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Question: According to MO theory which of the list ranks the oxygen species in terms of increasing Bond order ...

According to MO theory which of the list ranks the oxygen species in terms of increasing Bond order 1<1.5<2<2.51 < 1.5 < 2 < 2.5O2,O2+,O2−,O22−{O_2},{O_2}^ + ,{O_2}^ - ,{O_2}^{2 - }

  1. O22−,O2−,O2+O2{O_2}^{2 - },{O_2}^ - ,{O_2}^ + {O_2}
  2. O2+,O2,O2−,O22−{O_2}^ + ,{O_2},{O_2}^ - ,{O_2}^{2 - }
  3. O2,O2+,O2−,O22−{O_2},{O_2}^ + ,{O_2}^ - ,{O_2}^{2 - }
  4. O22−,O2−,O2,O2+{O_2}^{2 - },{O_2}^ - ,{O_2},{O_2}^ +
Explanation

Solution

Different molecules have different bond orders, here to determine the bond order, the formula is used. Stable bonds have a positive bond order. The bond order is used extensively in valence bond theory. An antibonding is when an atomic or molecular orbital whole energy increases as its constituent atoms converge, generating a repulsive force that hinders bonding.

Complete step by step answer:
Molecular orbital theory (MOT) gives an explanation of bonding and to determine the magnetic property of a particular compound. This theory also provides an explanation about the violations of the octet rule. Here, four different species of oxygen are present, having various electrons in them. The bond order can be determined by calculating the difference between the number of electrons in bonding molecular orbital and the number of electrons in antibonding molecular orbital divided by 2. By using the formula:-
Bond order =Number of electrons in Bonding molecular orbital − Number of electron in anti−bonding molecular orbital2\dfrac{{Number{\text{ }}of{\text{ }}electrons{\text{ }}in{\text{ }}Bonding{\text{ }}molecular{\text{ }}orbital{\text{ }}-{\text{ }}Number{\text{ }}of{\text{ }}electron{\text{ }}in{\text{ }}anti - bonding{\text{ }}molecular{\text{ }}orbital}}{2}
i. Bond order for O2{O_2}= 10−62\dfrac{{10 - 6}}{2}= 22
Therefore, the bond order for O2{O_2} is 22
ii. Bond order for O2+{O_2}^ + =10−52\dfrac{{10 - 5}}{2}= 2.52.5
Therefore, the bond order for O2+{O_2}^ + is 2.52.5
iii. Bond order for O2−{O_2}^ - =10−72\dfrac{{10 - 7}}{2}= 1.51.5
Therefore, the bond order for O2−{O_2}^ - = 1.51.5
iv. Bond order for O22−{O_2}^{2 - }=10−82\dfrac{{10 - 8}}{2}= 11
Therefore, the bond order for O22−{O_2}^{2 - }= 11
Hence, 1<1.5<2<2.51 < 1.5 < 2 < 2.5 or O22−<O2−<O2<O2+{O_2}^{2 - } < {O_2}^ - < {O_2} < {O_2}^ + is the increasing order of the bond order.
Thus, option 4) O22−,O2−,O2,O2+{O_2}^{2 - },{O_2}^ - ,{O_2},{O_2}^ + is the correct answer.

Note:
The oxygen molecule does not adhere to all the rules of Lewis theory. The double bonded oxygen O=OO = O is surrounded by eight electrons. The Lewis structure for the oxygen molecule is odd with respect to the magnetic behaviour of oxygen. Oxygen molecules are not magnetic, but they are attracted by magnetic fields.