Which of the following are isoelectronic species i.e., those having the same number of electrons? Na^+, K^+, M

Exercises · 2.22

Na^+, K^+, Mg^{2+}, Ca^{2+}, S^{2-}, Ar

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Concept understanding — Isoelectronic Species

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).

Note

Isoelectronic species share the same number of electrons and therefore the same electronic configuration. They differ in nuclear charge ( $Z$ ).

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

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).
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.

\text{Electrons in an ion} = Z - (\text{charge})

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

Species	$Z$	Electrons	Relative Radius
$\text{O}^{2-}$	8	10	Largest
$\text{F}^-$	9	10	↓
$\text{Ne}$	10	10	↓
$\text{Na}^+$	11	10	↓
$\text{Mg}^{2+}$	12	10	Smallest

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The key idea is to count the total electrons in each species (atomic number minus charge for ions, atomic number for neutral atoms). The species that share the same electron count are isoelectronic. Here, $Na^+$ , $Mg^{2+}$ , and $Ar$ all have 10 electrons; $K^+$ , $Ca^{2+}$ , and $S^{2-}$ all have 18 electrons.

Isoelectronic species are atoms or ions that have the same number of electrons. This is a fundamental concept in chemistry because species with identical electron configurations often show similar chemical properties, even if their nuclear charges differ. For example, $Na^+$ and $Ne$ are isoelectronic — both have 10 electrons arranged as $1s^2 2s^2 2p^6$ .

To check which of the given species are isoelectronic, we simply calculate the total number of electrons in each. For a neutral atom, the number of electrons equals its atomic number. For an ion, it’s the atomic number minus the charge (since a positive charge means electrons have been lost, and a negative charge means electrons have been gained).

Let’s go through each species step by step.

$Na^+$

Sodium has atomic number 11. The $+$ charge means it has lost 1 electron.

Electrons = $11 - 1 = 10$ .
$K^+$

Potassium has atomic number 19. It has lost 1 electron.

Electrons = $19 - 1 = 18$ .
$Mg^{2+}$

Magnesium has atomic number 12. It has lost 2 electrons.

Electrons = $12 - 2 = 10$ .
$Ca^{2+}$

Calcium has atomic number 20. It has lost 2 electrons.

Electrons = $20 - 2 = 18$ .
$S^{2-}$

Sulfur has atomic number 16. The $2-$ charge means it has gained 2 electrons.

Electrons = $16 + 2 = 18$ .
$Ar$

Argon is a neutral atom with atomic number 18.

Electrons = $18$ .

Now, group them by electron count:

10 electrons: $Na^+$ , $Mg^{2+}$ , $Ar$
18 electrons: $K^+$ , $Ca^{2+}$ , $S^{2-}$ …

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Q.Which of the following are isoelectronic species i.e., those having the same number of electrons? Na+,K+,Mg2+,Ca2+,S2−,ArNa^+, K^+, Mg^{2+}, Ca^{2+}, S^{2-}, ArNa+,K+,Mg2+,Ca2+,S2−,Ar.

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Q.Which of the following are isoelectronic species i.e., those having the same number of electrons? $Na^+, K^+, Mg^{2+}, Ca^{2+}, S^{2-}, Ar$ .

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