Understanding the electron clouds and sub-orbitals
The most basic way we educate young people about how electrons and atoms work is the Bohr’s atomic model. But, there is a disconnect when people grow up and get the shock of learning that orbitals are just probabilities which indicate electrons paths, and we categorize these high probability paths as orbitals.
Therefore, the above image is not accurate, it is a highly simplified version. The actual atom is much more discrete and hard to identify. The nucleus is not as prevalent and easy to locate, and the electron is so small that it can not be identified as a dot. The most accurate portrait imagined of an atom is this one:
In order to understand the orbitals born out of probability, we might refer to the electron shell category which is taught at advanced classes of high school chemistry. All orbitals are divided into sub-orbitals of s,p,d,f. These can be imagined as coordinates on a graph paper. And each coordinate has a range which is known as the magnetic quantum number. For instance, s has a path which is numbered 0, p has a path which ranges from -1, 0, 1, d has a path from -2 to +2 in the same order of a number line and so on.
Many high schoolers memorize these quantum paths, and simply do not understand what these numbered 0, 1, 2 quantum numbers actually indicate. One way for interpreting it is thinking of them as ranges or geographical locations of the electron orbitals. Simply, if there is a probability of an electron located in the p shell, it will exist between the geographical location of -1, 0,and +1. This is an effort to map the whole surrounding of the outer area of the nucleus in more than just three physical dimensions. As there is no fixed three dimensional plane in the quantum state. This is also a reason why they are known as magnetic quantum numbers.
This illustration is a hypothetical mapping of the electron cloud, although not fully complete, this cloud mapped the range from the s orbital to the d orbital. As illustrated, the red layered path is the 3rd orbital, and it is shown that the third orbital exists on the 0, +-1, +-2 planes. Thus it has the capability to predict the electrons’ existence in the 3s, 3p, and 3d sub-orbitals.
This chain of thought is not without its limitations, we are yet to understand how quantum fields actually work and if the quantum field has multiple dimensions, can it be mapped? Graphing it using a fixed range and imagining the ranges through the quantum numbers seems an easier way to understand why we imagine the electron’s placement as probabilities and not as fixed routes.
Accurate or not, this thought process will at least stop the brain from melting when high schoolers learn that there are no fixed orbitals that electrons follow, and that is the goal for each and every theory illustrated in the chemistry textbooks.
