Chapter 9, Problem 9.1P

Interpretation Introduction

Interpretation:

The ${\text{Be}}_{\text{2}}$ molecule does not exist under normal conditions.  This has to be explained on the basis of MOT theory.

Concept Introduction:

Molecular orbital theory:

Molecular orbital theory suggests the grouping of all atomic orbitals having comparable energy and proper symmetry.

Postulates of MOT is,

• Atomic orbitals of same energy and proper symmetry combine together to form molecular orbitals.
• The movement of electrons in a molecular orbital is influenced by all the nuclei of combining atoms.
• The number of molecular orbitals formed is equal to the number of combining atomic orbital when two atomic orbitals combine two molecular orbitals are formed.  One molecular orbital has high energy than the corresponding atomic orbitals and is called antibonding orbital and the other one with lower energy is called bonding orbital.
• In molecular orbitals, the electrons are filled according to the Pauli’s exclusion principle, Aufbau principle and the Hund’s rule.

Bond order$\text{=}\frac{\left({\text{N}}_{\text{b}}\right)\text{-}\left({\text{N}}_{\text{a}}\right)}{\text{2}}$

Where, ${\text{N}}_{\text{b}}$ is number of electrons in bonding orbital.

${\text{N}}_{\text{a}}$ is number of electrons in antibonding orbital.

Explanation of Solution

The atomic number of $\text{Be}$ is four.

The electronic configuration of $\text{Be}$=${\text{1s}}^{\text{2}}{\text{2s}}^{\text{2}}$

The molecular electronic configuration of ${\text{Be}}_{\text{2}}$ molecule=${\left(\text{σ1s}\right)}^{\text{2}}{\left({\text{σ}}^{\text{*}}\text{1s}\right)}^{\text{2}}{\left(\text{σ2s}\right)}^{\text{2}}{\left({\text{σ}}^{\text{*}}\text{2s}\right)}^{\text{2}}$

MO diagram of ${\text{Be}}_{\text{2}}$ is,

  Figure 1

The bond order can be calculated as,

  Bond order $\text{=}\frac{\left({\text{N}}_{\text{b}}\right)\text{-}\left({\text{N}}_{\text{a}}\right)}{\text{2}}$

There are four electrons in bonding and antibonding orbitals.

  $\begin{array}{l}\text{Bond order}\text{=}\frac{\left(\text{4}\right)\text{-}\left(\text{4}\right)}{\text{2}}\\ \text{ =0}\end{array}$

The zero bond order refers that the molecule does not exist.