Chapter 19, Problem 19.25P

a)

Interpretation Introduction

Interpretation:

The graph of $\frac{{\text{I}}_{\text{0}}}{{\text{I}}_{\text{Q}}}\text{(vs)}\left[\text{Q}\right]$ is not linear has to be proved.

Concept Introduction:

Stern Volmer equation

Stern Volmer equation can be obtained from the quantum yield of emission in the steady state and quantum yield for emission and the relative yield equation is given as,

$\frac{{\text{Φ}}_{\text{0}}}{{\text{Φ}}_{\text{Q}}}\text{=}\frac{{\text{k}}_{\text{e}}{\text{+k}}_{\text{d}}{\text{+k}}_{\text{q}}\left[\text{Q}\right]}{{\text{k}}_{\text{e}}{\text{+k}}_{\text{d}}}\text{=1+}\left(\frac{{\text{k}}_{\text{q}}}{{\text{k}}_{\text{e}}{\text{+k}}_{\text{d}}}\right)\left[\text{Q}\right]$

The Stern-Volmer tells about the measure of relative emission $\frac{{\text{Φ}}_{\text{0}}}{{\text{Φ}}_{\text{Q}}}$ as function of concentration of quencher. On plotting the graph $\frac{{\text{Φ}}_{\text{0}}}{{\text{Φ}}_{\text{Q}}}$ $\text{(vs)}\left[\text{Q}\right]$ a straight line has to be obtained. The factor $\frac{{\text{Φ}}_{\text{0}}}{{\text{Φ}}_{\text{Q}}}$ must be equivalent to $\frac{{\text{I}}_{\text{0}}}{{\text{I}}_{\text{Q}}}$ where ${\text{I}}_{\text{0}}$ = emission intensity in the absence of quencher and ${\text{I}}_{\text{q}}$ = emission intensity in the presence of quencher.

To show that the plot of $\frac{{\text{I}}_{\text{0}}}{{\text{I}}_{\text{Q}}}\text{(vs)}\left[\text{Q}\right]$ is not linear

b)

Interpretation Introduction

Interpretation:

The average number of Sodium dodecyl sulphate per micelle has to be calculated and a graph of $\frac{{\text{I}}_{\text{0}}}{{\text{I}}_{\text{Q}}}\text{(vs)}\left[\text{Q}\right]$ has to be prepared.

To calculate the average number of Sodium dodecyl sulphate per micelle

To draw graph of $\frac{{\text{I}}_{\text{0}}}{{\text{I}}_{\text{Q}}}\text{(vs)}\left[\text{Q}\right]$

c)

Interpretation Introduction

Interpretation:

The concentration of micelles and average number of molecules of Q per micelle has to be calculated.

To calculate the concentration of micelles and average number of molecules of Q per micelle

d)

Interpretation Introduction

Interpretation:

The fractions of micelles containing 0, 1 and 2 molecules of Q has to be calculated.

Concept Introduction:

The fraction of micelles can be calculated as,

${\text{P}}_{\text{n}}\text{=}\frac{\overline{{\text{Q}}^{\text{n}}}}{\text{n!}}{\text{e}}^{\text{-}\overline{\text{Q}}}$

Where n= number of molecules

To calculate the fractions of micelles containing 0, 1 and 2 molecules of Q