Count Number of Chemical Species with sp3 Hybridised Central Atom

To determine the total number of chemical species in which the central atom is $sp^3$ hybridised, we analyze the steric number (or hybridization state) for each given species:

1. $[\text{I}_3]^+$:

   • Central atom: Iodine ($\text{I}$)
   • Valence electrons on central $\text{I}^+ = 7 - 1 = 6$
   • Number of $\sigma$-bonds (with two terminal $\text{I}$ atoms) $= 2$
   • Number of lone pairs $= \frac{6 - 2}{2} = 2$
   • Steric Number $= 2 + 2 = 4 \implies \mathbf{sp^3}$ hybridised.

2. $[\text{SiO}_4]^{4-}$:

   • Central atom: Silicon ($\text{Si}$)
   • Valence electrons $= 4 + 4 = 8$
   • Number of $\sigma$-bonds $= 4$ (with four $\text{O}^-$ ions)
   • Number of lone pairs $= 0$
   • Steric Number $= 4 + 0 = 4 \implies \mathbf{sp^3}$ hybridised.

3. $\text{SO}_2\text{Cl}_2$:

   • Central atom: Sulfur ($\text{S}$)
   • Valence electrons $= 6$
   • Number of $\sigma$-bonds $= 2\ (\text{with O}) + 2\ (\text{with Cl}) = 4$
   • Number of lone pairs $= 0$
   • Steric Number $= 4 + 0 = 4 \implies \mathbf{sp^3}$ hybridised.

4. $\text{XeF}_2$:

   • Central atom: Xenon ($\text{Xe}$)
   • Number of $\sigma$-bonds $= 2$
   • Number of lone pairs $= \frac{8 - 2}{2} = 3$
   • Steric Number $= 2 + 3 = 5 \implies sp^3d$ hybridised.

5. $\text{SF}_4$:

   • Central atom: Sulfur ($\text{S}$)
   • Number of $\sigma$-bonds $= 4$
   • Number of lone pairs $= \frac{6 - 4}{2} = 1$
   • Steric Number $= 4 + 1 = 5 \implies sp^3d$ hybridised.

6. $\text{ClF}_3$:

   • Central atom: Chlorine ($\text{Cl}$)
   • Number of $\sigma$-bonds $= 3$
   • Number of lone pairs $= \frac{7 - 3}{2} = 2$
   • Steric Number $= 3 + 2 = 5 \implies sp^3d$ hybridised.

7. $\text{Ni(CO)}_4$:

   • Central atom: Nickel ($\text{Ni}$)
   • Ground state electronic configuration of $\text{Ni}(0) = [\text{Ar}] 3d^8 4s^2$
   • In the presence of strong field carbonyl ligands ($\text{CO}$), pairing occurs: $3d^8 4s^2 \rightarrow 3d^{10} 4s^0 4p^0$
   • The empty $4s$ and three $4p$ orbitals hybridise to give $\mathbf{sp^3}$ hybridisation.

8. $\text{XeO}_2\text{F}_2$:

   • Central atom: Xenon ($\text{Xe}$)
   • Number of $\sigma$-bonds $= 2\ (\text{with O}) + 2\ (\text{with F}) = 4$
   • Number of lone pairs $= \frac{8 - 6}{2} = 1$
   • Steric Number $= 4 + 1 = 5 \implies sp^3d$ hybridised.

9. $[\text{PtCl}_4]^{2-}$:

   • Central atom: Platinum ($\text{Pt}^{2+}$, a $5d^8$ metal ion)
   • Complexes of $5d^8$ transition metal ions with 4 ligands always form square planar geometry.
   • Hybridisation $= dsp^2$.

10. $\text{XeF}_4$:

    • Central atom: Xenon ($\text{Xe}$)
    • Number of $\sigma$-bonds $= 4$
    • Number of lone pairs $= \frac{8 - 4}{2} = 2$
    • Steric Number $= 4 + 2 = 6 \implies sp^3d^2$ hybridised.

11. $\text{SOCl}_2$:

    • Central atom: Sulfur ($\text{S}$)
    • Number of $\sigma$-bonds $= 1\ (\text{with O}) + 2\ (\text{with Cl}) = 3$
    • Number of lone pairs $= \frac{6 - 4}{2} = 1$
    • Steric Number $= 3 + 1 = 4 \implies \mathbf{sp^3}$ hybridised.

The species having an $sp^3$ hybridised central atom are: $[\text{I}_3]^+$, $[\text{SiO}_4]^{4-}$, $\text{SO}_2\text{Cl}_2$, $\text{Ni(CO)}_4$, and $\text{SOCl}_2$.

Thus, the total number of such species is 5.