Chapter 13, Problem 13.10P

Interpretation Introduction

Interpretation:

The given table has to be completed, in which nucleus require least energy and most energy.

Concept Introduction:

NMR Spectroscopy: NMR spectroscopy commonly known as MRI (Magnetic Resonance Spectroscopy), it is important Research tool of analysis for different organic molecule and its structures. (or) In other words hydrogen nuclei have spin (odd value) and all nuclei ae electrically charged. The extremal magnetic field is applied an some energy transfer is possible between the lower energy to excited level.

Spin state: The NMR is mosltly consult with nucleues spin quantum number $I=+1/2$. The proton having a $I=-1/2$ when place in extranal meganitc fileld $H_o$ it is start spin around the nuclear axis and generate a another magnitic field.

According to quantum mechanics ther are $(2I+1)$ so two spin stage $+1/2$ and $-1/2$ for the proton.

Radio frequancy: The energy difference between the states is dependent upon the frequency.  The expression is,

$\text{ΔE= hv}$

Here, $v$ is the frequency and $h$ is the Planck’s constant.

This frequency is dependent on the strength of the magnetic field and the gyromagnetic ratio. The expression is,

$v=\frac{\gamma }{2\pi }{B}_{\circ }$

Here, $\gamma$ is the gyromagnetic ratio and $B_{\circ }$ is the magnetic field strength.  The gyromagnetic ratio is dependent upon the type of nucleus and is a constant value.