The crystal field configuration of complexes `[Ru(en)_3]Cl_2` and `[Fe(H_2O)_6]^(2+)` respectively is:

Options

A. `t_(2g)^4,e_g^2`and `t_(2g)^6,e_g^0`
B. `t_(2g)^6,e_g^0`and `t_(2g)^4,e_g^2`
C. `t_(2g)^4,e_g^2`and `t_(2g)^4,e_g^2`
D. `t_(2g)^6,e_g^0`and `t_(2g)^6,e_g^0`

Answer

To determine the crystal field configuration of the complexes \([Ru(en)_3]Cl_2\) and \([Fe(H_2O)_6]^{2+}\), we will follow these steps:

### Step 1: Determine the oxidation states of the central metal ions.
- For \([Ru(en)_3]Cl_2\):
- Ethylenediamine (en) is a neutral ligand, contributing 0 to the charge.
- Each chloride ion (Cl) has a charge of -1. Since there are 2 chloride ions, they contribute -2.
- Let the oxidation state of Ru be \(x\). The overall charge of the complex is 0.
- Therefore, \(x - 2 = 0\) implies \(x = +2\).

- For \([Fe(H_2O)_6]^{2+}\):
- Water (H2O) is also a neutral ligand, contributing 0 to the charge.
- The overall charge of the complex is +2.
- Let the oxidation state of Fe be \(y\). Thus, \(y = +2\).

### Step 2: Write the electronic configurations of the metal ions.
- For Ru (Ruthenium):
- The atomic number of Ru is 44. Its ground state electronic configuration is \([Kr] 4d^7 5s^1\).
- In the +2 oxidation state, Ru loses 2 electrons (1 from 5s and 1 from 4d), resulting in the configuration: \(4d^6\).

- For Fe (Iron):
- The atomic number of Fe is 26. Its ground state electronic configuration is \([Ar] 3d^6 4s^2\).
- In the +2 oxidation state, Fe loses 2 electrons (both from 4s), resulting in the configuration: \(3d^6\).

### Step 3: Analyze the ligand field strength and predict the crystal field splitting.
- For \([Ru(en)_3]Cl_2\):
- Ethylenediamine (en) is a strong field ligand, which causes pairing of electrons.
- The \(4d^6\) configuration will fill the lower energy \(t_{2g}\) orbitals first, leading to the configuration: \(t_{2g}^6 e_g^0\).

- For \([Fe(H_2O)_6]^{2+}\):
- Water (H2O) is a weak field ligand, which does not favor electron pairing.
- The \(3d^6\) configuration will fill the orbitals singly first, leading to the configuration: \(t_{2g}^4 e_g^2\).

### Final Answer:
- The crystal field configurations are:
- For \([Ru(en)_3]Cl_2\): \(t_{2g}^6 e_g^0\) (low spin).
- For \([Fe(H_2O)_6]^{2+}\): \(t_{2g}^4 e_g^2\) (high spin).