One the basic of `CFT` predict the geometry of the compund `K_(3)[Mn(CN)_(6)]` Also calculate the value of `mu_(spin)` only of the compund .

Explanation

To solve the problem regarding the compound \( K_3[Mn(CN)_6] \), we will follow these steps:

### Step 1: Calculate the Oxidation State of Manganese
Let the oxidation state of manganese be \( x \). The cyanide ion \( (CN^-) \) has a charge of -1, and since there are 6 cyanide ions, their total contribution is -6. The overall charge of the coordination sphere is -3 due to the presence of 3 potassium ions, each with a +1 charge.

The equation can be set up as follows:
\[
x + 6(-1) = -3
...