We have been taught that the atomic orbitals we read about are probability density region of finding electrons of particular energies which are designated by the various quantum numbers.

Since, there is high degree of uncertainty when we talk about the position of merely the detection of an electron as well as the energy that we "observe" and which may pretty much not be the actual energy of the observed electron, what then is the significance of any atomic orbital?

I am not very well read in the various techniques and theories that we have developed over time, but still I think that atomic orbitals are at best a high probability region of finding certain electrons. Since we must not be able to do that with enough certainty how then can we check the validity of the existence of orbitals?

Is it possible, that the idea of atomic orbital is now outdated in terms of modern development and only used for simplistic explanations of complex electron motions and phenomenons?

Overall, I am interested in learning the significance of atomic orbitals. Google provides various links explaining the theory and listing its uses in modern chemistry but I could not find anything which properly explains the significance or even tries to explain the actual presence of something like an atomic orbital other than saying that we find so and so probability regions while working with Schrödinger equations.

Added after answers and comments: The answers are listing the uses of the contruct only, I tried to say that I am interested in finding out whether something like an orbital is actually there or not.

Maybe an example will help, there is no boundation for an electron of certain energy to move in an orbital that is dumbled or double dumbled shaped! I agree with electrons having certain energies described by quantum numbers, but how can one definitively prove that an electron belonging to say 2p_x resides in a dumbled shaped orbital?

Again, are orbitals true? Are they actually significant and not just a helpful mathematical construct? Can it be definitively proven?

  • $\begingroup$ See journals.aps.org/prl/abstract/10.1103/PhysRevLett.110.213001, we have actually measued the atomic orbitals of hydrogen. See also Anna's answer to Is there anyway to use a scientific instrument to measure the density of electron around the atomic orbital?. $\endgroup$ May 5, 2014 at 15:08
  • $\begingroup$ @JohnRennie : I have read this article before, but it has also dawned on me that the picture they have obtained has a node! According to what we are taught,a hydrogen atom with single electron should have had only 1s orbital, clearly we are getting a 2s or another orbital separated by a node just as well, undermining the theory! $\endgroup$ May 5, 2014 at 15:12
  • $\begingroup$ @rijulgupta in the article that JohnRennie cites, a laser is used to excite the H to a mixture of n=2 s and p states. $\endgroup$
    – DavePhD
    May 5, 2014 at 16:07
  • $\begingroup$ @DavePhD : I would have definitely agreed with you, but see here the image I was talking about is listed as 3rd state, there must be 2 nodes for 3rd state but apart from an extremely small spot like vacancy there is no clear node! I am just trying to point that something's amiss! $\endgroup$ May 5, 2014 at 17:09
  • $\begingroup$ @rijulgupta They are saying it is the (2,27,0) Stark state. I'm not knowledgeable about Starks states, but I think these are states of a hydrogen atom in an electric field. I don't think this is the same as the ordinary hydrogen states absent an applied field. $\endgroup$
    – DavePhD
    May 5, 2014 at 17:35

4 Answers 4


Yes, atomic orbitals are very significant.

An electron being in a particular orbital corresponds to a specific energy. If an electron transitions between two orbitals, the energy of the photon absorbed or emitted is the difference between the energy levels of the orbitals.

The probablilty density function is also important. For example, an s-orbital electron has a probabilty of being within the nucleus. The gives rise to Fermi Contact Interaction, which has observable effects in NMR and ESR spectroscopy and electron capture.

  • $\begingroup$ I am not educated in Fermi Contact Interaction, NMR or ESR but I do know that the emission or absorption spectrum was first developed for hydrogen atom and considers energy diff between orbits and not orbitals, please read and find the formula here It clearly uses the concept of orbits not orbitals. If you want to say that orbits are truer than orbitals because of this phenomenon, then the entire chemistry would be shaking at roots! $\endgroup$ May 5, 2014 at 15:31
  • 1
    $\begingroup$ The Bohr model of fixed orbits is false. The wave function solutions (orbitals) of the Schrodinger equation are good approximations. However, the energy levels of the Bohr model and Schrodinger model are exactly the same. For greater accuracy, the Sommerfeld extension of the Bohr model, or the Dirac extension of the Schrodinger equation are needed (again Sommerfeld and Dirac both give the same energy levels). For even greater accuracy, QED is needed. $\endgroup$
    – DavePhD
    May 5, 2014 at 15:53
  • $\begingroup$ Again I am no expert at all, but the energy differences of orbitals however minutely are different from those of orbits, the Rydberg formula uses $n$ as the orbit number and has nothing to do with orbital, sure it is invalid for multi electron system but still it does not involve orbitals, if you say that spectrum involves energy gap of orbitals and not orbits (both just mathematical constructs and unrealistic acc. to me) wouldn't that falsify the Rydberg's formula. My question is about actual and realistic significance of orbitals and not their mathematical need and uses! $\endgroup$ May 5, 2014 at 16:03
  • $\begingroup$ I think you are confusing the term "orbital" with a particular quantum number such as l or m in the last comment. The orbital is designated by (n,l,m), such as 1s, 2s, 2p_x, etc. The Rydberg formula and Schrodinger equation say the 1s orbit(al) has a different energy then the 2s orbit(al), and that the 2s and all the 2p orbit(al)s have the same energy. This is only approximately true, hence the Sommerfeld formula and Dirac theory, which show there is a small difference between the energies of the 2s orbit(al) and the 2p orbit(al)s. $\endgroup$
    – DavePhD
    May 5, 2014 at 16:30
  • $\begingroup$ Lets just assume that electrons do have only certain valid energies associated with the 4 quantum numbers; My question still remains! Is there something like an orbital? for all we care, those electrons could be anywhere! Is the probability density view/model a correct one? is it that only those electrons that we know are of certain energy found in those particular regions we say they must be found? $\endgroup$ May 5, 2014 at 17:03

There is another "usefulness" of orbitals other than probabilities that I think is important to keep in mind, and is not clear from your question whether you've been introduced to it.

The wave function $\Psi(x,t)$ representing some given atomic orbital satisfies the Schrodinger equation for the atom. This means that the eigenvalue one extracts from $\Psi(x,t)$ represent that orbital's energy level. In some sense, the energy level is "encoded" in the shape of $\Psi(x,t)$ (for a given potential).

Historically, this was how Schrodinger first made use of his equation; not from a probabilistic point of view, but from deriving the hydrogen energy spectrum.


It's hard to pinpoint the exact cause of your confusion.

For instance, you state that "atomic orbitals are at best a high probability region of finding certain electrons. Since we must not be able to do that with enough certainty how then can we check the validity of the existence of orbitals?"

The probability in this case is a probability for a single measurement, which is entirely uncorrelated with the same type of measurement on another atom a micrometer away. If you aggregate enough measurements, the uncertainties cancel out.

The importance of these orbitals is critical to chemists. Basic organic chemistry depends on s- and p-orbitals overlapping to form bonds. In essence, an orbital specifies where an electron pair can be (one spin up, one spin down). Where two atoms approach, they may develop a common orbital. If both atoms have orbitals with only a single unpaired electron, the common/merged orbital can hold a pair. Having an electron pair with opposite spins is energetically beneficial, which explains how the formation of such a pair in a common orbital forms a stable bond between atoms.

Even fancier orbitals exist, in particular in benzene and similar cyclic molecules. We know that benzene is pretty flat, which is the result of orbitals on either side of the ring. These give rise to the rather unusual behavior of benzene.


The existence of atomic orbitals as described by quantum mechanics has been directly probed in an experiment. Also, related is that STM is able to show electron density of a surface, and this density is roughly the same as electron orbital for many-atomic system.


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