Chapter 7, Problem 7D.5P

(a)

Interpretation Introduction

Interpretation:

The separation in energy between the ground state and the first excited state in which one electron occupies the state with $n=7$ has to be calculated.

Concept introduction:

The separation between the adjacent energy levels with quantum numbers $n$ and $n+1$ is given by the expression,

    $E_{n+1}-E_n=\left(2n+1\right)\frac{h^2}{8m{L}^2}$

(b)

Interpretation Introduction

Interpretation:

The frequency of the radiation required for the transition between the two states with quantum numbers $n=6$ and $n+1=7$ has to be calculated.

Concept introduction:

Frequency is defined as the number of transitions per second.  The frequency is denoted by $v$.  The relation between the energy and frequency is given by the expression.

    $\Delta E=hv$

(c)

Interpretation Introduction

Interpretation:

The words in the parentheses have to be chosen to generate a rule for the prediction of frequency shifts in the absorption spectra of linear polyene.

Concept introduction:

The separation between the adjacent energy levels with quantum numbers $n$ and $n+1$ is given by the expression,

    $E_{n+1}-E_n=\left(2n+1\right)\frac{h^2}{8m{L}^2}$