Chapter 9, Problem 9.12P

(a)

Interpretation Introduction

Interpretation:

The form of two occupied orbitals in butadiene predicted by free electron molecular orbital (FEMO) theory has to be sketched.  Also the minimum excitation energy has to be predicted.

Concept Introduction:

The orbitals are considered as particle in box wave functions.  The energy of particle can be written as follows,

  $E_n=\frac{n^2{h}^2}{8m{L}^2},n=1,2,3,\mathrm{...}$

Where,

    $\begin{array}{c}h=6.626\times {10}^{-34}Js\\ \\ m=9.1\times {10}^{-31}kg\end{array}$

$E_n$ is the energy of n^th orbital.

$n$ is the principal quantum number.

$L$ is the length of the box.

The wave function of particle in $n^{th}$ orbital (${\psi }_n$) can be written as follows,

  ${\psi }_n=\sqrt{\frac{2}{L}}\sin \frac{n\pi x}{L},n=1,2,3,\mathrm{...}$

(b)

Interpretation Introduction

Interpretation:

The minimum excitation energy of tetraene has to be calculated.  Also the HOMO and LUMO has to be sketched.

Concept Introduction:

The orbitals are considered as particle in box wave functions.  The energy of particle can be written as follows,

$E_n=\frac{n^2{h}^2}{8m{L}^2},n=1,2,3,\mathrm{...}$

Where,

    $\begin{array}{c}h=6.626\times {10}^{-34}Js\\ \\ m=9.1\times {10}^{-31}kg\end{array}$

$E_n$ is the energy of n^th orbital.

$n$ is the principal quantum number.

$L$ is the length of the box.

The wave function of particle in $n^{th}$ orbital (${\psi }_n$) can be written as follows,

${\psi }_n=\sqrt{\frac{2}{L}}\sin \frac{n\pi x}{L},n=1,2,3,\mathrm{...}$