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From what I have learned, the number of electrons on the outermost shell (called the valence electrons), determines the chemical properties of an atom, this is why elements in the same group have similar physical/chemical properties.

I was wondering, if you had a neutral sodium atom (Na), and you ionising it by making it lose an electron ($\ce{Na+}$), it now has a total of 10 electrons, and a full outer most shell. Does the $\ce{Na+}$ ion have the same chemical/physical properties as a neutral Neon atom and the rest of the elements in the noble gas group, if not how are they similar/different.

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    $\begingroup$ Atoms and their ions have totally different chemical and physical properties. Apart from the mass and the number of protons in the nucleus, there is no similarity between the properties of neutral atoms and the properties of corresponding ionized atoms. For example, the behavior of a given atom in contact with another one changes if the colliding atom is ionized or not. $\endgroup$
    – Maurice
    Commented Mar 5 at 17:14

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You're correct in that there are similarities in the spectra of $\ce{Na+}$ and $\ce{Ne}$. That is, in an isolated ion or atom of $\ce{Na+}$ and $\ce{Ne}$, there is a similarity in the mathematical relationship amongst the energy levels.

Meghnad Saha and Protap Kischen Kichlu, in the Indian Journal of Physics, are quoted as stating, "that when we take a number of successive elements, which, on account of loss of one or of more electrons by electric discharge, are reduced to have the same electronic structure, [e.g., $\ce{Na+ and Ne}$, ed.], then the frequencies of the corresponding lines of these elements arising from the same transition form an arithmetic progression, provided the transition takes place between levels having the same total quantum number."

This seems to me to be one of the fundamental studies in quantum mechanics, though not as easy to find on the internet as it should be. You can read an article by Saha and Kichlu, Extension of the Irregular Doublet Law to Complex Spectra, at arXiv.org.

However, it is more than a quantum jump to assume that ionized sodium and neutral neon behave in a similar chemical fashion, or that they have similar physical properties. Well, other than providing useful illumination via the neon lamp and the sodium vapor lamp. But then we're back to spectra, aren't we?

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