Question
Correct increasing order for the wavelengths of absorption in the visible region for the complexes of $$C{O^{3 + }}$$ is
A.
$${\left[ {Co{{\left( {en} \right)}_3}} \right]^{3 + }},{\left[ {Co{{\left( {N{H_3}} \right)}_6}} \right]^{3 + }},{\left[ {Co{{\left( {{H_2}O} \right)}_6}} \right]^{3 + }}$$
B.
$${\left[ {Co{{\left( {{H_2}O} \right)}_6}} \right]^{3 + }},{\left[ {Co{{\left( {en} \right)}_3}} \right]^{3 + }},{\left[ {Co{{\left( {N{H_3}} \right)}_6}} \right]^{3 + }}$$
C.
$${\left[ {Co{{\left( {{H_2}O} \right)}_6}} \right]^{3 + }},{\left[ {Co{{\left( {N{H_3}} \right)}_6}} \right]^{3 + }},{\left[ {Co{{\left( {en} \right)}_3}} \right]^{3 + }}$$
D.
$${\left[ {Co{{\left( {N{H_3}} \right)}_6}} \right]^{3 + }},{\left[ {Co{{\left( {en} \right)}_3}} \right]^{3 + }},{\left[ {Co{{\left( {{H_2}O} \right)}_6}} \right]^{3 + }}$$
Answer :
$${\left[ {Co{{\left( {en} \right)}_3}} \right]^{3 + }},{\left[ {Co{{\left( {N{H_3}} \right)}_6}} \right]^{3 + }},{\left[ {Co{{\left( {{H_2}O} \right)}_6}} \right]^{3 + }}$$
Solution :
Key concept Wavelength $$\left( \lambda \right)$$ of absorption is inversely proportional to $$CFSE$$ $$\left( {{\vartriangle _o}\,{\text{value}}} \right)$$ of ligands attached with the central metal ion
$${\text{i}}{\text{.e}}{\text{.}}\,\,\lambda \propto \frac{1}{{{\Delta _O}}}$$
According to spectrochemical series.
$${I^ - } < B{r^ - } < {S^{2 - }} < SC{N^ - }$$ $$ < C{l^ - } < {F^ - } < O{H^ - } < {C_2}O_4^{2 - }$$ $$ < {O^{2 - }} < {H_2}O < NS{S^ - } < N{H_3}$$ $$ < en < NO_2^ - < C{N^ - }$$

The $$CFSE$$ of ligands attached with $$C{O^{3 + }}$$ $$ion$$ is in the order $$en > N{H_3} > {H_2}O$$ ( From spectrochemical series )
$$\because $$ Wavelength of absorbed light $$\left( \lambda \right) \propto \frac{1}{{{\vartriangle _o}}}$$
$$\therefore $$ For ligand the order of wavelength of absorption in
the visible region will be : $$en < N{H_3} < {H_2}O$$
$${\text{or,}}{\left[ {Co{{\left( {en} \right)}_3}} \right]^{3 + }} < {\left[ {Co{{\left( {N{H_3}} \right)}_6}} \right]^{3 + }}$$ $$ < {\left[ {Co{{\left( {{H_2}O} \right)}_6}} \right]^{3 + }}$$