The coordination number of Th in K4[Th(C2O4)4(H2O)2] is:

🧠 Just a Multiplication

Coordination number = $\sum (\text{ligand count} \times \text{denticity})$. The "10" in the answer is what surprises people — it's an unusual number — but the arithmetic is routine. Thorium happily forms 10-coordinate complexes because it's a large $f$-block atom.

🗺️ Unpack the Sphere

Inside the bracket of $\mathrm{K_4[Th(C_2O_4)_4(H_2O)_2]}$:

• 4 oxalate ($\mathrm{C_2O_4^{2-}}$, bidentate): $4 \times 2 = 8$ donors.
• 2 water (monodentate): $2 \times 1 = 2$ donors.

CN = $8 + 2 = 10$.

⚡ The "Big Atom = Big CN" Heuristic

Lanthanides and actinides routinely show CNs of 8, 9, 10. Whenever you spot a Th, Ce, U, La complex with multiple bidentate ligands, expect double-digit CNs. Don't second-guess yourself when the answer comes out as 10 or 12.

⚠️ The "Ligands ≠ Bonds" Trap

There are 4 + 2 = 6 ligand particles but 10 bonds. CN counts bonds (donor atoms), not ligand particles. Reading "4 oxalates and 2 waters" and writing CN = 6 is the standard error here — students forget to multiply oxalate by 2.

$\boxed{\text{Answer: (4) 10}}$