Unpaired Electrons in Transition Metal Ions Based on Mn Oxidation States

To determine the correct set of ions, we first calculate the difference in the oxidation states of manganese in its highest fluoride and highest oxide.

Step 1: Oxidation State of Manganese in its Highest Fluoride

According to the properties of $d$-block elements, the highest fluoride formed by manganese is manganese(IV) fluoride, $\text{MnF}_4$.

• Oxidation state of $\text{Mn}$ in $\text{MnF}_4 = +4$.

Step 2: Oxidation State of Manganese in its Highest Oxide

The highest oxide formed by manganese is manganese(VII) oxide, $\text{Mn}_2\text{O}_7$.

• Oxidation state of $\text{Mn}$ in $\text{Mn}_2\text{O}_7 = +7$.

Step 3: Calculate $|x|$

The difference in oxidation states $|x|$ is: $|x| = |(+7) - (+4)| = 3$

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Step 4: Determine the Number of Unpaired Electrons in the Given Ions

1. $\text{Sc}^{3+}$ ($Z = 21$):

   • Electronic configuration of $\text{Sc}$: $[\text{Ar}]\,3d^1\,4s^2$
   • Electronic configuration of $\text{Sc}^{3+}$: $[\text{Ar}]\,3d^0$
   • Number of unpaired electrons = $0$

2. $\text{Zn}^{2+}$ ($Z = 30$):

   • Electronic configuration of $\text{Zn}$: $[\text{Ar}]\,3d^{10}\,4s^2$
   • Electronic configuration of $\text{Zn}^{2+}$: $[\text{Ar}]\,3d^{10}$
   • Number of unpaired electrons = $0$

3. $\text{V}^{2+}$ ($Z = 23$):

   • Electronic configuration of $\text{V}$: $[\text{Ar}]\,3d^3\,4s^2$
   • Electronic configuration of $\text{V}^{2+}$: $[\text{Ar}]\,3d^3$
   • Number of unpaired electrons = $3$

4. $\text{Fe}^{2+}$ ($Z = 26$):

   • Electronic configuration of $\text{Fe}$: $[\text{Ar}]\,3d^6\,4s^2$
   • Electronic configuration of $\text{Fe}^{2+}$: $[\text{Ar}]\,3d^6$
   • Number of unpaired electrons = $4$

5. $\text{Co}^{2+}$ ($Z = 27$):

   • Electronic configuration of $\text{Co}$: $[\text{Ar}]\,3d^7\,4s^2$
   • Electronic configuration of $\text{Co}^{2+}$: $[\text{Ar}]\,3d^7$
   • Number of unpaired electrons = $3$

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Conclusion

The ions with $|x| = 3$ unpaired electrons are $\text{V}^{2+}$ (C) and $\text{Co}^{2+}$ (E).

Thus, the correct answer is C and E Only (Option C).