electron spin resistance.doc

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ELECTRON SPIN RESONANCELast Revised: July 2007

QUESTION TO BE INVESTIGATED

How can we measure the Land g factor for the free electron in DPPHas redicted !y "uantum mechanics#

INTRODUCTION

$lectron sin resonance %$&R' is a useful tool for investigating the

energy a!sortion sectra of many materials with unaired electrons

%aramagnetic materials'( )n this la! e*ercise you will e*lore the a!sortion

of a aramagnetic molecule( + aramagnetic material has an electronic

structure that leaves an electron in a state such that it does not have a

artner of oosite sin( ,his imlies that the molecule will have an intrinsic

magnetic diole moment(

,his e*eriment will allow you to verify the "uantum mechanical model

used to descri!e the aramagnetic system( -ou will !e a!le to o!serve the

a!sortion !ehavior of the electron. as well as determine the Land g factor

associated with this system(

THEORY

$&R is a urely "uantum mechanical effect( )t relates the interaction of

an e*ternal magnetic field to an electron/s magnetic moment. which is a

result of its intrinsic sin( &ince the sin of an electron may either !e u or

down. so may its magnetic moment( ,his imlies that. in the resence of an

e*ternal magnetic field. one sin state will !e higher in energy than the

other( ore secifically. the sin with a moment ointing in the direction of

the e*ternal field is lowest in energy( ,hese states have an energy E. as

either

%1'


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here gis the Lande/ factor. 3is the 3ohr magneton %a constant'. and

Bis the value of the e*ternal magnetic field( ,hus. the change in energy

from the negative to the ositive sin state can !e written

%2'

,herefore. !ecause g and 3are constants. there are airs of values of

the energy Eand of the e*ternal field Bthat satisfy $"( %2' and result in a

transition of sin states( +t commonly attaina!le magnetic field strengths

the corresonding energy lies in the radio4fre"uency %R5' regime( here the

general e*ression for the energy of a hoton alies

%6'

here Eis the energy of an R5 hoton. his Plan/s constant. and is

the fre"uency of the hoton( hen a hoton of energy Eis incident on an

electron in a field of strength Belectron resonance will !e o!served(

EXPERIMENT

,he electrons that you will maniulate are located in the aramagnetic

molecule Dihenyl4Picryl4Hydra8yl %DPPH'( DPPH is ictured !elow9 notice

the unaired electron( ,his electron is also very wealy !ound to the

nitrogen atom( ,he com!ination of these two roerties maes this

molecule ideal for studying the magnetic roerties of the electron(

,he DPPH has !een loaded onto a iece of cotton and laced inside of

a samle tu!e( ,he samle tu!e should then !e laced in a coil and inserted

into the mount %light grey cylinder in 5igure 2'( onsult the manufacturer/s

manual for any necessary information concerning the setu of this device(


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5igure 2 shows a !loc diagram deicting the e*erimental setu(

,here are essentially two circuits: ,he first controls and monitors the R5

signal driving of the electrons %at left'. and the second controls the e*ternal

magnetic field %right'( -ou should o!serve the outut of the a!sortion of

the DPPH on one channel of the oscilloscoe %D coule the o4scoe channel'

and the voltage across the resistor on the other channel( ,he fre"uency of

the R5 inut can !e selected !y a no! located on the to of the samle4

Figure 1. Sketch of the structure of a DPPHmolecule showing the nitrogen (N) contributing the

free electron.

12 V

- G +

12 V

+ G -

Ch1 Ch2

T Amp

R~1; )?

R5 5re"(

@A, %3?:'

Figure . ! "rawing of the basic elements of the e#$eriment is shown. %he circuit is alsoshown.


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mount !o*( ,his !o* also contains a !ridge circuit to amlify the a!sortion

signal and cancel out the electronics resonance effects(

,he second circuit controls the current running through the Helmholt8

coils. and conse"uently the e*ternal magnetic field( + secial voltage source

is to !e used which alies a ramed signal with a long eriod( ,his signal is

one4half of a triangle wave. whose fre"uency. sign. and amlitude you may

adBust( -ou should o!serve the half triangle on the remaining oscilloscoe

channel !y monitoring the voltage dro across the 1C resistor in this circuit

%see 5igure 2'( Observing tese t!" sign#$s !i$$ #$$"! %"& t" '"rre$#te

te "''&rren'e "( res"n#n'e t" te v#$&e "( te e)tern#$ B (ie$*+

,he urose of the resistor is to limit the current in the circuit and

allow you to o!serve the signal on the oscilloscoe( + measurement of the

resistor/s value and the oscilloscoe trace will allow you to calculate the

current in the coils at any given time(

+s the voltage increases from the triangular current source so does the

current running through the coils. which in turn creates the desired magnetic

field around the samle( +t a secific value of this field %see $"( 2'

resonance will occur and you will see a very o!vious di in the outut of the

R5 device( -ou will see two symmetrical dis. one as the 3 field rams uthrough the value secified !y $"( 2 and another as it descends through this

same value( ,hese dis occur !ecause the electrons are a!sor!ing some of

the hotons( )f you ram the field too "uicly the eas will not !e

symmetric( an you e*lain why this haens# hoose a reetition rate and

raming eriod such that the entire shae of the resonance is seen during

the rams( )t may tae some ractice to achieve the right shae and

reetition rate for the ram(

+ uniform magnetic field can !e reasona!ly achieved using Helmholt8

coils( Helmholt8 coils are comosed of two coa*ial coils of wire searated !y

a distance e"ual to their radii( + derivation of the field from two coils in the

Helmholt8 configuration is in the +endi*( $ach coil should have the same

num!er of windings and the same radius( ,he coils should also have the


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same current running through them %wired in series. 5igure 2'( hen all of

these conditions are met there will !e a volume of nearly uniform field within

the coils( Ase the =aussmeter to rove that the field is uniform over the

length of the samle( How do you thin variations in the field will effect the

resonance of the samle/s electrons#

+t this time you should ause and !ecome more familiar with the

oscilloscoe/s functions9 the manual has !een rovided on the course

we!site( )n addition to the normal voltage and time range adBustments. you

will need to understand how to e*ort data to an e*ternal dis(

,ae resonance data for at least different fre"uencies of R5 radiation(

-ou may wish to utili8e the oscilloscoes averaging function in order to

reduce noise(

agnetic 5ield ali!ration:

,o use $"( %2' you will need to now the value of the magnetic field

where a!sortion occurs( ,his may !e accomlished !y using a =aussmeter(

+ =aussmeter is a long thin ro!e that measures the value of a magnetic

field via the Hall $ffect %which you may e*lore in another e*eriment'(

Remove the DPPH samle and lace the ro!e inside the coils( -ou cano!serve the =aussmeter/s read4out on the oscilloscoe while simultaneously

watching the triangle wave on another channel( ,his will allow you to create

an e*ression for Bas a function of time. or to simly correlate individual

values to true magnetic field strengths(

-ou must also measure the uniformity of the magnetic field( Remove

the samle and measure the field in a hori8ontal line starting 2cm !ehind the

center of the coils to 2cm in front of the coils in 2mm stes( Do the same for

a vertical line starting 1 cm !elow the center and ending 1cm a!ove the

center in stes of 2mm( 5rom each of the data sets. fit a smooth curve to

the field vs( osition( easure the si8e of the samle( Asing the fit curve.

average the field over the length of the samle( Reeat for the vertical

thicness of the samle( Do not include the glass thicness in your averages(


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Divide the results !y the field at the center of the target( ,hese will !e

correction factors that you will need to use in calculating g(

Resonance Data +nalysis:

,o get the value of the field at resonance tae your recorded data and

fit a gaussian lus !acground to your ea( 5it only the voltage values in

the vicinity of the ea( Do not try to fit the full ea shae as it is not

gaussian( ,he centroid of the gaussian is the time at which the resonance

was ma*imum( Ase the chis"uare of the fit to determine the aro*imate

uncertainty in the osition of the centroid(

Ase your fre"uencies and the measured field of each resonance to

calculate the Lande/ g factor and its error(

Reort:

-ou should reort:

- ,he value of the resistor

- ,he field vs( current cali!ration fit %lot re"uired'

- ,he field vs( distance curve and fits %lot re"uired'

- ,he correction factors- + fit of resonance curve you used to arrive at a value for the

magnet current %lot re"uired'

- ,he value of the Lande/ g factor %nominal E 2(006F' for this system

and its error(

- ,he variation in the magnetic field over the area of the DPPH

samle(

+s you have seen. the a!sortion aears as symmetrical dis in an

otherwise constant signal( However. anomalous !ehavior has !een o!served

when the fre"uency of the 3 field source is very low( e have seen the

signal develo a sie trailing the tyical a!sortion waveform. which is of

much higher magnitude than the standard !aseline( ,his henomenon has


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not !een fully investigated. !ut aears to !e intrinsic to this articular

system( ,here are several theories( @ne identifies the culrit as an

unwanted !ehavior of the current ower suly( +nother theory is that there

are resonances in the samle mount that were not corrected for at lower

fre"uencies of the 3 field current( -ou should investigate this !ehavior. as it

is an e*cellent e*amle of the fact that all e*erimental setus have

limitations and !ehaviors that deviate from theory( Determine the ma*imum

field at which this !ehavior occurs and mae sure that your field values are

a!ove this( Reort the ma*imum current where this effect is seen( Provide a

treatment of this issue in your discussion(

+endi*: Helmholt8 Derivation

e wish to derive an e*ression for the strength of the magnetic field B

along the a*is of a air of Helmholt8 coils( e !egin with the e*ression for


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the magnetic field of a single loo along the a*is running through the loo

%from the 3iot4&avart Law':

where 0 is the ermea!ility of the vacuum. Iis the current through the loo. R

is the radius of the coil. andxis any coordinate along the a*is of the two

coils( However. our Helmholt8 coils are not single coils. !ut consist of n

num!er of single turns. thus yielding:

e will lace our samle halfway in!etween the two coils( ,his setsxto R/2.

!ecause Helmholt8 coils are searated !y a distance e"ual to their radius(

,his su!stitution yields:

!lso& there are two coils so we must "ouble our e#$ression'


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%hus& our $owers of algebra hae le" us to a useful result'

$*tension: )f I = I(t) then you may also may achieve B(I,R,t)(

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