Step 1: Understanding the Concept:
Effective Atomic Number (EAN) represents the total number of electrons surrounding the nucleus of a metal atom in a complex.
Step 2: Formula Application:
$EAN = Z - ON + 2(CN)$, where $Z$ is atomic number, $ON$ is oxidation number, and $CN$ is coordination number.
Step 3: Explanation:
For Zinc ($Zn$): $Z = 30$.
In $[Zn(NH_3)_4]^{2+}$, ammonia is neutral, so $ON$ of $Zn = +2$.
There are 4 ligands, so $CN = 4$.
$EAN = 30 - 2 + 2(4) = 28 + 8 = 36$.
Step 4: Final Answer:
The EAN of Zn is 36.