Correct increasing order for the wavelengths of absorption in the visible region for the complexes of $Co^{3+}

Question

Correct increasing order for the wavelengths of absorption in the visible region for the complexes of $Co^{3+}$ is:

Accepted Answer

1.  **Relation between Energy and Wavelength:** The energy of the light absorbed corresponds to the crystal field splitting energy ($\Delta_o$). According to the Planck equation, energy ($E$) is inversely proportional to wavelength ($\lambda$): $E = hc/\lambda$. Therefore, a higher splitting energy results in the absorption of a shorter wavelength .
2.  **Spectrochemical Series:** The magnitude of the crystal field splitting energy ($\Delta_o$) depends on the field strength of the ligands. The spectrochemical series arranges ligands in order of increasing field strength. From the series provided in the text: $H_2O < NH_3 < en$ .
3.  **Order of $\Delta_o$:** Based on ligand strength, the crystal field splitting energy for the $Co^{3+}$ complexes follows the order: 
    $[Co(H_2O)_6]^{3+} < [Co(NH_3)_6]^{3+} < [Co(en)_3]^{3+}$
4.  **Order of Wavelength ($\lambda$):** Since wavelength is inversely proportional to energy, the order of absorbed wavelengths will be the reverse of the energy order:
    $[Co(en)_3]^{3+}$ (strongest field, highest energy, shortest $\lambda$) < $[Co(NH_3)_6]^{3+}$ < $[Co(H_2O)_6]^{3+}$ (weakest field, lowest energy, longest $\lambda$).

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