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Why [FeF6]3– is colourless whereas [CoF6]3– is coloured ? 

[FeF6]3- is a Fe (III) complex hence [Ar] 3d5. F- is a weak field ligand and the complex is high spin: 
                                     t2g (↑) (↑)(↑)   →Δoct     (↑)(↑)eg.


And there is 5 unpaired electrons hence it's spin multiplicity = (2S+1) = 6  , and multiplicity of  a excited is cannot be six thus The transitions in Fe +3 ion are spin forbidden and are extremely weak so as to make [FeF6]3- almost colorless.
[CoF6] 3- this is a Co (III) complex [Ar] 3d6. Again F- is a weak field ligand and [CoF6]3- is one of only two common cmplxs that is high spin:

                       t2g (↑↓) (↑)(↑)     →Δoct      (↑)(↑) eg

Only one band is expected namely the t2g→eg transition (d1). The complex is blue consistent with this transition being in the low energy red. 

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