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What are the definitions of these three things and how are they related? I've tried looking online but there is no concrete answer online for this question.

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Here's a graphic I use to explain the difference in my general chemistry courses:

Shells, sub-shells, and orbitals

  • All electrons that have the same value for $n$ (the principle quantum number) are in the same shell
  • Within a shell (same $n$), all electrons that share the same $l$ (the angular momentum quantum number, or orbital shape) are in the same sub-shell
  • When electrons share the same $n$, $l$, and $m_l$, we say they are in the same orbital (they have the same energy level, shape, and orientation)

So to summarize:

  • same $n$ - shell
  • same $n$ and $l$ - sub-shell
  • same $n$, $l$, and $m_l$ - orbital

Now, in the other answer, there is some discussion about spin-orbitals, meaning that each electron would exist in its own orbital. For practical purposes, you don't need to worry about that - by the time those sorts of distinctions matter to you, there won't be any confusion about what people mean by "shells" and "sub-shells." For you, for now, orbital means "place where up to two electrons can exist," and they will both share the same $n$, $l$, and $m_l$ values, but have opposite spins ($m_s$).

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  • $\begingroup$ The picture is really helpful! However, are orbits really circular? $\endgroup$ – user29731 Jun 24 '17 at 3:45
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    $\begingroup$ @Abcd the s orbitals are spherical on the surface of an electron density plot. Inside the orbital the density varies with radial distance from the nucleus, with one or more "nodes" of zero electron density. You can think of it as kind of like fuzzy concentric spheres. As n increases, the number of nodes increases. $\endgroup$ – thomij Jun 26 '17 at 20:32
  • $\begingroup$ I think you didn't understand what I asked. I want to know whether the picture you have inserted is merely an abstraction or do things actually look like that. $\endgroup$ – user29731 Jun 28 '17 at 9:46
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    $\begingroup$ @Abcd I think you didn't understand my answer :) It doesn't really make sense to talk about what things "look" like at this level - just how things are. The way things are is that the electrons in s orbitals are distributed so that if you choose a given probability of finding an electron within a region (say, 90%), and plot the boundary of that region, you will get a sphere. $\endgroup$ – thomij Jun 28 '17 at 22:32
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    $\begingroup$ @Abcd a "shell" is a collection of orbitals that share the same principal quantum number, and an energy level is an allowed energy state. This is too complex to give a good answer in a comment - you can create another question if you'd like, or read more about it at en.wikipedia.org/wiki/Atomic_orbital $\endgroup$ – thomij Jun 29 '17 at 20:40
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Have a look here:

Orbitals that have the same value of the principal quantum number $n$ form a shell. Orbitals within a shell are divided into subshells that have the same value of the angular quantum number $l$. Chemists describe the shell and subshell in which an orbital belongs with a two-character code such as 2p or 4f. The first character indicates the shell (n = 2 or n = 4). The second character identifies the subshell. By convention, the following lowercase letters are used to indicate different subshells.

  • s: l = 0
  • p: l = 1
  • d: l = 2
  • f: l = 3

What is called an orbital might differ according to the context. With orbitals in the context of shells and subshells one usually means atomic orbitals, i.e. two-electron eigenstates of an atom's Hamilton operator which are characterized by the three quantum numbers: the principal quantum number $n$, the angular quantum number $l$ and the magnetic quantum number $m$. But often the word orbital is also used for spin-orbitals, i.e. one-electron eigenstates of the system's one-electron Hamilton operator which are characterized not only by $n$, $l$ and $m$ but also by the spin quantum number $m_{\mathrm{s}}$ which can be either $+\frac{1}{2}$ or $-\frac{1}{2}$.

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    $\begingroup$ Actually, I believe the term "orbital" was first used to describe the one-electron functions. So orbitals would always differ in all quantum numbers ($n$, $l$, $m_l$, $m_s$). $\endgroup$ – tschoppi Oct 15 '14 at 21:48
  • $\begingroup$ @tschoppi I think what you mean is more frequently referred to as spin-orbital. At least whenever the term orbital was used in most of my chemistry courses, like in $\mathrm{d}_{xy}$ orbital, my tutors always meant the two-electron state. But there might be differences between universities and lecturers. $\endgroup$ – Philipp Oct 15 '14 at 21:51
  • $\begingroup$ @tschoppi That's also why I wrote 'With orbitals in the context of shells and subshells" because in that context the differentiation of states according to their spin usually isn't needed. $\endgroup$ – Philipp Oct 15 '14 at 21:53

protected by Martin - マーチン Sep 5 '15 at 9:19

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