Chapter 13, Problem 13.11P

Interpretation Introduction

Interpretation:

For a nuclei with spin-3/2, Pascal’s triangle has to be formulated.

Explanation of Solution

Given information,

  Spin-3/2 nuclei and N value from 1 to 5.

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

$\begin{array}{l}\text{2}\text{N}\text{I}\text{+}\text{1}\\ \text{here,}\text{N}\text{-}\text{number}\text{of}\text{equivalent}\text{nuclei's}\\ \text{therefore,}\\ \text{2}\left(5\right)\left(3/2\right)\text{+}\text{1}\text{=}16\text{lines}\end{array}$

Therefore, the number of lines in an EPR spectrum is 16.

For coupling with nuclei having spin value of 3/2, the relative intensities are given by modified version of Pascal’s triangle,

$\begin{array}{l}\text{1}\\ \text{1}\text{1}\text{1}\text{1}\text{N}\text{=1}\\ \text{1}\text{2}\text{3}\text{4}\text{3}\text{2}\text{1}\text{N}\text{=}\text{2}\\ \text{1}\text{3}\text{6}\text{10}\text{12}\text{12}\text{10}\text{6}\text{3}\text{1}\text{N}\text{=}\text{3}\\ \text{1}\text{4}\text{10}\text{20}\text{31}\text{40}\text{44}\text{40}\text{31}\text{20}\text{10}\text{4}\text{1}\text{N}\text{=}\text{4}\\ \text{1}\text{5}\text{15}\text{35}\text{65}\text{101}\text{135}\text{155}\text{155}\text{135}\text{101}\text{65}\text{35}\text{15}\text{5}\text{1}\text{N}\text{=}\text{5}\end{array}$