Physical Chemistry Third Edition

24.3 Electron Spin Resonance Spectroscopy 1011

Transitions between the spin states give rise to absorption of radiation. These transitions

aremagnetic dipole transitionsand the selection rule is

∆ms± 1 (24.3-2)

so that transitions betweenms 1 /2 andms− 1 /2 are allowed. The frequency of

radiation absorbed or emitted depends onBzand is given by

ν

∆Emag

h



gβeBz

h

(24.3-3)

Radiation that can be absorbed or emitted in these transitions is said to be in “resonance”

with the electrons. The spectroscopy based on these transitions is calledelectron spin

resonance (ESR)spectroscopy. It has also been calledelectron paramagnetic resonance

(EPR)spectroscopy.

EXAMPLE24.9

Find the magnetic field necessary to cause ESR absorption or emission of radiation with

wavelength 1.000 cm.

Solution

Bz

hc

gβeλ



(6. 6261 × 10 −^34 J s)(2. 9979 × 1010 cm s−^1 )

(2.0023)(9. 2740 × 10 −^24 JT−^1 )(1.000 cm)

 1 .070 T

Since every substance contains electrons, it might seem that every substance would

absorb radiation at the same frequency if placed in the same magnetic field. However,

most substances do not absorb at all because their electrons occupy space orbitals

in pairs with opposite spins. Because of the Pauli exclusion principle, such electrons

cannot change their spins unless both members of a pair change simultaneously. One

electron gains the same amount of energy that the other electron loses and no net

absorption takes place. Only a substance containing unpaired electrons will exhibit an

ESR spectrum.

It would still seem that every substance with unpaired electrons would absorb at

the same frequency. However, the magnetic field to which an electron is exposed is a

vector sum of the externally applied field,B 0 , and the contribution from the nuclei in

the molecule,Binternal. If the applied field is in thezdirection and the molecule hasn

nuclei,

BzB 0 +Binternal,zB 0 +

∑n

j 1

ajMIj (24.3-4)

The nuclear contributionBinternalis called theFermi contact interaction.MIjis the

quantum number for thezcomponent of the nuclear spin angular moment of nucleus

numberjand the constantajis called thecoupling constantfor that nucleus. The

coupling constants for nuclei in many molecules have values near 1 gauss (1× 10 −^4 T),

but the coupling constant is appreciably nonzero only if the electron approaches closely

to the nucleus. If an unpaired electron occupies an orbital that has a nodal surface at