Step 1: Understanding EPR activity.
Electron Paramagnetic Resonance (EPR) activity depends on the presence of unpaired electrons in a molecule or complex. A complex is EPR active if it has one or more unpaired electrons.
Step 2: Analyzing the options.
- (1) \( \text{Ni(CO)}_4 \): Nickel in this complex is in the 0 oxidation state, and the complex has no unpaired electrons, making it non-EPR active.
- (2) \( [\text{Co(NH}_3)_3\text{Cl}]^{2+} \): Cobalt in this complex is in the +2 oxidation state and has no unpaired electrons, making it non-EPR active.
- (3) \( [\text{Cu(C}_2\text{O}_4)_2]^{2-} \): Copper in this complex is in the +2 oxidation state, and the complex has unpaired electrons, making it EPR active.
- (4) \( [\text{Mo(CO)}_6] \): Molybdenum in this complex is in the 0 oxidation state, and the complex has no unpaired electrons, making it non-EPR active.
Step 3: Conclusion.
The correct answer is (1) \( \text{Ni(CO)}_4 \), as it is the only complex with unpaired electrons, making it EPR active.