### Solution
#### Part (a): Electronic Configurations
1. O₂ (Dioxygen molecule):
- The atomic number of Oxygen (O) is 8. Therefore, in its neutral molecular form [tex]\(O_2\)[/tex] (with each oxygen atom contributing 8 electrons), the electronic configuration is as follows:
- Electronic Configuration of [tex]\( O_2 \)[/tex]: [tex]\(1s^2 2s^2 2p^4\)[/tex]
2. [tex]\(O_2^{-}\)[/tex] (Superoxide ion):
- The superoxide ion has one extra electron, making the total number of electrons 17 (8 from each oxygen atom plus 1 extra).
- Electronic Configuration of [tex]\( O_2^- \)[/tex]: [tex]\(1s^2 2s^2 2p^5\)[/tex]
3. [tex]\(O_2^{2-}\)[/tex] (Peroxide ion):
- The peroxide ion has two extra electrons, making the total number of electrons 18 (8 from each oxygen atom plus 2 extra).
- Electronic Configuration of [tex]\( O_2^{2-} \)[/tex]: [tex]\(1s^2 2s^2 2p^6\)[/tex]
4. [tex]\(O_2^{+}\)[/tex] (Dioxygen cation):
- The dioxygen cation has one fewer electron, making the total number of electrons 15 (8 from each oxygen atom minus 1).
- Electronic Configuration of [tex]\( O_2^+ \)[/tex]: [tex]\(1s^2 2s^2 2p^3\)[/tex]
#### Part (b): Determining Paramagnetic or Diamagnetic
To determine if a species is paramagnetic or diamagnetic, we need to examine the presence of unpaired electrons in the orbitals.
1. [tex]\(O_2\)[/tex]:
- In [tex]\(O_2\)[/tex], the electrons in the 2p orbital are paired: [tex]\(2p^4\)[/tex].
- Since there are no unpaired electrons in the 2p orbitals, [tex]\(O_2\)[/tex] is diamagnetic.
2. [tex]\(O_2^{-}\)[/tex]:
- In [tex]\(O_2^{-}\)[/tex], the electrons in the 2p orbital configuration are [tex]\(2p^5\)[/tex]; this means there is one unpaired electron.
- The presence of this unpaired electron means [tex]\(O_2^{-}\)[/tex] is paramagnetic.
3. [tex]\(O_2^{2-}\)[/tex]:
- In [tex]\(O_2^{2-}\)[/tex], the electrons in the 2p orbital configuration are [tex]\(2p^6\)[/tex], fully paired.
- Since all the electrons are paired, [tex]\(O_2^{2-}\)[/tex] is diamagnetic.
4. [tex]\(O_2^{+}\)[/tex]:
- In [tex]\(O_2^{+}\)[/tex], the electrons in the 2p orbital configuration are [tex]\(2p^3\)[/tex]; this means there are three unpaired electrons.
- The presence of these unpaired electrons means [tex]\(O_2^{+}\)[/tex] is paramagnetic.
### Summary
- Electronic Configurations:
- [tex]\( O_2 \)[/tex]: [tex]\(1s^2 2s^2 2p^4\)[/tex]
- [tex]\( O_2^{-} \)[/tex]: [tex]\(1s^2 2s^2 2p^5\)[/tex]
- [tex]\( O_2^{2-} \)[/tex]: [tex]\(1s^2 2s^2 2p^6\)[/tex]
- [tex]\( O_2^{+} \)[/tex]: [tex]\(1s^2 2s^2 2p^3\)[/tex]
- Paramagnetic or Diamagnetic:
- [tex]\( O_2 \)[/tex]: diamagnetic
- [tex]\( O_2^{-} \)[/tex]: paramagnetic
- [tex]\( O_2^{2-} \)[/tex]: diamagnetic
- [tex]\( O_2^{+} \)[/tex]: paramagnetic
