Q.In which of the following pairs, the ions are iso-electronic? (Note: more than one of the given options may be correct.)

Isoelectronic Species – From Intuition to Precision

Imagine you are building atoms with LEGO blocks. Each block is a proton (positive charge) or an electron (negative charge). The number of protons decides which element you have — that's the atomic number $Z$. The number of electrons decides the charge on the particle.

Now, here is the key idea: two different particles can have the same number of electrons. When that happens, their electron clouds are arranged in the same way. They become isoelectronic.

The Intuition

Think of a neutral neon atom. It has 10 protons and 10 electrons. Now take a sodium atom (11 protons, 11 electrons) and remove one electron. You get $\text{Na}^+$, which has 11 protons but only 10 electrons. The electron count of $\text{Na}^+$ is exactly the same as that of neutral neon.

Even though $\text{Na}^+$ and $\text{Ne}$ are different elements with different nuclear charges, their electron configurations are identical: $1s^2 2s^2 2p^6$. They are iso (same) electronic (electron arrangement).

The Precise Statement

Definition: Two or more atoms, ions, or molecules are said to be isoelectronic if they have the same number of electrons.

That is the entire definition. But the real power comes from what follows: because their electron clouds are identical in structure, their properties — like ionic radii, ionization energy, and chemical behaviour — show clear, predictable trends when you compare them.

How to Identify Isoelectronic Species

1. Count the electrons in each species.

   • For a neutral atom: electrons = atomic number $Z$.
   • For a positive ion: electrons = $Z$ - (charge magnitude).
   • For a negative ion: electrons = $Z$ + (charge magnitude).

2. Compare the counts. If they match, the species are isoelectronic.

Example: Which of these are isoelectronic? $\text{O}^{2-}$, $\text{F}^-$, $\text{Na}^+$, $\text{Mg}^{2+}$, $\text{Ne}$.

• $\text{O}^{2-}$: $Z=8$, electrons = $8+2=10$
• $\text{F}^-$: $Z=9$, electrons = $9+1=10$
• $\text{Na}^+$: $Z=11$, electrons = $11-1=10$
• $\text{Mg}^{2+}$: $Z=12$, electrons = $12-2=10$
• $\text{Ne}$: $Z=10$, electrons = $10$

All five have 10 electrons. They form an isoelectronic series.

The Critical Consequence: Size Trends

Here is where the concept becomes exam-relevant. In an isoelectronic series, as nuclear charge ($Z$) increases, the ionic radius decreases.

Why? The same number of electrons is pulled more strongly by a larger positive nucleus. The electron cloud shrinks.

For the series above ($\text{O}^{2-}$, $\text{F}^-$, $\text{Na}^+$, $\text{Mg}^{2+}$, $\text{Ne}$):