Elements Of Physical Chemistry
Elements Of Physical Chemistry
7th Edition
ISBN: 9780198796701
Author: ATKINS, P. W. (peter William), De Paula, Julio
Publisher: Oxford University Press
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Chapter 13, Problem 13A.1ST
Interpretation Introduction

Interpretation:

The magnetic field that is necessary to induce the imbalance of population about 35 in a million for 13C with γN = 6.7272×107 T1 s1 has to be calculated.

Concept Introduction:

The relation between populations of the α and β states, Nα and Nβ is given by,

  Nα-Nβ = NB02kT

Where,

  Nα and Nβ are the populations of the α and β states.

   is the Planck’s constant.

  B0 is the magnetic field

  γN is the nuclear magnetogyric ratio.

  k is the Boltzmann’s constant

  T is the temperature

Expert Solution & Answer
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Explanation of Solution

Given data:

The 13C nuclei with γN = 6.7272×107 T1 s1 at 20°C.  The imbalance of population is 35 in a million population.

Calculation of Magnetic field:

The magnetic field that is necessary to induce the imbalance in population is calculated as follows,

  B0 =(Nα-Nβ)2kTN =35×2×(1.38×1023 JK1)×293 K1000000×6.7272×107 T1s1×1.055×1034 Js =28324.31×10237097196×1027T =0.0039909×104 T 40 T

The magnetic field that is necessary to induce the imbalance of population is 40 T.

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