The Electron Spin Resonance of DPPH By Joseph Dotzel With Jedidiah Riebling Date: 2/18/2014 Abstract In this paper, we consider the science of Electron spin resonance. We set out to find three things in this experiment. We were to determine the magnetic field as a function of the resonance frequency, to determine the land é splitting factor, and the find the width of resonance. Using our sample of DPPH, we took measurements of both DC current and Magnetic field strength over a range of frequencies from 15 MHz to 100 MHz. We also took measurements of the line width of resonance at 50 MHz. Using these measurements we were able to obtain a value of 2.00 ± 0.01 for the land é splitting factor, and a value of0.48 ± 0.20 mT for the width of resonance. The accepted values for each of these factors fell within the error bars of our experimental values. Introduction In this experiment we are using phenomena of electron spin resonance. Since its discovery by the Russian scientist Zavoisky in 1944, electron spin resonance (ESR) has proven useful in
Transcript
The Electron Spin Resonance of DPPHBy Joseph Dotzel
With Jedidiah RieblingDate: 2/18/2014
Abstract
In this paper, we consider the science of Electron spin resonance. We
set out to find three things in this experiment. We were to determine the
magnetic field as a function of the resonance frequency, to determine the
landé splitting factor, and the find the width of resonance. Using our sample
of DPPH, we took measurements of both DC current and Magnetic field
strength over a range of frequencies from 15 MHz to 100 MHz. We also took
measurements of the line width of resonance at 50 MHz. Using these
measurements we were able to obtain a value of 2 .00±0.01 for the landé
splitting factor, and a value of0.48±0.20mT for the width of resonance. The
accepted values for each of these factors fell within the error bars of our
experimental values.
Introduction
In this experiment we are using phenomena of electron spin
resonance. Since its discovery by the Russian scientist Zavoisky in 1944,
electron spin resonance (ESR) has proven useful in observing crystalline
structures and has many applications in the fields of physics, chemistry, and
medical fields.1
Electron spin resonance is performed by observing the absorption of
radiation of a paramagnetic sample placed within an oscillating magnetic
field. The magnetic field induces a change in the spin state in the electrons
of the sample, causing an emission of photons, which can be observed as a
change in the magnetic field. 2
In order to perform this experiment a special paramagnetic substance
is required. The substance that is used is 2,2-diphenyl-1-picrylhydrazyl or
DPPH. It is a free radical that is relatively stable and contains an unpaired
electron on the nitrogen chain (see fig 1).This electron contributes almost
zero orbital angular momentum or is “quenched”. This means that the
interaction of this electron with the magnetic field will be entirely from the
spin of the electron.2
Figure 1 DPPH3
This experiment will have three goals. The first is to determine the
magnetic field B0as a function of the resonance frequency. The second will
be to determine the landé splitting factor g. The last is to find the width of
resonance δB0. The rest of this paper will cover the theory, experimental
method, the data, and the results of the experiment.
Theory
The theory of electron spin resonance is based around the angular
momentum of the free electron in the DPPH. Since the electron is
“quenched”, we can assume the orbital angular momentum to be zero. The
spin angular moment whose magnitude is given by
SS=√ss (ss+1)ħ (1)
where the spin quantum number s=½ and ħ is Planck’s reduced constant.
With this we can determine the magnetic moment of the spin given by
μ= gmSħ
=± 12g μB (2)
Where μB= eSm
=12e ħm is the “Bohr magneton” and g is the landé splitting factor
or g-factor. Since we are considering the electron in DPPH a free electron
with no orbital angular momentum the g-factor should be g=2.0023. This
comes from the Dirac function and quantum electrodynamics.2
Using equation (2) we can determine the energy of an electron at a
given spin state using the equation E=− μ⃗ ⋅ B⃗ where B is the magnetic field.
As shown in figure 2 the two possible energy states will be E+12
=12g μB B and
E−12
=−12g μBB and the change in energy is given by Equation 3 where h is
planks constant and v is the resonance frequency.
△E=hv=¿ g μB B (3)
For the purposes of this experiment equation 3 will be used to solve for our
experimental landé splitting factor g.
Figure 2: electron splitting in applied magnetic field3
In order to determine the magnetic field used in equation 3, a
measurement can be taken using a tesla meter or it can be determined by
measuring the DC current using an ammeter. Using the current and the
following equation
B=μ0(45)32 NRI (4)
where μ0is the permeability of free space, N is the number of turns of the
Helmholtz coils, R is the radius of the Helmholtz coils, and I is the current
passing through the Helmholtz coils the magnetic field can be determined.
For our experiment we will use both methods.
In addition to the magnetic field and g factor, the width of resonance
δB is also worth exploring. For the purposes of this experiment, the width of
resonance is a representative of the uncertainty of energy splitting δE. The
uncertainty principle states that you cannot know the exact location and
momentum of an electron at the same time. As your measurement of one
becomes more precise the other becomes less precise. It can be applied as
δ E∗T ≥ ℏ2
where T is the lifetime of the energy state. Using equation 3 we can get the
relation of
δB= ℏ2g μBT
(5)
This equation theoretically proves that the width of resonance is
independent of the frequency.
For the purposing of this experiment the width of resonance will be
determined by taking measurements of the line width at resonance δW , the
Voltage of modulation Umod , and the AC current of the system Imod. The line
width can be converted to a voltage by using the following conversion factor
where δW is the line width.
δU=δW∗0.2 voltscm (6)
From this, a current can be found by using the following equation
δI= δUU mod
∗2√2∗I mod (7)
After obtaining this the width of resonance can be found by inserting this
value into equation 4. Having discussed the mathematics and physics of the
experiment, the experimental method can be explained.
Experimental Method
To perform the experiment the equipment was set up as in figure 3,
described in more detail in the lab manuel4, with the Helmholtz coils at a
distance of R apart (figure 4). Measurements were then made of the DC
current and magnetic field at resonance for a range of frequencies for each
RF probe.
Figure 3 Pasco SE-9634 Electron Spin Resonance Apparatus4 Figure 4
Helmholtz coil setup4
In order to get a sufficient amount of results across the spectrum of
frequencies 3 RF probes were used and measurements of the DC current
were taken using a ammeter . For the large probe 8 measurements were
made at frequencies between 15-35 fMHz . For the medium probe 11
measurements were made between 25-75 fMHz . Finally for the small probe 9
measurements were made between 60-100 fMHz , resulting in 28
measurements being made. These ranges were chosen to cover the range of
measurable frequencies for each RF probe.
In order To find the resonance at each frequency, the DC current was
adjusted so the resonance pulses on the oscilloscope occurred when the AC
current to the Helmholtz coils was zero (fig 5). The current was then
measured using an ammeter.
Figure 5 oscilloscope display screen at resonance. Figure 6 Measurement of Half
Width
The measurements for the magnetic field were made using a tesla meter for
each frequency at the location of the sample. The magnetic field was then
calculated using equation 4 to be compared to the measured values.
In order to determine the landé splitting factor g, the relationship
between the frequency and magnetic field was plotted and from that the
slope of the curve fit was obtained. This slope value vB can be used with
equation 3 in order to solve for g.
Finally, to obtain the width of resonance, a measurement of the line
width of the resonance peak is needed. To do this the oscilloscope was
switched to x-y mode at a frequency of 50 fMHz and the line width was
measured at the half minimum (Fig6) of the peak. A measurement of the AC
current was also taken using the ammeter. Using the line width, AC current,
and the voltage Umod the width of resonance can be determined using
equations 7 and 4.
Data and Analysis
The first set of data (Table 1) shows the measured Magnetic field vs.
the calculated magnetic field. The data shows figures that are very
comparable to each other. Most of the values fall within or just outside the
error bars. This is a good sign that the experimental equipment and
procedure are being used correctly.
Current amps Measured Magnetic Field mT Calculated Magnetic Field mTerror = ±0.01 error = ±0.03 error = ±0.02
