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on this website (https://physics.nist.gov/PhysRefData/ASD/levels_form.html), you can look up atomic spectra. For example, if you query "Na I", you will see that the Level (cm^-1) for the excited state of Sodium (2p63p electron configuration) is approximately 16 956, whereas for the ground state (electron configuration 2p63s) the Level is 0, of course. So far, so good.

But if you query Lithium ("Li I"), you will see that the Level of the excited state is 14 903 (electron configuration 1s22p) as compared to the ground state (electron configuration 1s22s).

Is it wrong for me to deduce that therefore the energy difference between the 2s and 2p orbital in Lithium is smaller than the energy difference between the 3s and 3p orbitals in Sodium? It confuses me because I always thought that it should be the other way around.

I really hope you can help me, thanks in advance!

Best regards

Thies

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  • $\begingroup$ you have to be careful when making extrapolations. You have to take into account nucleus-electron attraction and electron-electron repulsions. Li has a nuclear charge of +2, and 2 electrons in the nucleus. However, Na has a nuclear charge of +11, 10 core electrons and 1 valence electron. The interactions in the two atoms are very different. You have to compare the energies of atomic configurations which correspond to the same atom. $\endgroup$
    – PAEP
    Commented Feb 18 at 18:58
  • $\begingroup$ Thanks for the answer! But I do not extrapolate anything, I just compare two numbers that are showing what I describe in the post. These numbers also explain why the light emitted from Sodium in the flame test has more energy than the light emitted from Lithium. So what I describe seems to be the case, I just do not get it, since I had learned that it should be the other way around. $\endgroup$
    – Theiserino
    Commented Feb 18 at 19:16
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    $\begingroup$ The general question in the title "Is the energy difference between the 2s and 2p orbital smaller than the difference between 3s and 3p?" is different from the specific question "Is it wrong for me to deduce that therefore the energy difference between the 2s and 2p orbital in Lithium is smaller than the energy difference between the 3s and 3p orbitals in Sodium?". $\endgroup$
    – Andrew
    Commented Feb 18 at 23:56

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The energy difference between the s and p orbitals increases with atomic number

As the atomic number increases, the nuclear charge increases and the electrons move closer to the nucleus. This reduces the energy of all orbitals, but reduces the energy of the s orbitals more than the energy of the p orbitals. This is because s orbitals penetrate further into the nucleus and have a higher electron density than p orbitals, so they are more affected by the increase in nuclear charge.

As a result of these factors, the energy difference between the s and p orbitals increases with atomic number, just as you describe for Lithium and Sodium. Another example would be that in hydrogen (Z = 1), the energy difference between the 1s and 2p orbitals is only 10.2 eV. By contrast, in fluorine (Z = 9), the energy difference between the 1s and 2p orbitals is 52.5 eV.

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  • $\begingroup$ Thank you very much, that makes sense! $\endgroup$
    – Theiserino
    Commented Feb 19 at 14:09
  • $\begingroup$ I would like to ask one more question: Does energy difference between different electron shells increase with atomic number in general? (for example energy differences between second and third shell will be higher for elements with higher atomic number)? $\endgroup$
    – Theiserino
    Commented Feb 25 at 9:44

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