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According to Chemistry the Central Science 13 Edition, these ions are isoelectronic:

$\ce{Ca^2+}$ (18 electrons); $\ce{Cs+}$ (54 electrons); $\ce{Y^3+}$ (36 electrons)

Furthermore, the textbook states that the caesium ion is the largest.

Now, every definition I've looked up, including from the book, states that in an isoelectronic series, the atoms have the same number of electrons. Clearly, these don't. I have noticed, however, that they are in multiples of 18, where the Calcium ion is 18, and Caesium is 3 times 18, and Yttrium is 18 times 2.

A friend, who took chemistry 1 a few years ago, recalls that there was some formula (or something) to determine isoelectronic series.

I suspect that they have something to do with the electrons in their valence.

The book does not give an explanation. It moves on to ionization energy.

But it also states that of these three, caesium is the largest, which compounds my confusion since just a few lines up, the book states that the nuclear charge is inversely proportional to the ionic radius, so an increasing nuclear charge (atomic number) means a decreasing atomic radius. It would seem appropriate that the calcium ion has the largest ionic radius since it has the smallest nuclear charge.

Can anyone help?

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Core Electrons don't count. It's the valence electrons that are counted (outermost shell). The valence shell of all 3 is empty. So they all have 0 electrons in their valence shell.

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  • $\begingroup$ So isoelectronic is defined solely as atoms having the same number of electrons in its valence shell with the exclusion of core electrons? $\endgroup$
    – Danny Rodriguez
    Dec 4, 2016 at 19:29
  • $\begingroup$ @DannyRodriguez yeah $\endgroup$
    – user37142
    Dec 5, 2016 at 7:06
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1) They all have the configuration of a noble gas with a full P sublevel as the highest sublevel.

2) Nuclear charge is inversely proportional to anion radius within a given period.

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