To identify the transition metal ion pair with an identical number of unpaired electrons, we must examine the electronic configurations of the provided ions.
- Determine the ground-state electronic configuration for each ion:
- Vanadium (V), atomic number 23:
- Neutral Vanadium (V): \([Ar] 3d^3 4s^2\)
- For \(V^{2+}\): Electron removal from 4s yields \([Ar] 3d^3\), resulting in 3 unpaired electrons.
- Cobalt (Co), atomic number 27:
- Neutral Cobalt (Co): \([Ar] 3d^7 4s^2\)
- For \(Co^{2+}\): Electron removal from 4s yields \([Ar] 3d^7\), resulting in 3 unpaired electrons.
- Titanium (Ti), atomic number 22:
- For \(Ti^{2+}\) (following the same procedure): \([Ar] 3d^2\), with 2 unpaired electrons.
- For \(Ti^{3+}\): \([Ar] 3d^1\), with 1 unpaired electron.
- Iron (Fe), atomic number 26:
- For \(Fe^{3+}\): \([Ar] 3d^5\), with 5 unpaired electrons.
- Chromium (Cr), atomic number 24:
- For \(Cr^{2+}\): \([Ar] 3d^4\), with 4 unpaired electrons.
- Manganese (Mn), atomic number 25:
- For \(Mn^{2+}\): \([Ar] 3d^5\), with 5 unpaired electrons.
Analysis of these configurations shows that \(V^{2+}\) and \(Co^{2+}\) each possess 3 unpaired electrons. Consequently, the correct pair is:
\(V^{2+}, Co^{2+}\)