1. Goal: Count how many given species have pyramidal geometry around the central atom.

The species are: $\mathrm{S}_2\mathrm{O}_3^{2-},\ \mathrm{SO}_4^{2-},\ \mathrm{SO}_3^{2-},\ \mathrm{S}_2\mathrm{O}_7^{2-}$

We examine the geometry around sulfur in each case using VSEPR.

2. Analyze $\mathbf{SO_4^{2-}}$

In sulfate ion, sulfur is bonded to four oxygen atoms and has no lone pair on sulfur.

So the steric number is 4: $AX_4$ Hence geometry is tetrahedral, not pyramidal.

So, $\mathrm{SO}_4^{2-}$ is not pyramidal.

3. Analyze $\mathbf{SO_3^{2-}}$

In sulfite ion, sulfur is bonded to three oxygen atoms and has one lone pair on sulfur.

So the steric number is 4: $AX_3E$ Electron pair geometry is tetrahedral, and molecular geometry is trigonal pyramidal.

So, $\mathrm{SO}_3^{2-}$ is pyramidal.

4. Analyze $\mathbf{S_2O_3^{2-}}$

This is thiosulfate ion. Its structure can be viewed as one sulfur atom at the center bonded to:

• three oxygen atoms
• one terminal sulfur atom

Thus the central sulfur has four sigma bonds and no lone pair.

So its geometry is: $AX_4$ which is tetrahedral, not pyramidal.

The terminal sulfur is not pyramidal either.

So, $\mathrm{S}_2\mathrm{O}_3^{2-}$ is not pyramidal around the central atom.

5. Analyze $\mathbf{S_2O_7^{2-}}$

This is pyrosulfate ion, having structure: $\mathrm{O}_3\mathrm{S}-\mathrm{O}-\mathrm{SO}_3^{2-}$ Each sulfur is bonded to four oxygen atoms (including the bridging oxygen), with no lone pair on sulfur.

Thus each sulfur is: $AX_4$ So geometry around each sulfur is tetrahedral, not pyramidal.

Hence, $\mathrm{S}_2\mathrm{O}_7^{2-}$ is not pyramidal around the central sulfur atoms.

6. Count pyramidal species

Only: $\mathrm{SO}_3^{2-}$ shows pyramidal geometry.

Therefore, the number of such species is: $\boxed{1}$

7. Option matching

Option D corresponds to: $\boxed{1}$

So the correct option is D.