Periodic Table of Elements: Quantum Numbers
The periodic table of elements consists of 118 of the purest substances known to man. It is arranged in order of atomic numbers and specific properties that identify each element into certain columns and rows known as groups and periods. Not only do all of the elements hold a special place on the table, each element has a special number associated with it. These are known as quantum numbers, and they describe the identity of an element with the properties of its valence electrons.
To understand valence electrons one must first understand the structure of an atom. Within an atom there is the dense nucleus which is positively charged and then negatively charged electrons orbiting around it. In quantum mechanics, a branch of physics, the electrons are unstable particles whose existence varies from negligible to multiple places at once. But all physics aside, let’s just say that the electrons for our purposes swirl around the nucleus in what are called orbitals. Now there are four classes of these orbitals. An s class, p class, d class, and f class all of which have specific structures. Valence electrons consist of the s class and p class because these are the electrons furthest away from the nucleus and available for bonding with other atoms around them. The f and d classes are what one could call buried inside of the electron cloud (where the orbitals exist). That means that the d class exists one energy level below the p class, and the f class exists two energy levels below the p class. Energy levels are specific orbitals that exist around an atom.
For instance, hydrogen, the first element on the periodic table, has only one valence electron. Because of this it has only one orbital and one energy level for that orbital. The electron notation of hydrogen is 1s^1. The first one means that the s class occupies the first energy level of the atoms electron cloud. The s defines the shape and movement of the electrons at this particular level, and finally the final one is the number of electrons occupying said shell. The same principal can be applied to any element on the table. Such as Lithium (Li) has an electron notation of 1s^2,2s^1. Breaking this down you can see that each element’s electron notation is built upon one another. Lithium is the third element on the periodic table, before hydrogen and helium. The first grouping of letters (1s^2) means the first energy level, s class, and two electrons now fill it. The s class energy orbital can only hold two electrons before it becomes full, which then means a new energy level must be reached. That brings us to the (2s^1). That means the second energy level, s class once again, and one electron is in this shell. All energy levels past level one can hold up to eight electrons in them. Thus that is the reason why the p class of six electrons was created, which would then fill out the rest of the energy level of two.
The d class and f class complicate things a little more though. Once you reach the fourth energy level (which corresponds to the fourth period on the periodic table) you must compensate your notation for the d class. As said before, the d class exists one energy level below that of the current energy level. So the first time d comes into play would be at 4s^2,3d^10. This means that the d group (of ten electrons) exists in the third energy level. One would think that would interfere with the octet rule, which states that each energy level past one must have only eight electrons. This is true, but since the d energy level does not exist on the same plane as the s and p classes it does not violate said rule. The d class electrons form an almost figure eight shape perpendicular to the s class and its counterpart the p class. Of the seven energy levels present in the periodic table, the d class only exists from four to seven. That means that the any element with a d arrangement of electrons is between 3d and 6d, because they exist one level behind. An example of this is the electron notation of Zinc (Zn), which is a transition metal apart of the d class. Zinc’s notation is 1s^2,2s^2,2p^6,3s^2,3p^6,4s^2,3d^10. Please note that Zinc’s electron configuration contains all of the preceding elements, from Hydrogen all the way to Zinc. Also see that starting after the one energy level, each following energy level that is full contains exactly eight electrons. When the d class comes into play during the fourth energy level the electrons jump down and are buried deep within the electron cloud making bonding very hard to do with transition metals.
F class is not much different from the d class except that it occurs at a different region and jumps multiple energy levels. The same rules that apply to d apply to f except that instead of being buried one energy level in, the f class is buried two energy levels deeper. It begins in energy level six, right after 6s^2, comes 4f^14. That means that it is two energy levels deep and a full shell of the f class holds fourteen electrons. All elements in the f class are called lanthanides and the actinides, the latter of which is all radioactive. Now after the six energy level is full and we reach the seventh, the f class returns once again jumping down two levels to 5f^14. This is the same as the first level of the f class excluding the change in energy level.
Now what does all this mean? Well quantum numbers are a series of digits that describe these electron behaviors of each element and can uniquely identify each element by its electrons. There are four quantum numbers: n, l, m, and s. First we will start with n. The letter n denotes the energy level the atom’s electrons exist in. For instance hydrogen would have an n that equalled to one. On the same token sodium’s n would equal three. The d and f class rules apply to the n rule, so that zinc’s would equal three even though its s class was equivalent to four and uranium (member of the 5f class) would have an n of five.
The next letter is the l. L determines what class of orbital the energy level defined by in is a part of. The letter l has a range of four numbers for the four different classes. It begins with zero which amounts to the s class, one which is the p class, two which is the d class, and finally 3 which is the f class. A pattern can be recognized by looking back at the orbital notations of the elements used as examples above. For instance lithium has an electron notation of 1s^2,2s^1. And lithium’s n would quantify to 2 for the second energy level and its l would equal 0 for the s class. Yes, the n and l both equal the final set in the electron notation of an atom. See where the identification is starting to come it?
Next comes the m. It stands for the position of the electron on the orbital. It gets a little complicated at this point. Each class of orbitals (s,p,d,f) have a specific size and shape allowing electrons to exist across a wide range of places. That being said, electrons of each class have numbers that correspond to each position. View it as a pyramid to help you understand better:
s class – one position which is zero………………..0
p class – three positions from -1 to 1………….-1_0_+1
d class – five positions from -2 to 2………..-2_-1_0_+1_+2
f class – seven positions from -3 to 3…..-3_-2_-1_0_+1_+2_+3
The m is based upon the exponent which is attached to each class in the electron notation of an element. Not only does m correspond to the number of electrons present in an orbital it also corresponds to the spins of each electron. Just like in physics, where all actions have equal and opposite reactions, all electrons have equal and opposite spins on the orbital. The spins can be either positive or negative. So even if an element has an m of zero, it can have two electrons filing it because the s class holds two electrons. Both of these electrons will be spinning opposite directions. This is usually represented by a horizontal line with two vertical lines going through it, one pointing upward and the other downward. And essentially an orbital will fill up all of its positive spins before moving onto negative spins. So an m of positive one with an l of one (which means p class in case you forgot) means that there can either be three electrons or six electrons in the orbital. How is this so? Well the electrons always start filling up from the farthest left number, or the smallest number on the number line. That means that three positive spin electrons can be placed in each orbital to get you to positive one position on the m, or three positive spin and three negative spin electrons (at total of six electrons) can be placed to give you an m of positive one. So how do you know which is which?
Well our final letter to be defined is the s, which identifies the spin of the electrons on the position m of the orbital. The absolute value of s always equals 1/2, no matter what. But s can be either a positive 1/2 or a negative 1/2 depending on the spin of the electron. For instance like said earlier if an element with an l of one and a m of positive one can have either three or six electrons. By adding a negative 1/2 for s, you can then determine that the element has six electrons in its p class orbital. How? Well just remember that each orbital fills its positions positively first, meaning that an m of positive one already has a positive 1/2 attached to it. So in order to get to positive one once again, you must put another three electrons of opposite spins along each position. Which would give you a final total of six electrons in the electron shell.
So the four quantum numbers along with electron notation can identify any element on the periodic table with enough knowledge of the elements and their electrons. They once again are n, l, m, and s. N is the energy level the element’s electrons exist in. L defines the class in which the electrons exist. M defines the position upon the orbital that the final valence electron exists. And finally s defines the spin of the electron existing in m, which allows you to find the total number of valence electrons the element has. That combined with the energy level can then identify the element in question. Try it out! You’d be amazed at how the pieces all fit together perfectly like a nice elemental puzzle.
