Final answer:
The magnetic oxide of cobalt used in recording tapes has the formula Co3O4, as cobalt occupies one-eighth of the tetrahedral and one-half of the octahedral holes, which equates to 3 Co atoms balancing the charge of 4 oxide ions. The correct option is c.
Step-by-step explanation:
The formula of the magnetic oxide of cobalt, used in recording tapes, is determined by considering the positions that the cobalt atoms occupy within the packed array of oxide ion.
In this structure, cobalt atoms fill one-eighth of the tetrahedral holes and one-half of the octahedral holes. Given that each oxide ion has a 2- charge, and the cobalt ions must balance this charge, we can determine the formula as follows:
- In a cubic close-packed structure of oxide ions, there are 8 tetrahedral holes and 4 octahedral holes per formula unit.
- Cobalt atoms occupy one-eighth of tetrahedral holes, so 1 Co atom per oxide unit.
- Cobalt atoms also occupy one-half of the octahedral holes, so 2 Co atoms per oxide unit.
- Combining these, we get 3 Co atoms in total per formula unit.
- Since the oxide ions have a total charge of 6- (3 O2- ions), the cobalt needs to have a charge of 6+ to balance it.
- Divided equally among the 3 cobalt ions, each cobalt ion has a charge of 2+.
Thus, we have 3 cobalt ions with a +2 oxidation state and 4 oxide ions with a -2 oxidation state, resulting in the formula Co3O4, which is cobalt(II,III) oxide. Therefore, the answer is C. Co3O4. The correct option is c.