Determining Cobalt Oxidation State and Configuration

First, we find the oxidation state of the cobalt ion ($Co$) in each complex:

• For $[Co(H_2O)_6]^{2+}$: Water ($H_2O$) is a neutral ligand. Therefore, the cobalt ion must have a +2 charge ($Co^{2+}$).
• For $[CoCl_4]^{2-}$: Chloride ($Cl^-$) has a charge of -1. Let the charge on cobalt be $x$. Then, $x + 4(-1) = -2$, which means $x = +2$. The cobalt ion is $Co^{2+}$.

The atomic number of Cobalt (Co) is 27, with an electronic configuration of $[Ar] 3d^7 4s^2$. The $Co^{2+}$ ion has a $3d^7$ electron configuration.

Identifying Complex Geometry and Ligand Field

The geometry and ligand type determine how the $d$ orbitals split and influence the term symbols:

• $[Co(H_2O)_6]^{2+}$: This complex has octahedral geometry ($O_h$). Water is a weak field ligand, leading to a high-spin configuration for $d^7$.
• $[CoCl_4]^{2-}$: This complex has tetrahedral geometry ($T_d$). Tetrahedral complexes are always high-spin.

Deriving Ground State Term Symbols

We use the electron configuration ($d^7$) and the geometry to find the spectroscopic ground state term symbols. These are standard results often determined using Tanabe-Sugano diagrams:

• For a $d^7$ configuration in an octahedral ($O_h$) field, the ground state term symbol is $^4T_{1g}$.
• For a $d^7$ configuration in a tetrahedral ($T_d$) field, the ground state term symbol is $^4A_2$.

Therefore, the spectroscopic ground state term symbols for $[Co(H_2O)_6]^{2+}$ and $[CoCl_4]^{2-}$ are $^4T_{1g}$ and $^4A_2$, respectively.