Physical Chemistry , 1st ed.

units of s^1. Spectroscopy based on the splitting of the MIlevels of nuclei by

a magnetic field is called nuclear magnetic resonance,or NMR, spectroscopy.

NMR spectroscopy was developed largely by the efforts of Felix Bloch at

Stanford University and Edward Purcell at Harvard University in 1946. They

shared a 1952 Nobel Prize for their efforts.

Example 16.10

Predict the wavelength of transition for an^19 F nucleus exposed to a magnetic

field of 7730 G.^19 F has a nuclear spin of^12 and a gNof 5.2567. Use the nu-

clear magneton N.

Solution

Since I^12 , the only possible values ofMIare ^12 and ^12 , and the only pos-

sible transition is MI^12 →MI^12 . Using equation 16.23, we find

res

gN

h

NB

10,

1

00

T

0G



res3.098  107 Hz 30.98 MHz

This is in the radio wave region of the electromagnetic spectrum.

Instead of using nuclear gfactors, a magnetogyric ratiocan be defined as

the proportionality constant between the nuclear magnetic moment’s zcom-

ponent and the MIquantum number:

z

MI (16.24)

The relationship between the magnetogyric ratio and the nuclear gfactor is

gN

N (16.25)

NMR would be useless if all nuclei of the same element absorbed the same

frequency of light at some particular magnetic field strength (except perhaps

for elemental analysis). However, the local electronic environment around nu-

clei cause different atomic nuclei to experience a slightly different total mag-

netic field. This is because the electrons are also affected by the magnetic field.

(This should be obvious from our earlier treatment of ESR spectroscopy.) In

a particular chemical environment, the total magnetic field experienced by a

nucleus is the sum ofBplus an additional, small magnetic field induced by B

on the electrons. The additional magnetic field, B, is proportional to Band

is given by the expression

BB (16.26)

where is a dimensionless constant called the shielding constant.The total

magnetic field experienced by a nucleus is therefore

BtotBBB(1 ) (16.27)

The exact frequency of light that is absorbed depends on the totalmagnetic

field,Btot, not the applied magnetic field B. Shielding constants themselves are

very small, on the order of 1 to 3  10 ^5. Their existence was first demon-

strated by W. D. Knight in 1949, not long after the development of nuclear

magnetic resonance itself.

(5.2567)(5.051  10 ^27 J/T)(7730 G)



6.626  10 ^34 Js

574 CHAPTER 16 Introduction to Magnetic Spectroscopy