$[\text{Pt}(\text{NH}_3)_2\text{Cl}_2]$ is a square planar complex of the type $\text{MA}_2\text{B}_2$. It displays geometrical (cis-trans) isomerism:

• Cis-isomer (cisplatin): The two identical chloride ligands (and the two ammine ligands) occupy adjacent positions (at an angle of $90^\circ$). Cisplatin is an effective anti-cancer drug.
• Trans-isomer: The two chloride ligands occupy opposite positions (at an angle of $180^\circ$).
  Because it does not contain ambidentate ligands (no linkage isomerism), has no counter ions (no ionisation isomerism), and has only one coordination sphere (no coordination isomerism), it specifically exhibits geometrical isomerism.

IUPAC naming of $[\text{Co}(\text{NH}_3)_5\text{Cl}]\text{Cl}_2$:

• In the coordination entity, ligands are named in alphabetical order: 'ammine' precedes 'chlorido' $\rightarrow$ pentaamminechlorido.
• The coordination sphere is cationic ($[\text{Co}(\text{NH}_3)_5\text{Cl}]^{2+}$), so the central metal retains its regular English name 'cobalt' (not cobaltate).
• Oxidation state of cobalt: $x + 5(0) + (-1) = +2 \implies x = +3$, written in Roman numerals as (III).
• The ionizable anion is named as 'chloride' (the numerical prefix 'di-' is never used for counter ions).

Electronic configuration and magnetic moment:

• In $[\text{Co}(\text{NH}_3)_5\text{Cl}]\text{Cl}_2$, cobalt is in $+3$ oxidation state: $\text{Co}^{3+} = [\text{Ar}]3d^6$.
• Because the coordination sphere contains predominantly strong-field ammine ($\text{NH}_3$) ligands, crystal field splitting energy $\Delta_o \gt P$ (pairing energy).
• All six $3d$ electrons pair up in the lower $t_{2g}$ orbitals: configuration is $t_{2g}^6 e_g^0$.
• Number of unpaired electrons $n = 0$.
• Spin-only magnetic moment $\mu = \sqrt{n(n+2)} = \sqrt{0(2)} = 0.0\text{ BM}$ (diamagnetic).

Determination of hybridization according to VBT:

• $\text{Co}^{3+}$ has ground-state configuration $3d^6 4s^0 4p^0 4d^0$.
• Under the strong ligand field of ammine ligands, the six $3d$ electrons pair up into three $3d$ orbitals ($t_{2g}^6$).
• This leaves two inner $(n-1)d$ orbitals vacant, along with one $4s$ and three $4p$ orbitals.
• These six orbitals undergo $d^2sp^3$ hybridization to accept six lone pairs of electrons from the five $\text{NH}_3$ ligands and one $\text{Cl}^-$ ligand.
• Therefore, the complex is an inner orbital octahedral complex with $d^2sp^3$ hybridization.