Chapter 19, Problem 19.8QAP

Interpretation Introduction

(a)

Interpretation:

The Larmor frequency of ${}^{\text{13}}\text{C}$ in magnetic field of 1.41 T 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 19.8QAP

The Larmor frequency of ${}^{\text{13}}\text{C}$ in magnetic field of 1.41 T is 15 MHz.

Explanation of Solution

The Larmor 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 $6.7283\times {10}^7{\text{T}}^{-1}{\text{s}}^{-1}$.

The magnetic field is given as 1.41 T.

Substitute magnetogyric ratio and magnetic field in above expression.

$\begin{array}{c}{v}_0=\frac{6.7283\times {10}^7{\text{T}}^{-1}{\text{s}}^{-1}\times 1.41\text{T}}{2\times 3.14}\\ =\frac{9.486903\times {10}^7}{6.28}{\text{s}}^{-1}\\ =1.5\times {10}^7{\text{s}}^{-1}\\ =15\times {10}^6\text{Hz}\times \left(\frac{1\text{MHz}}{{10}^6\text{Hz}}\right)\\ =15\text{MHz}\end{array}$

Therefore, the Larmor frequency of ${}^{\text{13}}\text{C}$ in magnetic field of 1.41 T is 15 MHz.

Interpretation Introduction

(b)

Interpretation:

The Larmor frequency of ${}^{\text{13}}\text{C}$ in magnetic field of 4.69 T 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 19.8QAP

The Larmor frequency of ${}^{\text{13}}\text{C}$ in magnetic field of 4.69 T is 50 MHz.

Explanation of Solution

The Larmor 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 $6.7283\times {10}^7{\text{T}}^{-1}{\text{s}}^{-1}$.

The magnetic field is given as 4.69 T.

Substitute magnetogyric ratio and magnetic field in above expression.

$\begin{array}{c}{v}_0=\frac{6.7283\times {10}^7{\text{T}}^{-1}{\text{s}}^{-1}\times 4.69\text{T}}{2\times 3.14}\\ =\frac{31.555727\times {10}^7}{6.28}{\text{s}}^{-1}\\ =5.0\times {10}^7{\text{s}}^{-1}\\ =50\times {10}^6\text{Hz}\times \left(\frac{1\text{MHz}}{{10}^6\text{Hz}}\right)\\ =50\text{MHz}\end{array}$

Therefore, the Larmor frequency of ${}^{\text{13}}\text{C}$ in magnetic field of 4.69 T is 50 MHz.

Interpretation Introduction

(c)

Interpretation:

The Larmor frequency of ${}^{\text{13}}\text{C}$ in magnetic field of 7.05 T 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 19.8QAP

The Larmor frequency of ${}^{\text{13}}\text{C}$ in magnetic field of 7.05 T is 76 MHz.

Explanation of Solution

The Larmor 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 $6.7283\times {10}^7{\text{T}}^{-1}{\text{s}}^{-1}$.

The magnetic field is given as 7.05 T.

Substitute magnetogyric ratio and magnetic field in above expression.

$\begin{array}{c}{v}_0=\frac{6.7283\times {10}^7{\text{T}}^{-1}{\text{s}}^{-1}\times 7.05\text{T}}{2\times 3.14}\\ =\frac{47.434515\times {10}^7}{6.28}{\text{s}}^{-1}\\ =7.6\times {10}^7{\text{s}}^{-1}\\ =76\times {10}^6\text{Hz}\times \left(\frac{1\text{MHz}}{{10}^6\text{Hz}}\right)\\ =76\text{MHz}\end{array}$

Therefore, the Larmor frequency of ${}^{\text{13}}\text{C}$ in magnetic field of 7.05 T is 76 MHz.

Interpretation Introduction

(d)

Interpretation:

The Larmor frequency of ${}^{\text{13}}\text{C}$ in magnetic field of 11.7 T 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 19.8QAP

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

Explanation of Solution

The Larmor 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 $6.7283\times {10}^7{\text{T}}^{-1}{\text{s}}^{-1}$.

The magnetic field is given as 11.7 T.

Substitute magnetogyric ratio and magnetic field in above expression.

$\begin{array}{c}{v}_0=\frac{6.7283\times {10}^7{\text{T}}^{-1}{\text{s}}^{-1}\times 11.7\text{T}}{2\times 3.14}\\ =\frac{78.72111\times {10}^7}{6.28}{\text{s}}^{-1}\\ =12.5\times {10}^7{\text{s}}^{-1}\\ =125\times {10}^6\text{Hz}\times \left(\frac{1\text{MHz}}{{10}^6\text{Hz}}\right)\\ =125\text{MHz}\end{array}$

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

Interpretation Introduction

(e)

Interpretation:

The Larmor frequency of ${}^{\text{13}}\text{C}$ in magnetic field of 18.8 T 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 19.8QAP

The Larmor frequency of ${}^{\text{13}}\text{C}$ in magnetic field of 18.8 T is 201 MHz.

Explanation of Solution

The Larmor 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 $6.7283\times {10}^7{\text{T}}^{-1}{\text{s}}^{-1}$.

The magnetic field is given as 18.8 T.

Substitute magnetogyric ratio and magnetic field in above expression.

$\begin{array}{c}{v}_0=\frac{6.7283\times {10}^7{\text{T}}^{-1}{\text{s}}^{-1}\times 18.8\text{T}}{2\times 3.14}\\ =\frac{126.49204\times {10}^7}{6.28}{\text{s}}^{-1}\\ =20.1\times {10}^7{\text{s}}^{-1}\\ =201\times {10}^6\text{Hz}\times \left(\frac{1\text{MHz}}{{10}^6\text{Hz}}\right)\\ =201\text{MHz}\end{array}$

Therefore, the Larmor frequency of ${}^{\text{13}}\text{C}$ in magnetic field of 18.8 T is 201 MHz.

Interpretation Introduction

(f)

Interpretation:

The Larmor frequency of ${}^{\text{13}}\text{C}$ in magnetic field of 21.2 T 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 19.8QAP

The Larmor frequency of ${}^{\text{13}}\text{C}$ in magnetic field of 21.2 T is 227 MHz.

Explanation of Solution

The Larmor 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 $6.7283\times {10}^7{\text{T}}^{-1}{\text{s}}^{-1}$.

The magnetic field is given as 21.2 T.

Substitute magnetogyric ratio and magnetic field in above expression.

$\begin{array}{c}{v}_0=\frac{6.7283\times {10}^7{\text{T}}^{-1}{\text{s}}^{-1}\times 21.2\text{T}}{2\times 3.14}\\ =\frac{142.63996\times {10}^7}{6.28}{\text{s}}^{-1}\\ =22.7\times {10}^7{\text{s}}^{-1}\\ =227\times {10}^6\text{Hz}\times \left(\frac{1\text{MHz}}{{10}^6\text{Hz}}\right)\\ =227\text{MHz}\end{array}$

Therefore, the Larmor frequency of ${}^{\text{13}}\text{C}$ in magnetic field of 21.2 T is 227 MHz.