Step 1: Understanding the Question:
The objective is to determine the Effective Atomic Number (EAN) of the central metal ion, Cobalt, in the given coordination complex [Co(NH$_{3}$)$_{6}$]$^{3+}$.
The EAN represents the total number of electrons surrounding the nucleus of a metal atom in a complex.
Step 2: Key Formula or Approach:
The EAN is calculated using the standard formula:
\[ \text{EAN} = Z - \text{Oxidation State (OS)} + 2 \times (\text{Coordination Number (CN)}) \]
Where \( Z \) is the atomic number of the metal.
Step 3: Detailed Explanation:
1. Atomic Number (\( Z \)): For Cobalt (Co), the atomic number is 27.
2. Oxidation State: Ammine (NH$_{3}$) is a neutral ligand with zero charge.
Let the oxidation state of Co be \( x \).
\[ x + 6(0) = +3 \Rightarrow x = +3 \]
Thus, the oxidation state of Co is +3.
3. Coordination Number: There are 6 monodentate NH$_{3}$ ligands, so the coordination number is 6.
4. Calculation:
\[ \text{EAN} = 27 - 3 + (2 \times 6) \]
\[ \text{EAN} = 24 + 12 \]
\[ \text{EAN} = 36 \]
Step 4: Final Answer:
The EAN of cobalt in this complex is 36, which matches the electronic configuration of the noble gas Krypton.