The number of bridging CO ligand(s) and Co-Co bond(s) in $$Co_2(CO)_8$$, respectively are:

We begin by recalling that $$Co_2(CO)_8$$ is a dinuclear metal carbonyl of cobalt in the zero-oxidation state. Such compounds normally try to let every metal centre attain the very stable $$18$$-electron configuration.

First let us calculate the valence-electron requirement for one cobalt atom. In the elemental state cobalt is $$[Ar]\,3d^7 4s^2$$, so a neutral $$Co(0)$$ contributes $$9$$ valence electrons. To reach $$18$$ electrons it therefore still needs $$18-9 = 9$$ electrons supplied through coordination.

Now consider the carbonyl ligands. A terminal $$CO$$ donates a pair (that is, $$2$$) of electrons to the metal centre, whereas a $$\mu\text{-}CO$$ (bridging CO) donates only one electron to each of the two metals it bridges, because the same electron pair is shared between the two metal atoms.

The solid-state structure of $$Co_2(CO)_8$$ determined by X-ray diffraction shows exactly two $$\mu\text{-}CO$$ ligands. The remaining six carbonyls are terminal. We therefore distribute the ligands as follows:

• On each cobalt there are three terminal $$CO$$ groups.
• Both cobalts together share the two bridging $$CO$$ groups (each bridge counts once for each Co).

Let us now perform the electron count for one cobalt atom.

From the metal itself: $$9$$ electrons.

From the three terminal $$CO$$ ligands: each gives $$2$$ electrons, so $$3 \times 2 = 6$$ electrons.

From the two bridging $$CO$$ ligands: each gives $$1$$ electron, so $$2 \times 1 = 2$$ electrons.

So far the cobalt has $$9 + 6 + 2 = 17$$ electrons; it is still one electron short of the desired $$18$$.

To supply this last electron, a direct metal-metal bond is formed between the two cobalt atoms. In a single $$Co{-}Co$$ bond the two metals share a pair of electrons, each metal effectively receiving one additional electron.

After adding this contribution the electron count becomes $$17 + 1 = 18$$, satisfying the $$18$$-electron rule for each cobalt centre. The need to reach this count is exactly what forces the existence of a single $$Co{-}Co$$ bond in the molecule.

Summarising the structural features we have just derived:

• Number of bridging $$CO$$ ligands $$(\mu\text{-}CO) = 2.$$

• Number of $$Co{-}Co$$ bonds = 1.

Turning to the options given in the problem, the pair “2 and 1” appears as Option A.

Hence, the correct answer is Option A.