Organic Chemistry: Principles and Mechanisms (Second Edition)
Organic Chemistry: Principles and Mechanisms (Second Edition)
2nd Edition
ISBN: 9780393663556
Author: Joel Karty
Publisher: W. W. Norton & Company
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Chapter 16, Problem 16.1P
Interpretation Introduction

Interpretation:

It is to be explained at which magnetic field experienced by a hydrogen nucleus is the energy difference between the α and the β states is greater: 0.5 T or 5.0 T.

Concept introduction:

Protons have quantized magnetic dipoles and thus behave as tiny bar magnets, with a north and a south pole. When exposed to Bext, the magnetic dipoles of nuclei in the α spin state become aligned with Bext, whereas those of nuclei in the β spin state become aligned against it. In these orientations, the energy of the α state is slightly lower than the energy of the β state.

The difference in energy between the two spin states of a proton is given by the equation:

ΔEspin = γhBext = (constant) × Bext

The energy difference, ΔEspin, is directly proportional to the external magnetic field Bext.

Expert Solution & Answer
Check Mark

Answer to Problem 16.1P

The energy difference will be greater at 5.0 T than at 0.5 T.

Explanation of Solution

The difference in energy between the two spin states of a proton is given by the equation:

ΔEspin = γhBext = (constant) × Bext

The energy difference, ΔEspin, is directly proportional to the external magnetic field Bext, that is, greater the external magnetic field, greater the energy difference.

Thus, at greater external magnetic field, 5.0 T, greater is the energy difference between the α and the β states for hydrogen nucleus.

Conclusion

The magnetic field experienced by hydrogen nucleus, at which the energy difference between the α and the β states is greater is explained using the equation for the difference in energy between the two spin states of a proton.

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Chapter 16 Solutions

Organic Chemistry: Principles and Mechanisms (Second Edition)

Ch. 16 - Prob. 16.11PCh. 16 - Prob. 16.12PCh. 16 - Prob. 16.13PCh. 16 - Prob. 16.14PCh. 16 - Prob. 16.15PCh. 16 - Prob. 16.16PCh. 16 - Prob. 16.17PCh. 16 - Prob. 16.18PCh. 16 - Prob. 16.19PCh. 16 - Prob. 16.20PCh. 16 - Prob. 16.21PCh. 16 - Prob. 16.22PCh. 16 - Prob. 16.23PCh. 16 - Prob. 16.24PCh. 16 - Prob. 16.25PCh. 16 - Prob. 16.26PCh. 16 - Prob. 16.27PCh. 16 - Prob. 16.28PCh. 16 - Prob. 16.29PCh. 16 - Prob. 16.30PCh. 16 - Prob. 16.31PCh. 16 - Prob. 16.32PCh. 16 - Prob. 16.33PCh. 16 - Prob. 16.34PCh. 16 - Prob. 16.35PCh. 16 - Prob. 16.36PCh. 16 - Prob. 16.37PCh. 16 - Prob. 16.38PCh. 16 - Prob. 16.39PCh. 16 - Prob. 16.40PCh. 16 - Prob. 16.41PCh. 16 - Prob. 16.42PCh. 16 - Prob. 16.43PCh. 16 - Prob. 16.44PCh. 16 - Prob. 16.45PCh. 16 - Prob. 16.46PCh. 16 - Prob. 16.47PCh. 16 - Prob. 16.48PCh. 16 - Prob. 16.49PCh. 16 - Prob. 16.50PCh. 16 - Prob. 16.51PCh. 16 - Prob. 16.52PCh. 16 - Prob. 16.53PCh. 16 - Prob. 16.54PCh. 16 - Prob. 16.55PCh. 16 - Prob. 16.56PCh. 16 - Prob. 16.57PCh. 16 - Prob. 16.58PCh. 16 - Prob. 16.59PCh. 16 - Prob. 16.60PCh. 16 - Prob. 16.61PCh. 16 - Prob. 16.62PCh. 16 - Prob. 16.63PCh. 16 - Prob. 16.64PCh. 16 - Prob. 16.65PCh. 16 - Prob. 16.66PCh. 16 - Prob. 16.67PCh. 16 - Prob. 16.68PCh. 16 - Prob. 16.69PCh. 16 - Prob. 16.70PCh. 16 - Prob. 16.71PCh. 16 - Prob. 16.72PCh. 16 - Prob. 16.73PCh. 16 - Prob. 16.74PCh. 16 - Prob. 16.75PCh. 16 - Prob. 16.76PCh. 16 - Prob. 16.77PCh. 16 - Prob. 16.78PCh. 16 - Prob. 16.79PCh. 16 - Prob. 16.80PCh. 16 - Prob. 16.81PCh. 16 - Prob. 16.82PCh. 16 - Prob. 16.83PCh. 16 - Prob. 16.84PCh. 16 - Prob. 16.85PCh. 16 - Prob. 16.86PCh. 16 - Prob. 16.87PCh. 16 - Prob. 16.88PCh. 16 - Prob. 16.89PCh. 16 - Prob. 16.1YTCh. 16 - Prob. 16.2YTCh. 16 - Prob. 16.3YTCh. 16 - Prob. 16.4YTCh. 16 - Prob. 16.5YTCh. 16 - Prob. 16.6YTCh. 16 - Prob. 16.7YTCh. 16 - Prob. 16.8YTCh. 16 - Prob. 16.9YTCh. 16 - Prob. 16.10YTCh. 16 - Prob. 16.11YTCh. 16 - Prob. 16.12YTCh. 16 - Prob. 16.13YTCh. 16 - Prob. 16.14YTCh. 16 - Prob. 16.15YTCh. 16 - Prob. 16.16YTCh. 16 - Prob. 16.17YTCh. 16 - Prob. 16.18YTCh. 16 - Prob. 16.19YTCh. 16 - Prob. 16.20YTCh. 16 - Prob. 16.21YTCh. 16 - Prob. 16.22YTCh. 16 - Prob. 16.23YTCh. 16 - Prob. 16.24YTCh. 16 - Prob. 16.25YTCh. 16 - Prob. 16.26YTCh. 16 - Prob. 16.27YTCh. 16 - Prob. 16.28YTCh. 16 - Prob. 16.29YTCh. 16 - Prob. 16.30YTCh. 16 - Prob. 16.31YTCh. 16 - Prob. 16.32YTCh. 16 - Prob. 16.33YTCh. 16 - Prob. 16.34YT
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