I'm just a curious high school student. Sorry if this sounds dumb.

How exactly did the concept of atomic subshells and orbitals come about? And why exactly are there n-1 subshells and 2l+1 orbitals?

Based on what I've heard, these things were a step forward after the Sommerfeld atomic model. But orbitals???

Again, sorry if this sounds dumb. I just want to know how these things came about.

  • $\begingroup$ It is a simplification - the raw quantum mechanical description would be extremely complex. But sometimes it is needed (for example, to calculate the physical/chemical properties of unknown elements/compounds). $\endgroup$ – peterh - Reinstate Monica Jul 27 at 4:02
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    $\begingroup$ There's no such thing as a sub-orbital. Maybe you meant subshell. Basically, all of this comes about from quantum mechanics (to be precise, the orbitals are solutions of the Schrodinger equation for the hydrogen atom). The extension to other atoms (helium, lithium, ...) is an approximation that generally works well enough for chemistry. $\endgroup$ – orthocresol Jul 27 at 4:14
  • $\begingroup$ Oh yeah thanks for pointing that out I fixed it $\endgroup$ – CreeperGuyHQ Jul 28 at 2:56

Very nice question. I also had the same question. These orbitals are nothing more than functions (wavefunctions). They are solutions to Schrodinger's equation, a second order differential equation. So you solve the equation and the solutions you get are determined by $4$ numbers also called quantum numbers $n, l, m_l, m_s$. A shell consists of all orbitals with same value of $n$ whereas a subshell consists of all orbitals with same values of $n$ and $l$. As others have pointed out the solutions are exactly only for the hydrogen and hydrogen like atoms.

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If this is a serious question and you wish to get a conceptual grasp of it, there is a lovely thin book called "Hydrogen" by Rigden (from Harvard). It walks you through the conceptual development.

Briefly, the need of better and better model of hydrogen atom arose because of the need to completely rationalize the experimental hydrogen spectrum. By the 1920s, experimental atomic spectroscopy was very advanced and people already started to very high resolution spectrum of atomic hydrogen. If Bohr's theory could explain every experimental aspect of hydrogen spectrum, there would be no need of another approach. For example, in hydrogen atom spectrum you could see closely two spaced lines which under low resolution appear as a single line (search doublet of hydrogen).

The oldest was the planetary model and Bohr's model is similar. Then Sommerfeld improved the model but still it was not adequate.

Contrary to the common opinion, orbital was not coined by Schrodinger. Robert Mulliken (another Nobel laureate) proposed this term.

An orbital is not a physical object or structure inside an atom, no matter how many useless general chemistry books or websites show them as balloons and other drawings. Even leading journals fell prey to this non-sense saying that orbitals have been observed or imaged, only to be embarased later. Orbital is a short form name of "one-electron orbital wave function". It is a mathematical construct which exists on paper and in the mind of a physicist.

Roughly you can imagine orbital as a pattern of electron density around a nucleus. But again, there is no actual "white cloud" of an electron surrounding the nucleus (if we were able to see it). Do not take the small world of particles in a literal sense. Much is known and much more is not known.

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