Chapter 9, Problem 9A.3E

Interpretation Introduction

Interpretation:

The valence bond wavefunction for the one sigma and two pi bonds in a nitrogen molecule has to be written.

Concept Introduction:

In molecular hydrogen $\text{H-H}$, the two ground-state H atoms are far apart, electron 1 is

in ${\text{ψ}}_{\text{A}}$, the $\text{1s}$ orbital of atom A, denoted ${\text{ψ}}_{\text{A}}(1)$ , and electron 2 is in ${\text{ψ}}_{\text{B}}$, the $\text{1s}$ orbital of atom B, denoted ${\text{ψ}}_{\text{B}}\text{(2)}$.  The wavefunction for the two-electron system can be written as $\text{ψ(1,2)}\text{=}{\text{ψ}}_{\text{A}}\text{(1)}{\text{ψ}}_{\text{A}}\text{(2)}$.  An equally likely arrangement is for electron 1 to escape from A and be found on B and for electron 2 to be on A and the wave function is $\text{ψ(1,2)}\text{=}{\text{ψ}}_{\text{A}}\text{(2)}{\text{ψ}}_{\text{A}}\text{(1)}$.  According to quantum mechanics, the addition of two wave functions gives,

    ${\text{ψ}}_{\text{H-H}}\text{(1,2)}\text{=}{\text{ψ}}_{\text{A}}\text{(1)}{\text{ψ}}_{\text{A}}\text{(2)}\text{+}{\text{ψ}}_{\text{A}}\text{(2)}{\text{ψ}}_{\text{A}}\text{(1)}$