cloud. However, each sublevel is actually made up of characteristically shaped "orbitals". An orbital is a region in space occupied by one pair of electrons. We have learned that the s sublevel can hold two electrons. The shape of the s orbital is a sphere. The p orbital which holds a maximum of 6 electrons is actually 3 dumbbell shaped orbitals each holding two electrons. The d sublevel is comprised of 5 orbitals, and the f sublevel is made up of seven orbitals. Orbitals which are alike in size and shape and differ only in direction have the same energy. Orbitals of the same energy are said to be degenerate. We will only be concerned with the s and p orbital shapes.

The Third Quantum Number (ml)
The third quantum number, ml, defines each orbital more precisely by indicating its direction in space. For the p sublevel there are three possible values for m. The numbers would indicate the orbitals aligned along the x, y, and z axes. For example, the 6 electrons in a 2p orbital would be assigned m quantum numbers of -1, 0, and 1. The value of m is always -l to l. For the electrons in the 2p the l quantum number is 1 (recall p = 1), so the m quantum number can be any integer between -1 and 1. This gives three possible m numbers: -1, 0, and 1. -1 would represent the px orbital; 0 would represent the py orbital; and 1 would represent the pz orbital. For the electrons in the 4f the l quantum number is 3 (recall f = 3), and there are seven orbitals. The ml quantum number can be any integer between -3 and 3. This gives seven possible m numbers, (-3, -2, -1, 0, 1, 2, 3) one number for each of the seven orbitals.
Questions:
1. Draw the shape of an orbital in the sublevels s, p.
2. A s orbital can best be described as a _________________.
3. A p orbital can best be described as a _________________.
4. The sum of all orbitals for any particular sublevel would form a_______________.
5. Where would an electron with n, l, and ml quantum numbers of 3, 0, 0 be found? 4, 2, -1? 2, 1, 1? 3, 2, -2? 2, 0, 0?