Question

According to molecular orbital theory, which of the following is true with respect to \(Li_2^ +\)  and \(Li_2^ -\)?

1. Both are unstable
2. \(Li_2^ + {\rm{\;is\;unstable\;and\;}}Li_2^ - \) is stable
3. \(Li_2^ + {\rm{\;is\;stable\;and\;}}Li_2^ -\) is unstable
4. Both are stable

Answer 1

Correct Answer - Option 4 : Both are stable

Concept:

Molecular orbital (MO) theory is a method for describing the electronic structure of molecules using quantum mechanics. Electrons are not assigned to individual bonds between atoms, but are treated as moving under the influence of the nuclei in the whole molecule. 

The spatial and energetic properties of electrons are described by quantum mechanics as molecular orbitals surround two or more atoms in a molecule and contain valence electrons between atoms

Features of Molecular Orbital Theory:

• Bonding molecular orbital has lower energy and hence greater stability than corresponding antibonding molecular orbital.
• The electron probability distribution around a group of nuclei in a molecule is given by molecular orbital.

Salient features of molecular orbital Theory:

• The electron in a molecule are present in the various molecular orbitals as the electron of atoms are present in the various atom orbitals.
• The electron in molecule are present in the various molecular orbitals as the electron of atom are present in various atomic orbitals.
• Atomic orbitals of comparable energies and proper symmetry combined to form molecular orbital.

Calculation:

According to the molecular Orbital Theory

As we know that,

The electronic configuration of

\(LI_2^ +\) (Z = 5) = σ1s², σ*1s², σ2s¹

Bond Order (BO) = \(\frac{{{N_b} - {N_a}}}{2}\) 

Where N_b is a number of bonding electron

Where N_a is a number of antibonding electron.

Bond order is defined as half the difference between the number of bonding electrons and the number of antibonding electrons.

\(= {\rm{\;}}\frac{{3 - 2}}{2}\) 

\(= \frac{1}{2}\) 

The electronic configuration of

\(LI_2^ -\) (Z = 7) = σ1s², σ*1s², σ2s², σ*2s¹

Bond Order (BO) = \(\frac{{{N_b} - {N_a}}}{2}\)

= \(\frac{{4 - 3}}{2}\)

\(= {\rm{\;}}\frac{1}{2}\)

For both species having the same value of Bond Order, the species having lesser number of antibonding electrons N_a  will be more stable

Both \(LI_2^ +\) and \(LI_2^ - \) has 0.5 bond order and also both are stable