Why does every element have unique spectral lines?
I have studied that spectral lines help us to identify the properties of an element. This is because after excitation when the excited electron(s) fall back to their original energy level(s), photons of certain frequency corresponding to the difference between the energy levels are emitted.
Now I have a question, every substance consists of atoms, and each atom consists of electrons, electrons are fuzzy clouds and are described by wave-functions given by the solutions of the Schrodinger equation, so what makes the spectral lines different although every substance has the same thing?
I searched on the site and discussed with various members of the community and some of the conclusions I drew are mentioned below:
Electron-nucleus attraction and the electron-electron repulsion. Hydrogen is a special case because it has only a single electron so there is no electron-electron repulsion. Helium has two electrons so now we have some e-e repulsion, Lithium has three electrons so there is even more e-e repulsion and so on... Every atom has a different number of electrons and a different nuclear charge, so the balance of nuclear attraction and e-e repulsion is different. So every atom has its own set of atomic orbitals that are specific to it and are different from every other atom. The spectrum comes from transitions between orbitals, and since the orbitals are different for every atom the spectrum is different for every atom.
Are my conclusions reasonable or is there something else I missed to note?
But this answer creates one more question in my mind,
Do all noble gases or alkaline earth metals have similar spectral lines considering the above points I mentioned?