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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.

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  • $\begingroup$ Hey. I posted the question and would just want to add a few more things. First thing, I know my understanding of the Quantum Model might be flawed, simply because of how little we are taught about it and how difficult a concept it is. Please give any suggestions you might have about that. Second, please answer my questions based on the academic level of a typical high school student. Thanks a lot. $\endgroup$
    – Ayush Roy
    Mar 22 at 8:04
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    $\begingroup$ The format of this Qustions/Answers site is intended rather for filling the gaps, not for laying the foundations. Consider studying available textbook and online materials and rasing follow up questions. // Search valuable sites with the term like site:libretexts.org or site:hyperphysics.phy-astr.gsu.edu or site:en.wikipedia.org. See also Chemistry SE: resources-for-learning-chemistry $\endgroup$
    – Poutnik
    Mar 22 at 9:25
  • $\begingroup$ Thanks @Poutnik for the suggestion, I will definitely look up these resources. But I am afraid that most books don't answer these questions about size of orbitals and other stuff. I looked up a few books before posting the question myself, but in vain. It would be helpful if you could lead me to some specific text. Thanks, again. $\endgroup$
    – Ayush Roy
    Mar 22 at 9:39
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    $\begingroup$ Especially the libretexts site is specifically focused of education at level you can understand. Hyperphysics format is then done by very usable form of a "cheat cards", very easy to digest. See googled topic orbitals on the respective sites Libretexts and Hyperphysics $\endgroup$
    – Poutnik
    Mar 22 at 9:51
  • $\begingroup$ 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. $\endgroup$
    – Maurice
    Mar 22 at 10:30

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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 sharp, principal, diffuse and fundamental. 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

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

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".

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  • $\begingroup$ Thanks a lot @M. Farooq! This was exactly the kind of answer I was looking forward to my question. I have a few counter questions, and will be really glad if you answer them too. First, isn't the spectrum you mention the same thing we do for hydrogen and what Bohr used for justifying the quantisation of energy? Why don't we have different bands like these there as well? Second, can you please tell what source are you referring to, since that will be really helpful to me for further information. Thanks. (: $\endgroup$
    – Ayush Roy
    Mar 24 at 10:41
  • $\begingroup$ Ayush, Welcome, the source is already mentioned, "A Report on Series Spectra" by A Fowler. Go to Internet archive and locate the book. And post a separate question for Bohr. $\endgroup$
    – AChem
    Mar 24 at 12:01
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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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    $\begingroup$ The probabilistic interpretation of QM (see Born rule) has not all that much to do with the Heisenberg uncertainty principle at all. IMO, the HUP is often invoked in places where it shouldn't be, or needn't be. Basically: orbitals have a size because they represent a probability distribution -- that's true. The HUP doesn't state that, though; the HUP only enforces a constraint on that probability distribution (which the orbitals satisfy). $\endgroup$ Mar 23 at 19:06
  • $\begingroup$ @orthocresol, that is exactly I want to know. If it isn't the uncertainty principle which predicts the size of an orbital, then what does? All I have read about quantum numbers only tells about "how many" electrons are located in a specific orbital and not about where they are located. $\endgroup$
    – Ayush Roy
    Mar 24 at 10:48
  • $\begingroup$ @AyushRoy That depends on how you define the "size" of an orbital. Orbitals don't have a "volume"; they actually extend out to infinity (the conventional pictorial form essentially truncates it), so if you wanted to go by where their furthest extent is, then all orbitals are the same (a very lame conclusion). A more sensible metric might be the mean distance from the nucleus, which you can obtain through integration once you know the mathematical forms of the orbitals (e.g., google '1s wavefunction'). I don't want to go into the details here, but none of this has to do with the HUP, really. $\endgroup$ Mar 24 at 11:43
  • $\begingroup$ Here is the connection between Born, Heisenberg, and the hertofore not mentioned Jordan. It's a bit easier to comprehend than the previous link. aapt.scitation.org/doi/10.1119/1.3009634 $\endgroup$
    – LynneKLR
    Mar 25 at 0:39
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    $\begingroup$ @orthocresol, I meant orbital to the region of the maximum probability, something like 90-95 percent. Anyways, thanks a lot orthocresol and LynneKLR. I will definitely look up these sources. $\endgroup$
    – Ayush Roy
    Mar 25 at 8:43

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