Download Study and Determination of Lande g-Factor of DPPH

DOI 10.4010/2016.884
ISSN 2321 3361 © 2016 IJESC
Research Article
Volume 6 Issue No. 4
Study and Determination of Lande g-Factor of DPPH-Diphenyl
Picryl Hydrazyl using Electron Spin Resonance Spectrometer
Umar Gali Ahmad1, Sulaiman Shukur2, Abdulbasid Ibrahim Ridwan 3
Department of physics
Jodhpur National University, Rajasthan, India
[email protected], [email protected], [email protected]
Abstract:
Since the discovery of electron spin resonance (ESR) by Zaviosky in 1945, the technique has been an inevitable tool for physicist,
chemist and material scientist interested in the properties of solid on an atomic scale. Zavoisky was able to detect faint signals
corresponding to multiple para magnetic species. It involves atom and molecules with unpaired spins of electrons. Such systems
display net magnetic moment and they interact with the applied magnetic field. Electron spin resonance is an important tool in the
field of molecular analysis where free electrons are present. It gives insight to the spin interaction of a substance and therefore its
structure. The technique of electron spin resonance was used to study the lande g- Factor of DPPH (Diphenyl Picryl Hydrazyl) at
different frequencies by varying the current in the Helmholtz coils. From the experiment the lande g- Factor was found to be 1.97
and 1.99 for the frequencies 13MHz and 14MHz. a g- factor of 2.08 and 2.1 was obtained for the frequencies 15MHz and 16MHz.
The theoretical g- Factor for DPPH is 2.0036. The precautions to be taken for more accurate result were also stated.
Key Words: lande’s g- factor, magnetic field of sample at resonance in Gauss and the value of the slope QI.
INTRODUCTION
Electron Spin Resonance (ESR), also known as
electron paramagnetic resonance (EPR) is a special
technique used to investigate and determine the behavior of
semi-free electrons in a paramagnetic material. ESR can be
used to calculate the spin interactions of a substance and
therefore give clues to the structure. The technique is closely
related to Nuclear Magnetic Resonance –the technique used
in MRI machines. The fundamental difference being that
ESR is concerned with the magnetically induced splitting of
electronic spin states and electron has a much larger
magnetic moment and larger energy gap for spin transition
than the nuclei, while NMR describes the splitting of nuclear
spin states. MRI machines however, use the magnetic
moment of the atoms themselves instead of the electron
only. Since few stable molecules have free electrons, the
existence of those that do in a mixture can be detected by
ESR precisely. This can be useful in determining the
existence of free radicals in a material. Electrons have an
intrinsic, quantized spin that results in a magnetic moment.
When an external magnetic field is applied the magnetic
moments of all the electrons align in parallel or antiparallel
with the field. The difference in energy of these two states is
proportional to the magnetic field and determined by
Zeeman splitting. The electrons can be made to flip between
the two energy states with the application of resonant
electromagnetic radiation of the appropriate energy. A free
electron’s resonant frequency will be different from a bound
electron’s. The whole objective of ESR testing is to
determine this difference known as the Lande g-factor.
International Journal of Engineering Science and Computing, April 2016
This study analyzes the almost free electron in Diphenyl
Picryl Hydrazil also called DPPH in short. A nitrogen pair in
the center of the molecule has a trapped electron with no
orbital angular momentum. The magnetic moment of the
molecule is determine only by the spin moment of the
valence in the N- bridge. DPPH has been studied extensively
with ESR because of its ability to absorb free radicals. A
modulated frequency and a varying current flowing through
the Helmholtz coil is used in this dissertation to determine
the g-factor of DPPH as compared to the accepted theoretical
value.
NOMENCLATURE
g=lande g- factor
= magnetic moment
=magnetic field intensity
=magnetic field on the sample at resonance in Gauss
=larmor frequency
e=charge of electron, C
m=mass of electron, kg
c=speed of light, m/s
=resonance frequency, cycle/sec
= energy difference
= bohr magneton, 0.927
h= planck’s constant, 6.625
Hpp= peak to peak magnetic field, gauss/amp
p=total X- plate deflection in oscilloscope, 74.0mm
n= is the number of turns in each coil
a= is the radius of the coil, cm
I= is current in amperes
QI= slope of the graph of Q Vs 1/I
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EXPERIMENTAL SETUP
The following figure shows the block diagram of the ESR setup.
Figure 1.1: block Diagram of the ESR Setup
Description of the ESR spectrometer:
 Basic circuit: ESR spectrometer (model-105), the
circuit consists of critically adjusted radio frequency
oscillator having a frequency range of approximately
10-17MHz.

Phase shifter: this can compensate the undetermined
phase difference which may be introduced in the
amplification stages of the spectrometer and
oscilloscope.

50 Hz sweep unit: For modulation with low frequency
magnetic field, a 50 Hz current flows through the
Helmholtz coils.

Power supply: The Helmholtz coils power consists of
step down transformer (220 to 35V AC).

Helmholtz coils: There are two coils exactly alike and
parallel to each other, connected so that current passes
through them in the same direction. The number of
turns in each coil n=500, diameter of winding a= 7.6cm
and separation of the coil is 7.7cm.

Sample: the test sample, Diphenyl picryl Hydrazyl
(DPPH) is placed in a plastic tube inside the R.F coil.

Oscilloscope: The Oscilloscope for the observation of
ESR resonance has:
Screen diameter
: 12.5 cm
Vertical amplifier sensitivity : 50 m V/cm
Theory
In terms of simple classical concept, let us consider a particle
having a magnetic moment which is placed in a uniform
International Journal of Engineering Science and Computing, April 2016
magnetic field of intensity . Then the moment
precess around
with an angular larmor frequency,
will
………. (1)
g being the lande g- factor(g=1for pure orbital momentum
and g=2 for a free electron spin).
Let us proceed to the quantum picture of elementary
magnetic resonance. Suppose that the intrinsic angular
momentum of the electron couples with the orbital angular
momentum of the electron to give a resultant . We know,
that J+1 magnetic sublevels labelled by the magnetic field
by equal energy difference,
……….
(2)
Between adjacent sublevels where
is the Bohr magneton
(
) and g is the lande factor whose correct
quantum mechanical value is given as,
………. (3)
Also, if a particle is subjected to perturbation by an
alternate magnetic field with a frequency
such that the
quantum h
is exactly the same as the difference between
the levels,
and if the direction of the alternating field is
perpendicular to the direction of the static magnetic field,
then there will be induced transition between neighbouring
sublevels according to the selection rules
for
magnetic dipole radiation
Therefore the resonance condition is
……….
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(4)
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Where
is the resonance frequency. This requirement is
identical with classical condition
.
ii.
Frequency = 14MHz
iii.
Frequency= 15MHz
iv.
Frequency = 16MHz
Therefore, to find the lande’s g factor we use equation (4)
………. (5)
The magnetic field at the center of Helmholtz coil is
. I gauss
………. (6)
Since the current measured is in rms, the magntic field is
also rms. The peak to peak magnetic field will be,
………. (7)
= 168. I gauss/amp.
………. (8)
So the magnetic resonance frequency is
………. (9)
Therefore,
………. (10)
Result and Discussion
The main aim of this paper is to determine the Lande gfactor of DPPH. The result for four different frequencies was
obtained and a graph of Q Vs 1/I was plotted to get the slope
QI for the four frequencies. This was used to calculate the
Lande g-factor of DPPH.
i.
Frequency = 13MHz
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CONCLUSION
The main aim of this research work is to study and
determine the lande g- Factor of DPPH. The slope (QI) of
the frequency versus applied magnetic field was used to
calculate the lande g- Factor of DPPH using different
frequencies. The calculated g- values obtain from the
experiment for the four different frequencies are;
For frequency υ = 13MHz, g = 1.97,
For frequency υ = 14MHz, g = 1.99,
For frequency υ = 15MHz, g = 2.08 and
For frequency υ = 16MHz, g = 2.13
The expected value of g for DPPH is 2.0036. The first three
frequencies (13MHz, 14MHz and 15MHz) give a g value
close to the expected value of g and can be taken as 2.00.
While the fourth frequency (16MHz) has g = 2.13 which is a
bit high but it is still within the experimental uncertainty of
the expected value. I believe this is due to distortions in the
AC main’s wave forms and unstabilised current in the
Helmholtz coils which may change during observations.
From the result obtained one can see that the best possible
resonance peaks are obtained by varying the frequency in the
range of 13 and 14 MHz and the Y sensitivity of the
oscilloscope.
References
1. G. E. Pake, Paramagnetic
Benjamin, 1962).
Resonance,
(W.
A.
2.
Charles P. Poole (1996). Electron spin resonance: a
comprehensive treatise on experimental techniques.
Courier Dover Publications. p. 443. ISBN 0-48669444-5
3.
E. K. Dunn, paper presentation Department of Physics,
University of Kansas, Lawrence, Kansas, USA.
4.
SINGER, J.R., Paramagnetic Resonance, vol.II,
Proceedings of First International Conference,
Jerusalem 16-20July (New York), 577 (1963).
5.
S Eaton, G. Eaton, ‘Electron-Pramagnetic Resonance’,
Ewing’s Analytical Instrumentation Handbook. CRC
Press.2004.
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