The bond in peroxide ion and fluorine molecule is equal because

all of these

The correct answer is option 4. all of these.

Let us explain why the bond in the peroxide ion \((O_2^{2-})\) and the fluorine molecule \((F_2)\) can be considered equal based on the options provided:

1. These are isoelectronic:

Isoelectronic species have the same number of total electrons. The peroxide ion (O₂²⁻) has 18 electrons: each oxygen atom has 8 electrons (total 16), plus 2 extra electrons due to the 2- charge. The fluorine molecule (F₂) also has 18 electrons: each fluorine atom has 9 electrons (total 18). Therefore, the peroxide ion and the fluorine molecule are isoelectronic, meaning they have the same number of electrons and similar electron configurations, which often leads to similar chemical properties.

2. Their bond energies are nearly equal:

Bond energy refers to the amount of energy required to break one mole of bonds in a molecule. The O-O bond energy in the peroxide ion is approximately 146 kJ/mol, and the F-F bond energy in the fluorine molecule is approximately 158 kJ/mol. These values are close enough to be considered nearly equal, indicating that the strength of the bonds is similar.

3. Their bond lengths are nearly equal:

Bond length is the distance between the nuclei of two bonded atoms. The bond length of the O-O bond in the peroxide ion is around 149 pm (picometers), and the bond length of the F-F bond in the fluorine molecule is around 142 pm. These bond lengths are also quite close, indicating that the size of the bond is similar.

Given these explanations, we can see that:

Isoelectronic nature (same number of electrons): This suggests they have similar electron distribution and bonding characteristics.

Similar bond energies: This indicates that the energy required to break the bonds is nearly the same, implying similar bond strength.

Similar bond lengths: This suggests that the spatial arrangement of the atoms in each molecule is similar.

Thus, all these points contribute to the idea that the bond in the peroxide ion and the fluorine molecule is "equal" or similar in nature. Therefore, the correct answer, taking all the points into consideration, is (4) all of these.