1. Magnetic Moment (spin-only formula): $\mu = \sqrt{n(n+2)}\text{ BM}$ where n = number of unpaired electrons; BM = Bohr Magneton.

2. Crystal Field Splitting Relationship: $\Delta_t = \frac{4}{9}\Delta_o$

3. Charge/Oxidation State in a Complex: $\text{charge of complex} = \text{OS of metal} + \sum(\text{charges of ligands})$

Example: In [Co($NH_{3}$)_{4}$Cl_{2}$]^{+}, charge = OS(Co) + 4(0) + 2(−1) = +1, so OS(Co) = +3.

4. Crystal Field Stabilisation Energy (CFSE) — Octahedral: $\text{CFSE} = -0.4\Delta_o \times (\text{electrons in } t_{2g}) + 0.6\Delta_o \times (\text{electrons in } e_g)$

Example: $d^{3}$ low spin: 3 electrons in t_{2}g → CFSE = −3 × 0.4$\Delta o$ = −1.2$\Delta o$

5. Pairing Energy Decision Rule:

• If $\Delta_o > P$: pairing occurs → low spin (strong field ligand)
• If $\Delta_o < P$: no pairing → high spin (weak field ligand)

6. Number of d–d transitions possible: Equal to the number of spectroscopic terms, but for NEET: if d-subshell is empty ($d^{0}$) or full ($d^{10}$), no d–d transition → colourless.

7. Equivalent conductance / ionisation test: $[\text{Co(NH}_3)_5\text{Br}]\text{SO}_4 \rightarrow [\text{Co(NH}_3)_5\text{Br}]^{2+} + \text{SO}_4^{2-}$ Two ions in solution → behaves as 1:1 electrolyte equivalent of a 2-ion salt.