The number of bonds between sulphur and oxygen atoms in S$$_2$$O$$_8^{2-}$$ and the number of bonds between sulphur and sulphur atoms in rhombic sulphur, respectively are:

First, let us consider the peroxodisulphate ion, whose formula is $$\mathrm{S_2O_8^{2-}}$$. The name itself tells us that two sulphur atoms are present and the total number of oxygen atoms is eight.

Each sulphur atom in $$\mathrm{S_2O_8^{2-}}$$ is in the $$+6$$ oxidation state. When sulphur shows $$+6$$ oxidation state, its usual geometry is tetrahedral, meaning every sulphur is bonded to four oxygen atoms.

To write its actual structure we start with two separate $$\mathrm{SO_4^{2-}}$$ units and then join them through a peroxide ($$\mathrm{-O-O-}$$) bridge. Symbolically, the structure may be written as

$$\mathrm{O_3S-O-O-SO_3^{2-}}$$

Reading the formula from left to right we see:

• The left sulphur is bonded to two terminal doubly-bonded oxygens ($$\mathrm{S\!=\!O}$$) and to one oxygen of the $$\mathrm{-O-O-}$$ bridge by a single bond.
• Analogously, the right sulphur is also bonded to two terminal $$\mathrm{S\!=\!O}$$ oxygens and to the second oxygen of the $$\mathrm{-O-O-}$$ bridge.

Because each sulphur is attached to exactly four oxygens, the total number of sulphur-oxygen bonds is obtained by simple multiplication:

$$\text{Number of S-O bonds} \;=\; (4\;\text{bonds per S}) \times (2\;\text{S atoms}) \;=\; 8.$$

Hence, in $$\mathrm{S_2O_8^{2-}}$$ there are eight $$\mathrm{S-O}$$ bonds.

Now we examine rhombic sulphur. Rhombic sulphur consists of puckered eight-membered rings, each written as $$\mathrm{S_8}$$. In this ring every sulphur atom is bonded to its two neighbouring sulphur atoms by single covalent bonds, so each sulphur contributes two $$\mathrm{S-S}$$ bonds. Because the ring is closed, the total number of S-S bonds in one $$\mathrm{S_8}$$ molecule is equal to the number of atoms:

$$\text{Number of S-S bonds in } \mathrm{S_8} \;=\; 8.$$

Combining both results we obtain:

$$\begin{aligned} \text{S-O bonds in }\mathrm{S_2O_8^{2-}} &= 8,\\ \text{S-S bonds in rhombic sulphur} &= 8. \end{aligned}$$

These counts correspond to Option B, which states “8 and 8”.

Hence, the correct answer is Option B.