`[CoCl_(4)]` is a tetrahedral complex The electronic configuration of central metal ion is `e_{2}^n` .`t_2^(m)` find the value of `n` +`m` .

Answer

To solve the problem, we need to determine the oxidation state of the central metal ion in the complex \([CoCl_4]^{2-}\) and then find the electronic configuration of cobalt in that oxidation state. Finally, we will identify the values of \(n\) and \(m\) from the electronic configuration and calculate \(n + m\).

### Step-by-Step Solution:

1. **Determine the oxidation state of cobalt (Co):**
- The complex is \([CoCl_4]^{2-}\).
- Let the oxidation state of cobalt be \(x\).
- Each chloride ion (Cl) has an oxidation state of \(-1\).
- Therefore, the equation for the oxidation state is:
\[ x + 4(-1) = -2 \]
- Simplifying this gives:
\[ x - 4 = -2 \implies x = +2 \]

2. **Identify the electronic configuration of cobalt in the +2 oxidation state:**
- The atomic number of cobalt (Co) is 27.
- The ground state electronic configuration of cobalt is:
\[ [Ar] 3d^7 4s^2 \]
- In the +2 oxidation state, cobalt loses two electrons, which are removed from the 4s orbital first:
\[ Co^{2+}: [Ar] 3d^7 \]

3. **Determine the splitting of d-orbitals in a tetrahedral complex:**
- In a tetrahedral field, the d-orbitals split into two sets: \(t_2\) (lower energy) and \(e\) (higher energy).
- The splitting pattern for tetrahedral complexes is such that \(t_2\) has three orbitals and \(e\) has two orbitals.

4. **Fill the d-orbitals with electrons:**
- Since \([CoCl_4]^{2-}\) is a tetrahedral complex and Cl is a weak field ligand, cobalt will be in a high spin state.
- For \(Co^{2+}\) with \(3d^7\), the electrons will fill as follows:
- The \(t_2\) orbitals will be filled first, followed by the \(e\) orbitals.
- The filling will be: \(t_2^3 e^4\) (3 electrons in \(t_2\) and 4 in \(e\)).

5. **Identify \(n\) and \(m\):**
- From the configuration \(t_2^3 e^4\):
- \(n\) (the number of electrons in the \(e\) orbitals) = 4
- \(m\) (the number of electrons in the \(t_2\) orbitals) = 3

6. **Calculate \(n + m\):**
- Therefore, \(n + m = 4 + 3 = 7\).

### Final Answer:
\[ n + m = 7 \]