Molecular Orbital Theory

To determine which statement is incorrect, let's analyze each option concerning the principles of atomic and quantum theory:

1. Total orbital angular momentum of electron in ‘s’ orbital is equal to zero.
   • In quantum mechanics, the angular momentum of an electron in an orbital is quantified. For an 's' orbital, the orbital angular momentum quantum number, , is 0. The formula for orbital angular momentum is given by \sqrt{l(l+1)}\hbar . For , it becomes 0. Therefore, this statement is correct.
2. The electronic configuration of N atom is:

   

   • Nitrogen (N) has an atomic number of 7. The electronic configuration is: .
   • This image correctly represents the nitrogen atom's electronic arrangement, hence the statement is correct.
3. An orbital is designated by three quantum numbers while an electron in an atom is designated by four quantum numbers.
   • An orbital is indeed specified by three quantum numbers: principal ( ), azimuthal ( ), and magnetic ( ).
   • An electron is described by these three plus the spin quantum number ( ), totaling four. Thus, this statement is correct.
4. The value of m for d_z2 is zero.
   • For a d-orbital, the magnetic quantum number ( ) can have values ranging from to . Generally, for the orbital, the value is taken as 0.
   • Thus, this statement seems correct; however, interpretation depends on the context within different quantum mechanical models.

Considering the context and conventional interpretations, the options may vary in understanding. However, given typical textbook discussions, "The value of m for d_z2 is zero" is correct as per the context often encountered in chemistry educational materials. Therefore, no statement is wrong upon refining the context. But adhering strictly to quantum mechanical definitions for angular momentum distribution, if misunderstood, might lead to this being identified, although it's broadly validated in its context within quantum chemistry pedagogy.

The question requires us to determine which diatomic molecular species have only pi bonds according to Molecular Orbital Theory. The options given are: , , , . Let's analyze each molecule based on Molecular Orbital Theory.

Molecular Orbital (MO) Configuration:

• : The electron configuration is . Here, there are both sigma and pi bonds.
• : The electron configuration is . This molecule consists of a strong triple bond (one sigma and two pi bonds).
• : The electron configuration is . There are only pi bonds according to its MO configuration, since the sigma bond from \sigma_{2p_z} is not populated.
• : The electron configuration is . It has only one pi bond.

Conclusion:

Among the given options, is the only molecule that, according to Molecular Orbital Theory, has only pi bonds. It lacks a sigma bond in the \sigma_{2p_z} orbital, which is unoccupied.