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Question from the online class:

Can two s-orbitals overlap as shown?

overlapping s-orbitals

Dotted circles in diagram depict maximum probability region of s-orbitals in ideal situation when atoms A and B are not bonded. Black dots denote nuclei.

Answer by teacher: no because extent of overlapping should always be less than 50 %.

My answer and argument:

  1. Practically the two spheres are not overlapping 50 % mathematically even if the nucleus are on radius of each atoms (as shown in diagram).

  2. Van der Waals radius of hydrogen is $\pu{120 pm}.$ Bond length of $\ce{H-H}$ bond is $\pu{74 pm}$ in hydrogen molecule. The above two data clearly states that nucleus of hydrogen atom lies inside the sphere of another hydrogen atom (as bond length is less than two times the radius of an atom).

Second argument provides a supportive example (for my answer) of hydrogen molecule that the overlapping shown in diagram (infact better than diagram) is possible. So, given diagram is correct or at least possible.

What is right at undergraduate level? Even a small answer (with authentic source if possible) is also welcome because question itself contains much opposing reasons.

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    $\begingroup$ To answer the question, you have to first define what those circles actually mean? s-orbitals are just wavefunctions i.e. a probability distribution, you cannot directly draw them. You can draw a surface that covers some percentage (like 95%) of probability of finding the electron. $\endgroup$
    – S R Maiti
    May 20 at 9:20
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    $\begingroup$ Uhhh. The problem isn't merely geometric. In the macroscopic world you are asking if two football balls can superpose each other and be in compenrtration. Electrons comes with charge, nuclei too. This means there is a potential requisite to fulfil. That is what quantum mechanics do. At this stage better trust sources (though I have no idea about the 50% figure). $\endgroup$
    – Alchimista
    May 20 at 13:05
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    $\begingroup$ @Jay because in doing so you are again in a merely geometric scenario. The VdW radius of H isn't much of a help discussing H-H. It can be seen as a limit of closest approach. But it does not say much in case the two bond togheter. Take the discussion about overlap with a grain of salt. For what matters, the message should be that s orbitals can have good overlap independent of orientation. Moreover the figure 50% or whatever wouldn't be reflected by those distance. We are dealing with "balls" (assuming the draw means the percentage bla bla...) at the end. $\endgroup$
    – Alchimista
    May 20 at 13:41
  • $\begingroup$ You're confounding vdW radius with atomic radius. for vdW it's a distance to a neighboring nucleus $\endgroup$
    – Mithoron
    May 20 at 17:11
  • $\begingroup$ If you all want I shall delete this post (just asking to confirm) $\endgroup$
    – Jay
    May 21 at 6:09