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Question: For elements in the same period with different numbers of valance electrons, why does the same electron transition release photons of different frequencies?

Example: For valance electrons moving from the 4d sub-level to the 4p sub-level, $\ce{Ca^2+}$ emits violet light, while $\ce{Cu^2+}$ emits green light.

Example case referring to JavaLab: Flame Test, which in turn claims to refer to NIST Basic Atomic Spectroscopic Data.

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    $\begingroup$ The energy levels are different, as are the differences between a given pair of energy levels. $\endgroup$
    – Ed V
    Commented Oct 10, 2022 at 22:24
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    $\begingroup$ @EdV Does that mean that energy levels, like the 4d sub-level, have different energies for different atoms? $\endgroup$
    – Bryan351018
    Commented Oct 10, 2022 at 22:27
  • $\begingroup$ @Bryan351018, Could you add more details. Calcium I and Copper I (I = unionized atom) atomic spectra are horribly complex and dense (too many lines). What figures are you referring to? You must have a reference which shows violet vs. green emission. I did not down vote your question, rather upvoted it. Don't worry about them. $\endgroup$
    – ACR
    Commented Oct 10, 2022 at 23:55
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    $\begingroup$ @AChem I have updated the question for more details and better formatting; hopefully it's a bit better now. $\endgroup$
    – Bryan351018
    Commented Oct 11, 2022 at 2:27
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    $\begingroup$ You should ask Why should they have the same frequencies, considering different nucleus charges and different electron configuration? Orbital energy levels are not like fixed heights of book shelves. $\endgroup$
    – Poutnik
    Commented Oct 11, 2022 at 6:54

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I am glad that you updated the question because it highlights a very common misconception. First of all the JavaLab Flame Test is completely wrong for both copper, calcium and many more salts especially the Group II and transition metal salts. Consequently, the NIST reference does not apply (see below). Secondly, it is a cruelty to science if a cartoon flame test is being shown instead of the real flame test. Search Youtube for real flame tests.

Basically, the brick red color and the green color of calcium and copper respectively is not from atomic emission of Ca or Cu atoms nor it comes $\ce{Ca^{2+}}$ or $\ce{Cu^{2+}}$ ions. This color comes from small molecular species of those elements in the flame. If you had a pocket spectroscope (it is not difficult to make one at home from a DVD/CD), copper green color will appear as a range of wavelengths, which is an indication of molecular spectrum.

When we talk about atomic spectrum, we need very high temperature flames, which usually ~ 3000 K. Ordinary Bunsen burner produces a cool flame by that standards. Cooler flames cannot break molecular compounds to free atoms. Let us think of this way: You introduce $\ce{CaCl2}$ into the flame in the form of a solution. The solution will dry and produce solid salt, which will begin to vaporize and decompose in the flame. High temperature flames are electron rich, and then free calcium ion is reduced to calcium atom. In that case, one can talk about atomic emission and its corresponding electronic transitions. In those cases, one can refer to NIST tables.

For the sake of completion only the alkali metals produce an incomplete atomic emission in a Bunsen burner.

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