Chapter 13, Problem 13C.6E

(a)

Interpretation Introduction

Interpretation:

In an EPR spectrum, the intensity distribution in the hyperfine lines of ${}^{\text{•}}{\text{CH}}_{\text{3}}$ has to be predicted.

Explanation of Solution

Given information,

  $\text{Methyl}\text{radical}\text{-}{}^{\text{•}}{\text{CH}}_{\text{3}}$

The spin value of ${}^{\text{1}}\text{H}$ nuclei is $\text{I}\text{=}\text{1/2}$.

The number of lines obtained in the spectrum is given by,

$\begin{array}{l}\text{2}\text{N}\text{I}\text{+}\text{1}\\ \text{here,}\text{N}\text{-}\text{number}\text{of}\text{equivalent}\text{nuclei's}\\ \text{therefore,}\\ \text{2}\left(\text{3}\right)\left(\text{1/2}\right)\text{+}\text{1}\text{=}\text{4}\text{lines}\end{array}$

Therefore, for the given radical the number of lines obtained in the hyperfine structure is 4.

For coupling with nuclei having spin value of 1/2, the relative intensities are given by Pascal’s triangle,

$\begin{array}{l}\text{1}\\ \text{1}\text{1}\left(\text{by}\text{the}\text{first}\text{nuclei}\right)\\ \text{1}\text{2}\text{1}\left(\text{by}\text{the}\text{second}\text{nuclei}\right)\\ 1331\left(\text{by}\text{the}\text{third}\text{nuclei}\right)\end{array}$

(b)

Interpretation Introduction

Interpretation:

In an EPR spectrum, the intensity distribution in the hyperfine lines of ${}^{\text{•}}{\text{CD}}_{\text{3}}$ has to be predicted.

Explanation of Solution

Given information,

  $\text{Radical}\text{-}{}^{\text{•}}{\text{CD}}_{\text{3}}$

The spin value of $\text{D}$ nuclei is $\text{I}\text{=}\text{1}$.

The number of lines obtained in the spectrum is given by,

$\begin{array}{l}\text{2}\text{N}\text{I}\text{+}\text{1}\\ \text{here,}\text{N}\text{-}\text{number}\text{of}\text{equivalent}\text{nuclei's}\\ \text{therefore,}\\ \text{2}\left(\text{3}\right)\left(\text{1}\right)\text{+}\text{1}\text{=}7\text{lines}\end{array}$

Therefore, for the given radical the number of lines obtained in the hyperfine structure is 7.

For coupling with nuclei having spin value of 1, the relative intensities are given by modified version of Pascal’s triangle,

$\begin{array}{l}\text{1}\\ \text{1}\text{1}\text{1}\left(\text{by}\text{the}\text{first}\text{nuclei}\right)\\ \text{1}\text{2}\text{3}\text{2}\text{1}\left(\text{by}\text{the}\text{second}\text{nuclei}\right)\\ 1367631\left(\text{by}\text{the}\text{third}\text{nuclei}\right)\end{array}$