1. Identify the metal ion and geometry

All three complexes contain $Ni^{2+}$.

$Ni^{2+} : [Ar]3d^8$

Given ligands $en$, $NH_3$, and $H_2O$, these are all typical octahedral complexes:

• $A = [Ni(en)_3]^{2+}$
• $B = [Ni(NH_3)_6]^{2+}$
• $C = [Ni(H_2O)_6]^{2+}$

For octahedral complexes, the energy of absorption corresponds to the crystal field splitting energy, $\Delta_o$.

Thus, larger $\Delta_o$ means higher energy absorbed.

2. Use the spectrochemical series

The relevant ligand field strengths are:

$H_2O < NH_3 < en$

So the crystal field splitting follows:

$\Delta_o([Ni(H_2O)_6]^{2+}) < \Delta_o([Ni(NH_3)_6]^{2+}) < \Delta_o([Ni(en)_3]^{2+})$

That is,

$C < B < A$

3. Relate splitting to absorption energy

Since absorption energy is directly proportional to $\Delta_o$,

$E_{abs} \propto \Delta_o$

Hence the order of energy of absorption is:

$C < B < A$

4. Check options

• Option A: $C < B < A$ ✅
• Option B: $B < C < A$ ❌
• Option C: $C < A < B$ ❌
• Option D: $A < C < B$ ❌

Therefore, the correct option is A.