Step 1: Understanding the concept of effective atomic number.
The effective atomic number (EAN) is the total number of electrons surrounding the metal ion. In \([Zn(NH_3)_4]SO_4\), the Zn\(^{2+}\) ion is surrounded by four NH\(_3\) molecules. Each NH\(_3\) donates 2 electrons, and the Zn\(^{2+}\) ion contributes 2 electrons. The total effective atomic number is:
\[
EAN = 30 (\text{Zn electrons}) + 4 \times 2 (\text{electrons from NH}_3) = 36
\]
Step 2: Conclusion.
The effective atomic number of Zn is 36.