To solve this problem, we need to determine the number of electrons in the t2g-orbitals for the product of the reaction between [Co(H2O)6]2+ and excess ammonia in the presence of oxygen, resulting in a diamagnetic product.
Start by considering the initial complex [Co(H2O)6]2+. Here, cobalt is in the +2 oxidation state, leading to a d7 electron configuration for Co2+ since cobalt's atomic number is 27 (resulting in an electron configuration of [Ar] 3d7 4s2 for the neutral atom, minus two electrons for the Co2+ ion).
In the reaction, excess ammonia acts as a ligand, forming a more stable complex. Ammonia is a strong field ligand due to its ability to cause pairing of electrons in the d orbitals. The oxidation of Co2+ in the presence of oxygen will form Co3+, resulting in the electron configuration d6 for the cobalt ion in this state.
Since the produced compound is diamagnetic, all electrons must be paired according to Hund's rule and ligand field theory. The Co3+ ion in an octahedral field, influenced by strong field ammonia ligands, will have a low spin configuration:
d6 results in the distribution of electrons as t2g6eg0, with all six electrons paired in the lower energy t2g orbitals.
Thus, the number of electrons in the t2g orbitals is 6.
This value of 6 falls within the expected range of 6 to 6, confirming the solution's correctness.