GATE 2025 CY – Question 49
The UV-visible spectrum of $[\mathrm{Ni(en)_3}]^{2+}$ (en = ethylenediamine) shows absorbance maxima at 11200, 18350, and 29000 $\mathrm{cm^{-1}}$.
| Absorbance maximum | Electronic transition |
|---|---|
| (a) 11200 $\mathrm{cm^{-1}}$ | (i) $^3A_{2g}\to{}^3T_{1g}(F)$ |
| (b) 18350 $\mathrm{cm^{-1}}$ | (ii) $^3A_{2g}\to{}^3T_{2g}$ |
| (c) 29000 $\mathrm{cm^{-1}}$ | (iii) $^3A_{2g}\to{}^3T_{1g}(P)$ |
[Given: Atomic number of Ni = 28] The correct match(es) between absorbance maximum and electronic transition is/are
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Correct answer: (A) (a) → (ii); (B) (b) → (i); (D) (c) → (iii)
Explanation
In an octahedral field, a $d^8$ ion such as Ni(II) has the ground term $^3A_{2g}$. The spin-allowed transitions (triplet to triplet) are, in order of increasing energy:
1. $^3A_{2g}\to{}^3T_{2g}$ (this energy equals $\Delta_o$), the lowest-energy band;
2. $^3A_{2g}\to{}^3T_{1g}(F)$, the middle band;
3. $^3A_{2g}\to{}^3T_{1g}(P)$, the highest-energy band (this one arises from the $^3P$ free-ion term).
**Assign the observed maxima:**
- (a) 11 200 cm⁻¹ (lowest) $\to$ (ii) $^3A_{2g}\to{}^3T_{2g}$
- (b) 18 350 cm⁻¹ $\to$ (i) $^3A_{2g}\to{}^3T_{1g}(F)$
- (c) 29 000 cm⁻¹ (highest) $\to$ (iii) $^3A_{2g}\to{}^3T_{1g}(P)$
So the correct matches are **(a)→(ii), (b)→(i) and (c)→(iii)**, which are options A, B and D.