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According to Molecular Orbital Theory, (JEE Adv. 2016)
  • a)
    C22- is expected to be diamagnetic
  • b)
    O22+ is expected to have a longer bond length than O2
  • c)
    N+2 an d N2- have th e same bond or der
  • d)
    He+2 has the same ener gy as two isolated He atoms
Correct answer is option 'A,C'. Can you explain this answer?
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According to Molecular Orbital Theory, (JEE Adv. 2016)a)C22- is expect...
(A) The molecular orbital energy configuration of C22– is
In the MO of C22– there is no unpaired electron hence it is diamagnetic
(B) Bond order of O22+ is 3 and O2 is 2 therefore bond length of O2 is greater than O22+
(C) The molecular orbital energy configuration of N+2 is
Bond order of 
The molecular orbital energy configuration of N2 is
Bond order of 
(D) He+2 has less energy in comparison to two isolated He atoms because some energy is released during the formation of He+2 from 2 He atoms.
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According to Molecular Orbital Theory, (JEE Adv. 2016)a)C22- is expect...
Molecular Orbital Theory and its Applications:

Molecular Orbital Theory (MOT) is a theoretical approach used to describe the nature of chemical bonding in molecules. MOT is based on the concept of overlapping atomic orbitals to form molecular orbitals (MOs).

(a) C22- is expected to be diamagnetic:

- Carbon has six valence electrons (2s2 2p2) and when two carbon atoms combine, they form four molecular orbitals (MOs).
- The two lowest-energy MOs are bonding MOs and the two highest-energy MOs are antibonding MOs.
- When C22- is formed by adding two electrons to the antibonding MO, the total number of electrons becomes 12, which is an even number.
- According to Hund's rule, electrons fill up MOs singly with parallel spins before pairing up. Since all the electrons are paired up in C22-, it is diamagnetic.

(b) O22 is expected to have a longer bond length than O2:

- Oxygen has eight valence electrons (2s2 2p4) and when two oxygen atoms combine, they form eight MOs.
- The two lowest-energy MOs are bonding MOs and the two highest-energy MOs are antibonding MOs.
- In O2, there are two unpaired electrons in the antibonding MO, which results in a shorter bond length.
- However, in O22, the two electrons in the antibonding MO pair up, which results in a longer bond length.

(c) N2 and N2- have the same bond order:

- Nitrogen has seven valence electrons (2s2 2p3) and when two nitrogen atoms combine, they form ten MOs.
- The two lowest-energy MOs are bonding MOs and the two highest-energy MOs are antibonding MOs.
- The bond order is given by the difference between the number of electrons in the bonding MOs and the number of electrons in the antibonding MOs divided by 2.
- For N2, the bond order is (5-2)/2 = 1.5 and for N2-, the bond order is (5-3)/2 = 1.
- Therefore, N2 and N2- have the same bond order.

(d) He2 has the same energy as two isolated He atoms:

- Helium has two valence electrons (1s2) and when two helium atoms combine, they form four MOs.
- The two lowest-energy MOs are bonding MOs and the two highest-energy MOs are antibonding MOs.
- Since there are no unpaired electrons in He2, the energy of He2 is the same as two isolated He atoms.
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