Explain why `[Fe(H_(2)O)_(6)]^(3+)` has magnetic moment value of 5.92 BM where as `[Fe(CN)_(6)]^(3-)` has a value of only 1.74 BM ?

Explanation

`{:("As we know", mu_(m)=sqrt(n(n+2))BM),("Where",mu_(m)="magnetic moment"),(,mu_(n)="number of unpaired electrons"),("It",mu_(m)=1.74" i.e., "n=1),("and",mu_(m)=5.92" i.e., "n=5):}`
`[Fe(CN)_(6)]^(3-)` involves `d^(2)sp^(3)` hybridisation with one unpaired electron (as shown by its magnetic moment 1.74 BM) and `[Fe(H_(2)O)_(6)]^(3+)` involves `sp^(3)d^(2)` hybridisation with five unpaired electrons (because magnetic moment equal to 5.92 BM).
`CN^(-)` is stronger ligand than `H_(2)O` according to spectrochemical series. `Delta_(0) gt P` for `CN^(-)` hence, fourth electron will pair itself. whereas for water pairing will not happen for `[Fe(CN)_(6)]^(3-)` the electronic configuration of `Fe^(3+)` is

One unpaired electron
For unpaired electron
For `[Fe(H_(2)O)_(6)]^(3+)` the electronic configuration of `Fe^(3+)` is

Five unpaired electron
Hence, `[Fe(CN)_(6)]^(3-)` and `[Fe(H_(2)O)_(6)]^(3+)` are inner orbital and outer orbital complex respectively.