Size of Orbitals, Making Intuitive Sense of Quantum Model, Nomenclature of Subshells in the Quantum Model

Alright, so I am doing the Quantum Mechanical (or what some people call the Wave Mechanical model) of an atom. There's this part where we have different zones of the probablity of finding electrons, the orbitals. The orbitals are a part of our imaginary concept of shells and subshells. (I know that it might not be completely true at the higher academic levels, but that is the vocabulary I know for now.) I have a few different questions about this atomic model.


A. What is the size of an orbital, or a subshell, or a shell in this model? Is it somewhere related to the Heisenberg postion uncertainty? Like, the size of an orbital being equal to how much uncertain we are about the postion of an electron?


B. My teacher keeps saying that all these shapes of orbitals and even their existence is purely mathematical. Is there really no intuitive sense we can make of the reason of their presence as such without involving any differential equations?


C. Why are the names of subshells based on completely random letters (s, p, d and f)? I tried searching for some source on the internet but it simply dwells deeper into their shapes and planes and graphs rather than explaining their names.




Addressing the last part of your post



> 
> Why are the names of subshells based on completely random letters (s,
> p, d and f)? I tried searching for some source on the internet but it
> simply dwells deeper into their shapes and planes and graphs rather
> than explaining their names.
> 
> 
> 


These letters are not random and as you can see all over the internet (e.g., Wikipedia) they stand for **s**harp, **p**rincipal, **d**iffuse and **f**undamental. After that the story ends without telling what is sharp, principal, etc. What are those adjective for and what do they describe? These letters described the nature of the lines in an atomic spectrum and this system was not universal (Taken from "A Report on Series Spectra by A Fowler).
[![Spectra](https://i.stack.imgur.com/ginmP.jpg)](https://i.stack.imgur.com/ginmP.jpg)


Basically, long before the concept of orbitals originated, people were fascinated by the spectrum of alkali metals. They have a rich spectrum if you excite them under an electric arc. When you view the arc through a spectroscope (=a device that separates wavelengths), you see a number of lines these letters described those lines as they appeared to the viewer! Pure visual labels.


[![enter image description here](https://i.stack.imgur.com/YnbSU.jpg)](https://i.stack.imgur.com/YnbSU.jpg)


Now you don't see **fundamental** there because the fundamental series was discovered in the infrared region. So no visual label, it is just a label. Nothing fundamental about it.


Now, spectroscopists, mathematicians, physicists wanted to find out a mathemtical relation among the wavelengths of those lines. They came up with mathematical series that described the wavelengths as *terms* of a *series*. When quantum mechanics was developed this nomenclature was retained since they were able to assign the electronic transitions in orbitals corresponding to those wavelengths. I will have check original papers from 1920s to see who first assigned them.


P.S. Saw an interesting comment below the original post. I want to correct it since some student later on start to spread this reasoning in future on other websites.



> 
> You may remember the order of the subshells spdf by the following
> reasoning : s is the first letter of "spherical", because the s
> orbitals have a spherical symmetry. p is the first letter of "plane",
> meaning that the p orbital has a planar symmetry. d is the first
> letter of "different", because these orbitals have different symmetry
> surfaces. Other orbitals are defined by alphabetic order after "d",
> avoiding the letter e which is used for exponential. Historically
> speaking, the letters s,p,d,f were named after other criterias, which
> are harder to explain.
> 
> 
> 


I am afraid this is completely imaginary and there is no historical work which justifies the choice of the names orbitals using the above reasoning. The letters do not stand for spherical, plane, and different. The letter f was not chosen to avoid "exponential".


 4

The orbital sizes and shapes represent the probability of finding an electron in that space with 95% confidence. You are correct that it is related to the uncertainty principle - we can only describe electron positions as probabilities.


s, p, d, f are short terms for the funny names physicists give to things when they first observe them but don't know what they are. In the case of orbitals, these are "sharp," "principal," "diffuse," and "fine" (or "fundamental").


Based on your question and curiosity abut these things, I think you may enjoy reading Richard Rhodes' book **The Making of the Atomic Bomb**. The first half of the book is a fascinating and accessible history of quantum physics. That's where I learned what s, p, d, and f stand for.


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