Chapter 19, Problem 19.7QAP

Interpretation Introduction

(a)

Interpretation:

The absorption frequency of ${}^1\text{H}$ in a 11.7-T magnetic field should be predicted.

Concept introduction:

Nuclear magnetic reasonance is a technique that is used to predict the structural formula of the compound. NMR spectroscopy involves the examination of the nucleus under the external magnetic field.

Answer to Problem 19.7QAP

The absorption frequency of ${}^1\text{H}$ in a 11.7-T magnetic field is 499 MHz.

Explanation of Solution

The absorption frequency is calculated by the formula:

$v_0=\frac{\gamma B_0}{2\pi }$

Where,

• $B_0$ is the magnetic field.
• $\gamma$ is the magnetogyric ratio.

The magnetogyric ratio for ${}^1\text{H}$ is $2.68\times {10}^8{\text{T}}^{-1}{\text{s}}^{-1}$. The magnetic field is given as 11.7 T.

Substitute magnetogyric ratio and magnetic field in above expression.

$\begin{array}{c}{v}_0=\frac{2.68\times {10}^8{\text{T}}^{-1}{\text{s}}^{-1}\times 11.7\text{T}}{2\times 3.14}\\ =\frac{31.356\times {10}^8}{6.28}{\text{s}}^{-1}\\ =4.99\times {10}^8{\text{s}}^{-1}\\ =499\times {10}^6\text{Hz}\times \left(\frac{1\text{MHz}}{{10}^6\text{Hz}}\right)\\ =499\text{MHz}\end{array}$

Therefore, the absorption frequency of ${}^1\text{H}$ in a 11.7-T magnetic field is 499 MHz.

Interpretation Introduction

(b)

Interpretation:

The absorption frequency of ${}^{\text{13}}\text{C}$ in a 11.7-T magnetic field should be predicted.

Concept introduction:

Nuclear magnetic reasonance is a technique that is used to predict the structural formula of the compound. NMR spectroscopy involves the examination of the nucleus under the external magnetic field.

Answer to Problem 19.7QAP

The absorption frequency of ${}^{\text{13}}\text{C}$ in a 11.7-T magnetic field is 125 MHz.

Explanation of Solution

The absorption frequency is calculated by the formula,

$v_0=\frac{\gamma B_0}{2\pi }$

Where,

• $B_0$ is the magnetic field.
• $\gamma$ is the magnetogyric ratio.

The magnetogyric ratio for ${}^{\text{13}}\text{C}$ is taken as $6.72\times {10}^7{\text{T}}^{-1}{\text{s}}^{-1}$.

The magnetic field is given as 11.7 T.

Substitute magnetogyric ratio and magnetic field in above expression.

$\begin{array}{c}{v}_0=\frac{6.72\times {10}^7{\text{T}}^{-1}{\text{s}}^{-1}\times 11.7\text{T}}{2\times 3.14}\\ =\frac{78.624\times {10}^7}{6.28}{\text{s}}^{-1}\\ =12.5\times {10}^7{\text{s}}^{-1}\\ =125\times {10}^6\text{Hz}\times \left(\frac{1\text{MHz}}{{10}^6\text{Hz}}\right)\\ =125\text{MHz}\end{array}$

Therefore, the absorption frequency of ${}^{\text{13}}\text{C}$ in a 11.7-T magnetic field is 125 MHz.

Interpretation Introduction

(c)

Interpretation:

The absorption frequency of ${}^{\text{19}}\text{F}$ in a 11.7-T magnetic field should be predicted.

Concept introduction:

Nuclear magnetic reasonance is a technique that is used to predict the structural formula of the compound. NMR spectroscopy involves the examination of the nucleus under the external magnetic field.

Answer to Problem 19.7QAP

The absorption frequency of ${}^{\text{19}}\text{F}$ in a 11.7-T magnetic field is 469 MHz.

Explanation of Solution

The absorption frequency is calculated by the formula,

$v_0=\frac{\gamma B_0}{2\pi }$

Where,

• $B_0$ is the magnetic field.
• $\gamma$ is the magnetogyric ratio.

The magnetogyric ratio for ${}^{\text{19}}\text{F}$ is taken as $2.52\times {10}^8{\text{T}}^{-1}{\text{s}}^{-1}$.

The magnetic field is given as 11.7 T.

Substitute magnetogyric ratio and magnetic field in above expression.

$\begin{array}{c}{v}_0=\frac{2.52\times {10}^8{\text{T}}^{-1}{\text{s}}^{-1}\times 11.7\text{T}}{2\times 3.14}\\ =\frac{29.484\times {10}^8}{6.28}{\text{s}}^{-1}\\ =4.69\times {10}^8{\text{s}}^{-1}\\ =469\times {10}^6\text{Hz}\times \left(\frac{1\text{MHz}}{{10}^6\text{Hz}}\right)\\ =469\text{MHz}\end{array}$

Therefore, the absorption frequency of ${}^{\text{19}}\text{F}$ in a 11.7-T magnetic field is 469 MHz.

Interpretation Introduction

(d)

Interpretation:

The absorption frequency of ${}^{31}\text{P}$ in a 11.7-T magnetic field should be predicted.

Concept introduction:

Nuclear magnetic reasonance is a technique that is used to predict the structural formula of the compound. NMR spectroscopy involves the examination of the nucleus under the external magnetic field.

Answer to Problem 19.7QAP

The absorption frequency of ${}^{31}\text{P}$ in a 11.7-T magnetic field is 201 MHz.

Explanation of Solution

The absorption frequency is calculated by the formula,

$v_0=\frac{\gamma B_0}{2\pi }$

Where,

• $B_0$ is the magnetic field.
• $\gamma$ is the magnetogyric ratio.

The magnetogyric ratio for ${}^{31}\text{P}$ is taken as $1.08\times {10}^8{\text{T}}^{-1}{\text{s}}^{-1}$.

The magnetic field is given as 11.7 T.

Substitute magnetogyric ratio and magnetic field in above expression.

$\begin{array}{c}{v}_0=\frac{1.08\times {10}^8{\text{T}}^{-1}{\text{s}}^{-1}\times 11.7\text{T}}{2\times 3.14}\\ =\frac{12.636\times {10}^8}{6.28}{\text{s}}^{-1}\\ =2.01\times {10}^8{\text{s}}^{-1}\\ =201\times {10}^6\text{Hz}\times \left(\frac{1\text{MHz}}{{10}^6\text{Hz}}\right)\\ =201\text{MHz}\end{array}$

Therefore, the absorption frequency of ${}^{31}\text{P}$ in a 11.7-T magnetic field is 201 MHz.