where ̃resis the frequency of the absorbed light in units of wavenumbers, his
Planck’s constant,cis the speed of light in units of cm/s,ge is the electron g
factor,Bis the Bohr magneton, and Bis the magnetic field strength in units
of T.In units of s^1 or Hz, the equation is rewritten asres
ge
hBB (16.16)
Given the magnetic field strengths that are available in most laboratory in-
struments today (0.3 T), the transitions due to the splitting of the electron
spin states occur in the microwave region of the spectrum (whose frequencies
are usually expressed in units of gigahertz, or GHz). Control of microwaves is
relatively straightforward, and spectrometers are readily available that take ad-
vantage of the resonance condition. Spectroscopy based on this method is
called electron spin resonance,or ESR, spectroscopy. A schematic diagram of an
ESR spectrometer is shown in Figure 16.9.Example 16.5
In a 0.35-T magnetic field, what is the expected frequency, in GHz, of a free
electron ms^12 →ms ^12 transition?Solution
Using equation 16.16:res(2.002)(9.274 ^10 9.81 109 s^1 9.81 GHz (^24) J/T)(0.35 T)
(6.626 10 ^34 Js)
568 CHAPTER 16 Introduction to Magnetic Spectroscopy
or
B 0 B 0
Energy
Figure 16.8 In the absence of a magnetic field
(left), an unpaired electron of a free radical has
the same energy no matter what direction its spin.
However, in the presence of a magnetic field
(right), the two spin directions have different en-
ergies, and electromagnetic radiation can cause a
transition between the two energy levels.
From microwave
generator
to detector
Sample
Resonance
cavity
Waveguide
Electromagnet pole Electromagnet pole
Figure 16.9 A diagram of an ESR spec-
trometer. A sample is exposed to microwaves
of known wavelength, and a slowly varying
magnetic field is applied. When the resonance
condition is established, microwaves are ab-
sorbed and the transition from ground state to
excited state occurs. The spectrometer detects
the absorption of the microwaves to generate
the spectrum.