Step 1: Understanding the Concept:
According to Crystal Field Theory (CFT), the energy of absorbed light depends on the field strength of the ligands.
Stronger ligands cause greater splitting ($\Delta_{o}$), requiring higher energy photons for d-d transitions.
Key Formula or Approach:
Energy absorbed $\propto \Delta_{o} \propto$ Strength of the ligand field.
From spectrochemical series: $en$ (ethylenediamine) is a stronger ligand than $H_{2}O$.
Step 2: Detailed Explanation:
Let's look at the ligands in each complex:
(C) $[Ni(en)_{3}]^{2+}$: Has 3 $en$ ligands (strongest field).
(A) $[Ni(H_{2}O)_{2}(en)_{2}]^{2+}$: Has 2 $en$ and 2 $H_{2}O$.
(B) $[Ni(H_{2}O)_{4}(en)]^{2+}$: Has 1 $en$ and 4 $H_{2}O$ (weakest field).
More $en$ ligands mean higher $\Delta_{o}$ and higher absorbed energy.
Order of Energy: (C) > (A) > (B).
Step 3: Final Answer:
The correct order is (C) > (A) > (B). Option (3) is correct.