Final answer:
The set containing Mg²⁻, Sr²⁻, and Ba²⁻ includes species that are isoelectronic; they all have the same number of electrons, as they are all two electrons short of the electron counts of Ne, Kr, and Xe respectively.
Step-by-step explanation:
The question is about finding a set of species in which all members have the same number of electrons, meaning they are isoelectronic. To be isoelectronic, species must have electron configurations that are identical. For example, N³⁻, O²⁻, and F⁻ all have the electron configuration of Ne (1s²2s²2p⁶). Therefore, we are looking for a list where every species shares a similar electron configuration and, thereby, their total count of electrons.
Out of the sets provided, the set containing Mg²⁻, Sr²⁻, and Ba²⁻ has species that all have the same number of electrons. Each of these species has 10 electrons less than their neutral atoms since they all have lost 2 electrons to achieve a charge of +2. The neutral atoms Mg, Sr, and Ba are from the second column of the periodic table and, in their neutral forms, would have 12, 38, and 56 electrons respectively. Subtracting 2 from each gives us 10, 36, and 54 electrons for Mg²⁻, Sr²⁻, and Ba²⁻, which are the same numbers of electrons as the noble gases Ne, Kr, and Xe respectively, making them isoelectronic.