Chapter 13, Problem 13A.4E

(a)

Interpretation Introduction

Interpretation:

For protons, the value of $\left({\text{N}}_{\text{α}}\text{-}{\text{N}}_{\text{β}}\right)\text{/}\text{N}$ has to be calculated.

Concept Introduction:

The relation between populations of the $\text{α and β}$ states, ${\text{N}}_{\text{α}}{\text{ and N}}_{\text{β}}$ is given by,

  ${\text{N}}_{\text{α}}{\text{-N}}_{\text{β}}\text{ = }\frac{{\text{Nγ}}_{\text{N}}\hslash {\text{B}}_{\text{0}}}{2k\text{T}}$

Where,

${\text{N}}_{\text{α}}{\text{ and N}}_{\text{β}}$ are the populations of the $\text{α and β}$ states.

$h$ is the Planck’s constant.

${\text{B}}_{\text{0}}$ is the magnetic field

${\text{γ}}_{\text{N}}$ is the nuclear magnetogyric ratio.

k is the Boltzmann’s constant

T is the temperature

(b)

Interpretation Introduction

Interpretation:

Forcarbon-13, the value of $\left({\text{N}}_{\text{α}}\text{-}{\text{N}}_{\text{β}}\right)\text{/}\text{N}$ has to be calculated.

Concept Introduction:

The relation between populations of the $\text{α and β}$ states, ${\text{N}}_{\text{α}}{\text{ and N}}_{\text{β}}$ is given by,

  ${\text{N}}_{\text{α}}{\text{-N}}_{\text{β}}\text{ = }\frac{{\text{Nγ}}_{\text{N}}\hslash {\text{B}}_{\text{0}}}{2k\text{T}}$

Where,

${\text{N}}_{\text{α}}{\text{ and N}}_{\text{β}}$ are the populations of the $\text{α and β}$ states.

$h$ is the Planck’s constant.

${\text{B}}_{\text{0}}$ is the magnetic field

${\text{γ}}_{\text{N}}$ is the nuclear magnetogyric ratio.

k is the Boltzmann’s constant

T is the temperature