Properties and Electronic Configurations of Chromium and Manganese Ions

To determine the correct statements regarding $\text{Cr}^{2+}$ and $\text{Mn}^{3+}$ ions, we analyze their electronic configurations and redox properties:

1. Electronic Configurations:

   • The atomic number of Chromium ($\text{Cr}$) is $24$. Its ground-state electronic configuration is: $\text{Cr}: [\text{Ar}] 3d^5 4s^1$ Upon losing two electrons to form $\text{Cr}^{2+}$, the configuration becomes: $\text{Cr}^{2+}: [\text{Ar}] 3d^4$

   • The atomic number of Manganese ($\text{Mn}$) is $25$. Its ground-state electronic configuration is: $\text{Mn}: [\text{Ar}] 3d^5 4s^2$ Upon losing three electrons to form $\text{Mn}^{3+}$, the configuration becomes: $\text{Mn}^{3+}: [\text{Ar}] 3d^4$

   Therefore, both $\text{Cr}^{2+}$ and $\text{Mn}^{3+}$ possess a $d^4$ electronic configuration. Statement (C) is correct.

2. Reducing Nature of $\text{Cr}^{2+}$:

   • $\text{Cr}^{2+}$ ($d^4$) gets oxidized to $\text{Cr}^{3+}$ ($d^3$) by losing an electron: $\text{Cr}^{2+} (d^4) \rightarrow \text{Cr}^{3+} (d^3) + e^-$
   • In aqueous medium, $\text{Cr}^{3+}$ forms an octahedral complex with a $t_{2g}^3$ half-filled, extra-stable electronic configuration.
   • Because of the stability gained by forming $\text{Cr}^{3+}$, $\text{Cr}^{2+}$ acts as a strong reducing agent. Statement (A) is correct.

3. Oxidizing Nature of $\text{Mn}^{3+}$:

   • $\text{Mn}^{3+}$ ($d^4$) gets reduced to $\text{Mn}^{2+}$ ($d^5$) by gaining an electron: $\text{Mn}^{3+} (d^4) + e^- \rightarrow \text{Mn}^{2+} (d^5)$
   • The $d^5$ subshell in $\text{Mn}^{2+}$ is half-filled and exceptionally stable.
   • Therefore, $\text{Mn}^{3+}$ readily accepts an electron and acts as a strong oxidizing agent. Statement (B) is correct.

4. Electronic Configuration of Chromium after Reduction/Oxidation:

   • When $\text{Cr}^{2+}$ functions as a reducing agent, it undergoes oxidation to form $\text{Cr}^{3+}$, which has a $d^3$ electronic configuration (not $d^5$). Statement (D) is incorrect.

Thus, the correct statements are A, B, and C.