To determine the number of complexes with an even number of electrons in $t_{2g}$ orbitals, we calculate the electronic configuration of the central metal ion in each complex:
$[\text{Fe}(\text{H}_2\text{O})_6]^{2+}$: Fe$^{2+}$ has $(3d^6)$ configuration. In an octahedral field:
\[t_{2g}^4e_g^2 \quad (4 \, \text{electrons in } t_{2g})\]
Even number of electrons in $t_{2g}$.
$[\text{Co}(\text{H}_2\text{O})_6]^{2+}$: Co$^{2+}$ has $(3d^7)$ configuration. In an octahedral field:
\[t_{2g}^5e_g^2 \quad (5 \, \text{electrons in } t_{2g})\]
Odd number of electrons in $t_{2g}$.
$[\text{Co}(\text{H}_2\text{O})_6]^{3+}$: Co$^{3+}$ has $(3d^6)$ configuration. In an octahedral field:
\[t_{2g}^6e_g^0 \quad (6 \, \text{electrons in } t_{2g})\]
Even number of electrons in $t_{2g}$.
$[\text{Cu}(\text{H}_2\text{O})_6]^{2+}$: Cu$^{2+}$ has $(3d^9)$ configuration. In an octahedral field:
\[t_{2g}^6e_g^3 \quad (6 \, \text{electrons in } t_{2g})\]
Even number of electrons in $t_{2g}$.
$[\text{Cr}(\text{H}_2\text{O})_6]^{2+}$: Cr$^{2+}$ has $(3d^4)$ configuration. In an octahedral field:
\[t_{2g}^3e_g^1 \quad (3 \, \text{electrons in } t_{2g})\]
Odd number of electrons in $t_{2g}$.
Complexes with even number of electrons in $t_{2g}$ orbitals are:
\[[\text{Fe}(\text{H}_2\text{O})_6]^{2+}, \, [\text{Co}(\text{H}_2\text{O})_6]^{3+}, \, [\text{Cu}(\text{H}_2\text{O})_6]^{2+}\]
Final Answer: 3 complexes.
Match List-I with List-II
Choose the correct answer from the options given below :
Identify the diamagnetic octahedral complex ions from below ;
A. [Mn(CN)\(_6\)]\(^{3-}\)
B. [Co(NH\(_3\))\(_6\)]\(^{3+}\)
C. [Fe(CN)\(_6\)]\(^{4-}\)
D. [Co(H\(_2\)O)\(_3\)F\(_3\)]
Choose the correct answer from the options given below :
Number of stereoisomers possible for the complexes, $\left[\mathrm{CrCl}_{3}(\mathrm{py})_{3}\right]$ and $\left[\mathrm{CrCl}_{2}(\mathrm{ox})_{2}\right]^{3-}$ are respectively} (py = pyridine, ox = oxalate)
Match List-I with List-II: List-I