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Electron affinity is the energy change that occurs when an electron is added to a gaseous atom. It represents the amount of energy released (exothermic) or absorbed (endothermic) when an electron is added to an isolated atom in the gas phase to form a negative ion.

The factors that affect electron affinity include atomic size, nuclear charge, and electron-electron repulsion in the atom's electron cloud. Generally, electron affinity increases from left to right across a period and decreases from top to bottom within a group in the periodic table.

To analyze the electron affinity of oxygen and sulfur, we need to determine their electron configurations. Oxygen has an atomic number of 8, and its electron configuration is \(1s^{2}\,2s^{2}\,2p^{4}\). Sulfur has an atomic number of 16, and its electron configuration is \(1s^{2}\,2s^{2}\,2p^{6}\,3s^{2}\,3p^{4}\).

When an electron is added to oxygen to form an O^(-) ion, it will have the electron configuration \(1s^{2}\,2s^{2}\,2p^{5}\). The added electron goes to the same energy level (second principal energy level) and occupies one of the available p-orbitals. Since the added electron is relatively closer to the nucleus, the energy change will result in the release of energy (exothermic process). However, when another electron is added to form O^(2-), the electron configuration becomes \(1s^{2}\,2s^{2}\,2p^{6}\). In this case, both the 2p subshell and the second principal energy level are completely filled. The incoming electron will experience strong electron-electron repulsion, which requires energy to overcome, making the process endothermic (unfavorable). Similarly, for sulfur, adding an electron to form S^(-) ion, the electron configuration becomes \(1s^{2}\,2s^{2}\,2p^{6}\,3s^{2}\,3p^{5}\). In this case, the process is exothermic as the added electron goes to the third principal energy level (3p subshell). However, when another electron is added to form S^(2-), it will have the electron configuration \(1s^{2}\,2s^{2}\,2p^{6}\,3s^{2}\,3p^{6}\). The electron-electron repulsion from the completely filled 3p subshell will make the process endothermic (unfavorable).

In summary, the second electron affinities of both oxygen and sulfur are unfavorable (endothermic) because of the strong electron-electron repulsion in the completely filled subshells (2p for oxygen and 3p for sulfur). The energy required to overcome this repulsion results in an absorption of energy, making the processes unfavorable.