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Subjective

Why are different colours observed in octahedral and tetrahedral complexes for the same metal and same ligands?

Explanation

Extent of splitting of $d$-orbitals is different in octahedral and tetrahedral field. CFSE in octahedral and tetra federal field are closely related as.

$$\Delta_t=\left(\frac{4}{9}\right) \Delta_o$$

where, $\quad \Delta_t=$ crystal field splitting energy in tetrahedral field

$\Delta_0=$ crystal field splitting energy in octahedral field

Wavelength of light and CFSE are related to each other by formula

$$\begin{aligned} \Delta_0=E & =\frac{h c}{\lambda} \\ E & \propto \frac{1}{\lambda} \end{aligned}$$

So, higher wavelength of light is absorbed in octahedral complexes than tetrahedral complexes for same metal and ligands. Thus, different colours are observed.