The correct order of the wavelength of light absorbed by the following complexes is,

A.  $[\mathrm{Co}{\left(\mathrm{NH}\mathrm{₃}\right)}_6{]}^{\mathrm{3+}}$

B.  $[\mathrm{Co}{\left(\mathrm{CN}\right)}_6{]}^{\mathrm{3-}}$

C.  $[\mathrm{Cu}{\left(H\mathrm{₂}O\right)}_4{]}^{\mathrm{2+}}$

D.  $[\mathrm{Ti}{\left(H\mathrm{₂}O\right)}_6{]}^{\mathrm{3+}}$

Choose the correct answer from the options given below.

The four complexes are:

A: $[\mathrm{Co}{\left(\mathrm{NH}3\right)}_6{]}^{\mathrm{3+}}$

B: $[\mathrm{Co}{\left(\mathrm{CN}\right)}_6{]}^{\mathrm{3‑}}$

C: $[\mathrm{Cu}{\left(H2O\right)}_4{]}^{\mathrm{2+}}$

D: $[\mathrm{Ti}{\left(H2O\right)}_6{]}^{\mathrm{3+}}$

To compare the wavelengths of light each complex absorbs we look at the crystal‑field splitting energy ($\Delta$_oct). A larger $\Delta$_oct means the complex absorbs higher‑energy (shorter‑wavelength) light, because the energy of the absorbed photon equals the splitting: $E\; =\; h\nu \; =\; hc/\lambda \; =\; \Delta$_oct.

Two main factors govern $\Delta$_oct:

1. **Ligand field strength** – given by the spectrochemical series. Strong‑field ligands (e.g., $CN⁻$) produce a larger $\Delta$ than medium‑field ligands (e.g., $NH₃$), which in turn produce a larger $\Delta$ than weak‑field ligands (e.g., $H₂O$).

2. **Metal oxidation state and identity** – a higher oxidation state increases the metal‑ligand electrostatic attraction, raising $\Delta$. Among different metal ions, a 3+ ion generally gives a larger splitting than a 2+ ion of similar size.

Applying these rules:

• B ([Co(CN)₆]³⁻) contains the strongest field ligand $CN⁻$. Hence it has the largest $\Delta$ and therefore absorbs the shortest wavelength.
• A ([Co(NH₃)₆]³⁺) has a medium‑field ligand $NH₃$. Its $\Delta$ is smaller than that of B but larger than complexes with only $H₂O$ ligands.
• D ([Ti(H₂O)₆]³⁺) uses the weak‑field ligand $H₂O$, but the metal is Ti³⁺, a 3+ ion. The higher oxidation state partially compensates for the weak ligand, giving a $\Delta$ that is larger than that of Cu²⁺ (complex C) but still smaller than the medium‑field Co³⁺ complex A.
• C ([Cu(H₂O)₄]²⁺) also has $H₂O$ as the ligand, but the metal is Cu²⁺, a 2+ ion. The lower oxidation state results in the smallest crystal‑field splitting of the four, so it absorbs the longest wavelength.

Thus the order of increasing crystal‑field splitting (and consequently decreasing wavelength) is:

$\Delta \_B\; >\; \Delta \_A\; >\; \Delta \_D\; >\; \Delta \_C$

Since wavelength is inversely related to $\Delta$, the wavelength order is the reverse:

Therefore the correct ordering of the wavelength of light absorbed by the complexes is:

B < A < D < C