Identify how many unpaired electrons are present in each of the following in the ground state: \(\mathrm{O}, \mathrm{O}^{+}, \mathrm{O}^{-}, \mathrm{Os}, \mathrm{Zr}, \mathrm{S}, \mathrm{F}, \mathrm{Ar}\).

First, we need to determine the electron configurations for each species in their ground state. To do this, we look at their atomic numbers and fill the orbitals following the Aufbau principle, which states that we fill orbitals from lowest energy to highest energy (1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, and so on). 1. \(\mathrm{O}\): Oxygen has an atomic number of 8, so its electron configuration is \(\mathrm{1s^2 2s^2 2p^4}\). 2. \(\mathrm{O}^+\): The positive charge indicates that one electron has been removed from the neutral oxygen atom. Thus, there are 7 electrons in the configuration, which is \(\mathrm{1s^2 2s^2 2p^3}\). 3. \(\mathrm{O}^{-}\): The negative charge indicates that one electron has been added to the neutral oxygen atom. Thus, there are 9 electrons in the configuration, which is \(\mathrm{1s^2 2s^2 2p^5}\). 4. \(\mathrm{Os}\): Osmium has an atomic number of 76, so its electron configuration is \(\mathrm{[Xe] 6s^2 4f^{14} 5d^6}\). Here, we use the noble gas shorthand to simplify the notation and show that the electron configuration is "complete" up to the previous noble gas in the periodic table, xenon, which has 54 electrons. 5. \(\mathrm{Zr}\): Zirconium has an atomic number of 40, so its electron configuration is \(\mathrm{[Kr] 5s^2 4d^2}\). 6. \(\mathrm{S}\): Sulfur has an atomic number of 16, so its electron configuration is \(\mathrm{1s^2 2s^2 2p^6 3s^2 3p^4}\). 7. \(\mathrm{F}\): Fluorine has an atomic number of 9, so its electron configuration is \(\mathrm{1s^2 2s^2 2p^5}\). 8. \(\mathrm{Ar}\): Argon has an atomic number of 18, so its electron configuration is \(\mathrm{1s^2 2s^2 2p^6 3s^2 3p^6}\).

Next, we need to count the number of unpaired electrons in each species' ground state electron configuration, focusing on the highest energy orbitals. 1. \(\mathrm{O}\): In \(\mathrm{2p^4}\), there are two unpaired electrons since we can have a maximum of two electrons with the same spin in each orbital. 2. \(\mathrm{O}^+\): In \(\mathrm{2p^3}\), there are three unpaired electrons, as the three electrons with the same spin occupy all three orbitals. 3. \(\mathrm{O}^{-}\): In \(\mathrm{2p^5}\), there is only one unpaired electron. 4. \(\mathrm{Os}\): There are six unpaired electrons in \(\mathrm{5d^6}\) orbitals. 5. \(\mathrm{Zr}\): In the electron configuration \(\mathrm{4d^2}\), there are two unpaired electrons. 6. _\(\mathrm{S}\):_ In \(\mathrm{3p^4}\), there are two unpaired electrons. 7. \(\mathrm{F}\): In \(\mathrm{2p^5}\), there is only one unpaired electron. 8. \(\mathrm{Ar}\): In this configuration, all the electrons are paired, so there are 0 unpaired electrons. In conclusion, the number of unpaired electrons in each species in their ground state is as follows: \(\mathrm{O}\) (2), \(\mathrm{O}^+\) (3), \(\mathrm{O}^{-}\) (1), \(\mathrm{Os}\) (6), \(\mathrm{Zr}\) (2), \(\mathrm{S}\) (2), \(\mathrm{F}\) (1), and \(\mathrm{Ar}\) (0).