Question

Which of the following pair of ions have equal number of unpaired electrons

• A. \( \mathrm{V^{2+}} \) and \( \mathrm{Ni^{2+}} \)
• B. \( \mathrm{Cr^{2+}} \) and \( \mathrm{Mn^{2+}} \)
• C. \( \mathrm{Fe^{2+}} \) and \( \mathrm{Sc^{2+}} \)
• D. \( \mathrm{Mn^{3+}} \) and \( \mathrm{Fe^{2+}} \)

Hint:

For transition metal ions, always remove electrons from the \( 4s \) orbital before the \( 3d \) orbital. Then apply Hund's rule to count the number of unpaired electrons correctly.

Answer 1

The Correct Option is D

To determine which pair of ions have an equal number of unpaired electrons, we need to examine the electron configurations of each ion.

1. Identify the atomic numbers of the elements:
   • \( \text{V (Vanadium)}: Z = 23 \)
   • \( \text{Ni (Nickel)}: Z = 28 \)
   • \( \text{Cr (Chromium)}: Z = 24 \)
   • \( \text{Mn (Manganese)}: Z = 25 \)
   • \( \text{Fe (Iron)}: Z = 26 \)
   • \( \text{Sc (Scandium)}: Z = 21 \)
2. Determine the electron configurations:
   • \( \mathrm{V}: [\mathrm{Ar}] \, 3d^3 \, 4s^2 \)
   • \( \mathrm{Cr}: [\mathrm{Ar}] \, 3d^5 \, 4s^1 \)
   • \( \mathrm{Mn}: [\mathrm{Ar}] \, 3d^5 \, 4s^2 \)
   • \( \mathrm{Fe}: [\mathrm{Ar}] \, 3d^6 \, 4s^2 \)
   • \( \mathrm{Ni}: [\mathrm{Ar}] \, 3d^8 \, 4s^2 \)
   • \( \mathrm{Sc}: [\mathrm{Ar}] \, 3d^1 \, 4s^2 \)
3. Calculate the electron configurations of the given ions by removing electrons from the outermost shell:
   • \( \mathrm{V^{2+}} \): Remove 2 electrons from \( 4s \) and \( 3d \): \([ \mathrm{Ar}] \, 3d^3 \) 
     Unpaired electrons = 3
   • \( \mathrm{Ni^{2+}} \): Remove 2 electrons from \( 4s \) and \( 3d \): \([ \mathrm{Ar}] \, 3d^8 \) 
     Unpaired electrons = 2
   • \( \mathrm{Cr^{2+}} \): Remove 2 electrons from \( 4s \) and \( 3d \): \([ \mathrm{Ar}] \, 3d^4 \) 
     Unpaired electrons = 4
   • \( \mathrm{Mn^{2+}} \): Remove 2 electrons from \( 4s \) and \( 3d \): \([ \mathrm{Ar}] \, 3d^5 \) 
     Unpaired electrons = 5
   • \( \mathrm{Fe^{2+}} \): Remove 2 electrons from \( 4s \) and \( 3d \): \([ \mathrm{Ar}] \, 3d^6 \) 
     Unpaired electrons = 4
   • \( \mathrm{Sc^{2+}} \): Remove 2 electrons from \( 3d \): \([ \mathrm{Ar}] \, 3d^1 \) 
     Unpaired electrons = 1
   • \( \mathrm{Mn^{3+}} \): Remove 3 electrons from \( 4s \) and \( 3d \): \([ \mathrm{Ar}] \, 3d^4 \) 
     Unpaired electrons = 4
4. Compare the numbers of unpaired electrons in each pair:
   • \( \mathrm{V^{2+}} \) and \( \mathrm{Ni^{2+}} \): 3 and 2 unpaired electrons respectively.
   • \( \mathrm{Cr^{2+}} \) and \( \mathrm{Mn^{2+}} \): 4 and 5 unpaired electrons respectively.
   • \( \mathrm{Fe^{2+}} \) and \( \mathrm{Sc^{2+}} \): 4 and 1 unpaired electrons respectively.
   • \( \mathrm{Mn^{3+}} \) and \( \mathrm{Fe^{2+}} \): Both have 4 unpaired electrons.

Hence, the pair \(\mathrm{Mn^{3+}}\) and \(\mathrm{Fe^{2+}}\) have equal numbers of unpaired electrons, both having 4 unpaired electrons each.