An atom a possesses 30 massive, positively charged particles, and the atom b possesses 8 massive, positively charged particles. What are the identities of a and b?

We gots $Z = 30$, i.e. $a = Z n$, and $Z = 8$, i.e. $b = O$.
The element is characterized by its $\text{atomic number, Z}$, where $Z$ is the number of nuclear protons, which are massive, positively charged particles. Now we were given the number of electrons for each element, however, for the neutral element, AND THIS WE MUST ASSUME given the problem, if there are 30, and 8 electrons respectively, we must have $Z = 30$, and $Z = 8$ for the reason of electrical neutrality.
Of course, oxygen is usually present as the diatomic gas, ${O}_{2}$, but there is no ambiguity in the question.