Animated Solution for Chemistry - Periodicity in Properties: Which one of the following sets of ions represents a collection of isoelectronic species ?

When we dive into the periodic table, we often encounter species that look completely different but share a hidden secret: their electron count. The term isoelectronic is a combination of 'iso', meaning same, and 'electronic', referring to electrons. Therefore, isoelectronic species are atoms or ions that possess the exact same number of electrons.

Why does this matter? Elements constantly strive for stability, which usually means achieving the electron configuration of the nearest noble gas. By losing or gaining electrons, different elements can end up with the exact same stable electron cloud.

To determine if a set of ions is isoelectronic, we need to calculate the number of electrons for each one. The formula is straightforward:

Here, $Z$ represents the atomic number (the number of protons). If an ion has a positive charge (a cation), it has lost electrons, so we subtract that positive value. If it has a negative charge (an anion), it has gained electrons, so subtracting a negative value effectively adds to the total.

Let's put our formula to the test by evaluating the first option, which contains ${\text{K}}^{+}$, ${\text{Cl}}^{-}$, ${\text{Ca}}^{2+}$, and ${\text{Sc}}^{3+}$.

1. Potassium Ion (${\text{K}}^{+}$): Potassium has an atomic number $Z=19$. The $+1$ charge indicates it has lost one electron.

2. Chloride Ion (${\text{Cl}}^{-}$): Chlorine has an atomic number $Z=17$. The $-1$ charge means it has gained one extra electron.

3. Calcium Ion (${\text{Ca}}^{2+}$): Calcium sits at atomic number $Z=20$. A $+2$ charge tells us it has lost two electrons.

4. Scandium Ion (${\text{Sc}}^{3+}$): Scandium has an atomic number $Z=21$. Losing three electrons gives it a $+3$ charge.

Look at the results! Every single ion in this set has exactly 18 electrons. They have all achieved the highly stable electron configuration of the noble gas Argon ($Z=18$). Because they all share this identical electron count, they form a perfect isoelectronic series.

If you were to test the other options, you would find mismatches. For example, in option (d), ${\text{Li}}^{+}$ has 2 electrons, while ${\text{Na}}^{+}$ has 10. They are definitely not isoelectronic. Thus, the correct answer is undeniably the first set.