PHYSICAL CHEMISTRY-WEBASSIGN
PHYSICAL CHEMISTRY-WEBASSIGN
11th Edition
ISBN: 9780357087411
Author: ATKINS
Publisher: CENGAGE L
Question
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Chapter 12, Problem 12A.4AE
Interpretation Introduction

Interpretation:

The energies of the nuclear spin state of S33 in magnetic field of 6.8T have to be stated.

Concept introduction:

The frequency of electromagnetic radiation is given by resonance condition.  This resonance condition gives an equation that relates the frequency of nuclei with the magnetic field.  The frequency of a nuclei is given by the equation as shown below.

  v=γNBo2π

The above stated frequency is known as the Larmor precession frequency.  Larmor precession is a phenomenon in which the magnetic moment of nuclei precesses about an external magnetic field.

Expert Solution & Answer
Check Mark

Answer to Problem 12A.4AE

The energies of the nuclear spin state of S33 in magnetic field of 6.8T are 2.21×10-26J_, 7.365×10-27J_, 7.365×10-27J_, and 2.21×10-26J_.

Explanation of Solution

The energies of the nuclear spin in a magnetic field is calculated by the formula shown below.

    EmI=gIμNB0mI        (1)

Where,

  • μN is the nuclear magneton (5.051×1027JT1).
  • gI is the nuclear g factor.
  • mI is the possible value of spin quantum number.
  • Bo is the magnetic field.

For S33, the spin quantum number (I) is 32.  Therefore, the possible values of spin quantum number (mI) for S33 are calculated as shown below.

    mI=I,(I1),(I2),(I3)        (2)

Substitute the value of the spin quantum number (I) as 32 in equation (2).

    mI=I,(I1),(I2),(I3)=32,(321),(322),(323)=32,12,12,32

The value of nuclear g factor and magnetic field (Bo) is 0.4289 and 6.8T respectively.

Substitute the value of nuclear g factor, magnetic field (Bo), and nuclear magneton (μN) in equation (1).

    EmI=gIμNB0mI=0.4289×(5.051×1027JT1)×6.8T×mI=mI(14.73×1027J)=mI(1.473×1026J)

At mI=32, the energy of the nuclear spin in a magnetic field is calculated as shown below.

    EmI=mI(1.473×1026J)=32×1.473×1026J=2.21×10-26J_

At mI=12, the energy of the nuclear spin in a magnetic field is calculated as shown below

    EmI=mI(1.473×1026J)=12×1.473×1026J=0.7365×1026J=7.365×10-27J_

At mI=12, the energy of the nuclear spin in a magnetic field is calculated as shown below

    EmI=mI(1.473×1026J)=(12)×1.473×1026J=0.7365×1026J=7.365×10-27J_

At mI=32, the energy of the nuclear spin in a magnetic field is calculated as shown below.

    EmI=mI(1.473×1026J)=(32)×1.473×1026J=2.21×10-26J_

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Chapter 12 Solutions

PHYSICAL CHEMISTRY-WEBASSIGN

Ch. 12 - Prob. 12A.2BECh. 12 - Prob. 12A.3AECh. 12 - Prob. 12A.3BECh. 12 - Prob. 12A.4AECh. 12 - Prob. 12A.4BECh. 12 - Prob. 12A.5AECh. 12 - Prob. 12A.5BECh. 12 - Prob. 12A.6AECh. 12 - Prob. 12A.6BECh. 12 - Prob. 12A.7AECh. 12 - Prob. 12A.7BECh. 12 - Prob. 12A.8AECh. 12 - Prob. 12A.8BECh. 12 - Prob. 12A.9AECh. 12 - Prob. 12A.9BECh. 12 - Prob. 12A.1PCh. 12 - Prob. 12A.3PCh. 12 - Prob. 12B.1DQCh. 12 - Prob. 12B.2DQCh. 12 - Prob. 12B.3DQCh. 12 - Prob. 12B.4DQCh. 12 - Prob. 12B.5DQCh. 12 - Prob. 12B.1AECh. 12 - Prob. 12B.1BECh. 12 - Prob. 12B.2AECh. 12 - Prob. 12B.2BECh. 12 - Prob. 12B.3AECh. 12 - Prob. 12B.3BECh. 12 - Prob. 12B.4AECh. 12 - Prob. 12B.4BECh. 12 - Prob. 12B.5AECh. 12 - Prob. 12B.5BECh. 12 - Prob. 12B.6AECh. 12 - Prob. 12B.6BECh. 12 - Prob. 12B.7AECh. 12 - Prob. 12B.7BECh. 12 - Prob. 12B.8AECh. 12 - Prob. 12B.8BECh. 12 - Prob. 12B.9AECh. 12 - Prob. 12B.9BECh. 12 - Prob. 12B.10AECh. 12 - Prob. 12B.10BECh. 12 - Prob. 12B.11AECh. 12 - Prob. 12B.11BECh. 12 - Prob. 12B.12AECh. 12 - Prob. 12B.12BECh. 12 - Prob. 12B.13AECh. 12 - Prob. 12B.13BECh. 12 - Prob. 12B.14AECh. 12 - Prob. 12B.14BECh. 12 - Prob. 12B.1PCh. 12 - Prob. 12B.2PCh. 12 - Prob. 12B.3PCh. 12 - Prob. 12B.5PCh. 12 - Prob. 12B.6PCh. 12 - Prob. 12B.7PCh. 12 - Prob. 12B.8PCh. 12 - Prob. 12B.9PCh. 12 - Prob. 12C.1DQCh. 12 - Prob. 12C.2DQCh. 12 - Prob. 12C.3DQCh. 12 - Prob. 12C.4DQCh. 12 - Prob. 12C.5DQCh. 12 - Prob. 12C.1AECh. 12 - Prob. 12C.1BECh. 12 - Prob. 12C.2AECh. 12 - Prob. 12C.2BECh. 12 - Prob. 12C.3AECh. 12 - Prob. 12C.3BECh. 12 - Prob. 12C.4AECh. 12 - Prob. 12C.4BECh. 12 - Prob. 12C.5AECh. 12 - Prob. 12C.5BECh. 12 - Prob. 12C.4PCh. 12 - Prob. 12C.5PCh. 12 - Prob. 12C.6PCh. 12 - Prob. 12C.10PCh. 12 - Prob. 12D.1DQCh. 12 - Prob. 12D.2DQCh. 12 - Prob. 12D.1AECh. 12 - Prob. 12D.1BECh. 12 - Prob. 12D.2AECh. 12 - Prob. 12D.2BECh. 12 - Prob. 12D.3AECh. 12 - Prob. 12D.3BECh. 12 - Prob. 12D.4AECh. 12 - Prob. 12D.4BECh. 12 - Prob. 12D.5AECh. 12 - Prob. 12D.5BECh. 12 - Prob. 12D.6AECh. 12 - Prob. 12D.6BECh. 12 - Prob. 12D.1PCh. 12 - Prob. 12D.2PCh. 12 - Prob. 12D.4PCh. 12 - Prob. 12D.5PCh. 12 - Prob. 12D.6PCh. 12 - Prob. 12D.7PCh. 12 - Prob. 12D.8PCh. 12 - Prob. 12.3IACh. 12 - Prob. 12.4IA
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