# A chemical question, but I suspect it has something to do with math & physics **URL:** \ **Category:** Factual Questions\ **Created:** [May 26, 2023, 5:01am UTC](https://boards.straightdope.com/t/a-chemical-question-but-i-suspect-it-has-something-to-do-with-math-physics/984615 "2023-05-26T05:01:04Z")\ **Posts on this page:** 7\ **Page:** 1
**Author:** ![longtry](https://avatars.discourse-cdn.com/v4/letter/l/839c29/32.png) [@longtry](https://boards.straightdope.com/u/longtry)\ **Post date:** [May 26, 2023, 5:01am UTC](https://boards.straightdope.com/t/a-chemical-question-but-i-suspect-it-has-something-to-do-with-math-physics/984615/1 "2023-05-26T05:01:04Z")
OK, so I was relearning about the electron orbitals. 1 thing I’ve noticed for quite some time is that the periodic table repeats its lines exactly once (line 2, Li…, has the same number of 8 elements as line 3, Na…; line 4K = 18 = line 5Rb; line 6 = line 7). Well, except for line 1, which isn’t duplicated. Perhaps it’s easier to illustrate the point when we look at the [electron orbitals’ energy graph](https://imgur.com/a/Z9RrhGp). There are 4 columns, corresponding to the s, p, d & f orbitals. We can see that with each introduction of a new column, there are 2 line iterations (black boxes and green boxes). So why aren’t there 2 lines for the 1st column? Or, hell, why are there repetitions in the 1st place? Why can’t it be just 1 iteration for everything? If possible, please kindly elaborate any points in your answer that are at college level or above. Thanks! ---
**Author:** ![DPRK](https://avatars.discourse-cdn.com/v4/letter/d/4491bb/32.png) [@DPRK](https://boards.straightdope.com/u/DPRK)\ **Post date:** [May 26, 2023, 8:00am UTC](https://boards.straightdope.com/t/a-chemical-question-but-i-suspect-it-has-something-to-do-with-math-physics/984615/2 "2023-05-26T08:00:47Z")
I started to write a complicated mathematical explanation, but you can see what is going on by means of a simple picture. This is basically the “Aufbau principle”: we can get into what this has to do with electrons and why, but from the diagram [![](https://upload.wikimedia.org/wikipedia/commons/1/15/Aufbau_Principle.png) ](https://upload.wikimedia.org/wikipedia/commons/1/15/Aufbau_Principle.png) you can combinatorially see that the first row of the periodic table corresponds to 1s; the second to 2s, 2p; the third to 3s, 3p; then 4s 3d 4p 5s 4d 5p 6s 4f 5d 6p and so on so just by following the pattern and counting you can see that the first row is an exception. ---
**Author:** ![Isilder](https://avatars.discourse-cdn.com/v4/letter/i/cc9497/32.png) [@Isilder](https://boards.straightdope.com/u/Isilder)\ **Post date:** [May 26, 2023, 11:05am UTC](https://boards.straightdope.com/t/a-chemical-question-but-i-suspect-it-has-something-to-do-with-math-physics/984615/3 "2023-05-26T11:05:52Z")
Its physics. Hydrogen and Helium can only have an S shell, so it doesnt have the P as the outer shell. The other atoms all have P as the outer shell… and this causes “3d” to actually go to the next row of the periodic table… the periodic table row is from the truncated, as “4s” has lower energy than 3d. The periodic table is done like this to show the chemical property due to the p shell, rather than doing it by the ‘n’ property… The result is that transition elements grow in number in each row… they have the similarly filled and its the inner shells taking up the next electron…so there are the halides,noble gases, and the metals -1 , -2 … but the middle becomes a line up of clones. > **[Atomic orbital](https://en.wikipedia.org/wiki/Atomic_orbital#/media/File:Electronic_levels.svg)** > > In atomic theory and quantum mechanics, an atomic orbital (/ɒrbədl/) is a function describing the location and wave-like behavior of an electron in an atom. This function can be used to calculate the probability of finding any electron of an atom in any specific region around the atom's nucleus. The term atomic orbital may also refer to the physical region or space where the electron can be calculated to be present, as predicted by the particular mathematical form of the orbital. > Each orbital... ---
**Author:** ![longtry](https://avatars.discourse-cdn.com/v4/letter/l/839c29/32.png) [@longtry](https://boards.straightdope.com/u/longtry)\ **Post date:** [May 26, 2023, 2:16pm UTC](https://boards.straightdope.com/t/a-chemical-question-but-i-suspect-it-has-something-to-do-with-math-physics/984615/4 "2023-05-26T14:16:25Z")
> [@DPRK](#): > > This is basically the “Aufbau principle”: we can get into what this has to do with electrons and why, but from the diagram Actually I was aware of the Aufbau diagram - it’s pretty popular in chemistry courses. But when I think about it, the diagram and the graph are like 2 representations of the same core principle, and thus using 1 to explain the other doesn’t really answer the question (for me). I’m afraid you might have to use the intimidating math explanation… > [@Isilder](#): > > The periodic table is done like this to show the chemical property due to the p shell, rather than doing it by the ‘n’ property… That begs the question, why is p so special that it gets to define the property of elements? And I think that makes H and He the oddballs of elements, because placing them like that on the periodic table now doesn’t really make sense - it feels quite ‘forced’. Going 1 step further, the fact that the universe follows a math-physics rule as described by the quantum numbers gives me a sense that this whole universe is, um, arbitrary? Just because l \< n leads to no p for n = 1, therefore 1s is “alone”… Now coupled with the fact that H & He comprise most of matter, I feel like there is some deep truth that’s hidden yet quite near, but I just can’t grasp. Something almost philosophical, you know. ---
**Author:** ![moes\_lotion](https://avatars.discourse-cdn.com/v4/letter/m/7ba0ec/32.png) [@moes\_lotion](https://boards.straightdope.com/u/moes_lotion)\ **Post date:** [May 26, 2023, 9:05pm UTC](https://boards.straightdope.com/t/a-chemical-question-but-i-suspect-it-has-something-to-do-with-math-physics/984615/5 "2023-05-26T21:05:39Z")
> [@longtry](#): > > That begs the question, why is p so special that it gets to define the property of elements? While it has been more that 30 years since I was studying physics at university, I will take a stab at this. The behavior of electrons in an atom are described by the Schrödinger equation, the solutions of which involve spherical Bessel functions. These solutions contain 4 quantum numbers which are related to each other in fairly simple ways. It is because the electron orbitals of individual atoms are solutions of the Schrödinger equation that the structure of the standard arrangement of the periodic table is what it is. References: > **[Schrödinger equation](https://en.wikipedia.org/wiki/Schr%C3%B6dinger_equation)** > > The Schrödinger equation is a linear partial differential equation that governs the wave function of a quantum-mechanical system.: 1–2  Its discovery was a significant landmark in the development of quantum mechanics. It is named after Erwin Schrödinger, who postulated the equation in 1925 and published it in 1926, forming the basis for the work that resulted in his Nobel Prize in Physics in 1933. > Conceptually, the Schrödinger equation is the quantum counterpart of Newton's second law in class... > **[Principal quantum number](https://en.wikipedia.org/wiki/Principal_quantum_number)** > > In quantum mechanics, the principal quantum number (symbolized n) is one of four quantum numbers assigned to each electron in an atom to describe that electron's state. Its values are natural numbers (from 1) making it a discrete variable. > Apart from the principal quantum number, the other quantum numbers for bound electrons are the azimuthal quantum number ℓ, the magnetic quantum number ml, and the spin quantum number s. > As n increases, the electron is also at a higher energy and is, therefore... ---
**Author:** ![DPRK](https://avatars.discourse-cdn.com/v4/letter/d/4491bb/32.png) [@DPRK](https://boards.straightdope.com/u/DPRK)\ **Post date:** [May 26, 2023, 9:19pm UTC](https://boards.straightdope.com/t/a-chemical-question-but-i-suspect-it-has-something-to-do-with-math-physics/984615/6 "2023-05-26T21:19:01Z")
We can talk in more detail about atomic orbitals, but it is important to understand that while the periodic table is organized according to the Aufbau principle, that does not mean that the electronic structure of every single element literally follows this rule! However, it does succeed in showing general trends. > [@longtry](#): > > why is p so special that it gets to define the property of elements? It doesn’t… But, electrons with different values of this quantum number have different distributions of distance from the nucleus, so for a typical element the energy levels within a shell go like s \< p \< d \< f [whereas for a hydrogen atom they would be approximately the same] because the smaller ones are more attracted to the nucleus; it’s not just “p”. If you look at, e.g. the 4th row, you have 4s1, 4s2, 4s23d1, etc — 3d gets filled before 4p. ---
**Author:** ![Riemann](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/riemann/32/3133_2.png) [@Riemann](https://boards.straightdope.com/u/Riemann)\ **Post date:** [May 31, 2023, 2:18am UTC](https://boards.straightdope.com/t/a-chemical-question-but-i-suspect-it-has-something-to-do-with-math-physics/984615/7 "2023-05-31T02:18:47Z")
> [@longtry](#): > > why is p so special that it gets to define the property of elements? Are you confusing the p shell with the number of protons?