ZeemanError.pdf

7/27/2019 ZeemanError.pdf

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The Zeeman EffectBenjamin Topper

Lab partner : Clayton S. Ohair

Spring2007 - Dr Hoffmann


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b!tra"tThis report describes the experimental procedure we used to observe and quantify the Zeeman

effect in a mercury atom i.e the splitting of a single spectral line of an atom into three distinct

components when subject to a magnetic field. Results are shown and discussed for the the 54!"

green line splitting and for the 4#4#" violet line splitting.

#ntro$%"tion

&la"e an atom in a magneti" fiel$' an$ a! &ieter (eeman $i"o)ere$ *an$ got the +obel &ri,e in 02

for that $i!"o)ery/' it! !pe"tral line! ill !plit.

1or !ome atom!' they ill !plit into three $i!tin"t !pe"tral line!. Thi! i! "alle$ the normal (eeman

effe"t' an$ it i! that effe"t that a! initially $i!"o)ere$. B%t for other atom!' it t%rne$ o%t that the

!pe"tral line! ere !plitting into more than line!. Thi! "o%l$n3t be e4plaine$ by the theory an$ !o it

a! "alle$ the 5anomalo%!5 (eeman effe"t.

The 5anomaly5 a! !ol)e$ hen the "on"ept of ele"tron !pin a! f%lly %n$er!too$ an$ in"orporate$int he theory.

The green 68ng!trom! line of the mer"%ry e are !t%$ying "orre!pon$! to the anomalo%!

(eeman effe"t 9 it !plit! into "omponent! :

8 "omponent! for ;m-

"omponent! for ;m


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4perimental &ro"e$%re

!"hemati" of o%r e4periment :

The alignment i! tri"@y' !o e %!e$ a la!er to ma@e !%re that e)erything a! at the !ame height an$

properly aligne$.

The light from the Hg lamp goe! thro%gh the len!' hi"h fo"ali,e! it on the 1abry-&erotinterferometer. The 1abry-&erot !harpen! the image an$ ma@e! it "ir"%lar' then it goe! in the

tele!"ope' that e %!e to magnify the image. D%e to a bro@en eyepie"e' e are %!ing a len! right in

front of the "amera in!tea$ of the original eypie"e of the tele!"ope.

Thi! te"hniE%e or@! perfe"tly' an$' a! e ill !ee later' alloe$ %! to )ie the hole image of the

ring! *more than 7ring! at B


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The "ar$boar$ on the right i! %!e$ to a)oi$ any refle"tion : e only ant the light $ire"tly pro$%"e$

by the Hg lamp to be !ent on the len!.

!heet a! al!o %!e$ to "o)er the hole apparat%!. ! e !a on the image!' it "o%l$ greatly

re$%"e refle"tion! *e!pe"ially refle"tion from e4ternal on the tele!"ope bo%n"ing ba"@ on the "amera

that ere "reating )ery bright !pot! on the image/.

The mer"%ry lamp an$ the ele"tromagnet

The ele"tromagnet range! from 0 to 0 mp!' hi"h t%rn$ o%t to be beteen 0 an$ 6@a%!!

appro4imately.

?e are %!ing a polari,er to !ele"t the !pe"tral line! e ant to !ee. ! alrea$y e4plaine$ in theintro$%"tion' e are !ele"ting the ;m


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4perimental re!%lt! analy!i!

#n thi! part are !hon an$ $i!"%!!e$ o%r e4perimental re!%lt!.

O%r fir!t ta!@ a! to "alibrate the ele"tromagnet' a! e)erything i! in$i"ate$ in mp! an$ e ant

o%r $ata to be in a%!! *to be able to "ompare it ith theory ea!ily/.

A/ Calibration of the electromagnet

I!ing a magneti" probe *hi"h or@! %!ing the Hall effe"t/' e ere able to mea!%re the magneti"

fiel$ beteen the to magnet! *i.e. here the Hg lamp/.

The relation t%rn! o%t to be linear *a! e4pe"te$/ : B=1.41*I. O%r )al%e! !eem higher than the one!from pre"e$ent re!%lt!. #t !eem! that they ha$ not been %!ing the probe properly an$ $i$n3t p%t it!

!%rfa"e perpen$i"%lar to the file$ *BJmea!%re$ i! proportional to the fl%4 going thro%gh the !%rfa"e

of the probe' therefore if the probe i! parallel to B' BJmea!%re$ ill be 0/.

B/ Observing the fll rings s!litting

O%r ne4t ta!@ a! to ob!er)e the !plitting. ! in$i"ate$ in the progre!! report' e ha$ lot! of

tro%ble! getting f%ll image! of the ring!. ?e finally fo%n$ o%t that repla"ing the eyepie"e by an

e4ternal len!' e "o%l$ get really goo$ image! really ea!ily. O%r fir!t image! only !ho the fir!t 2

ring!' an$ barely the r$ one. ?e are no able to get the 8 fir!t ring! perfe"tly an$ almo!t all the

7th one' hi"h i! a )ery goo$ impro)ment * # $on3t thin@ it i! po!!ible to !ee any more ring! !imply

be"a%!e of the !i,e of the 1abry-&erot/.


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B < 0 @a%!!

+o line! !plit

B < 8 @a%!!

Line! are !tarting to !plit

C/ E"tracting the reslts

O%r ne4t ta!@ a! of "o%r!e to e4tra"t !ome re!%lt! from tho!e pi"t%re!.

Thi! a! $one %!ing gimp' a! !hon belo :

1ir!t' yo% ha)e to open the image %!ing gimp.

Then' !ele"t the tool to mea!%re 3angle an$ $i!tan"e!3 an$ %!e it to mea!%re the $i!tan"e from the

"enter of the ring! to the inner one.

Kepeat that for e)ery image *i.e for $ifferent )al%e! of B/ 9 a! the ring !plit!' yo% get mea!%rment!

for ea"h image *for ea"h )al%e of B/ : the ra$i%! of the inner ring' of the o%ter ring' an$ of the

"entral ring.

Tho!e to table! !ho o%r re!%lt!' fir!t a table to !ho the )al%e!' an$ then a plot !hoin )ery

"learly the per"entage of in"rea!e or $e"rea!e in the $i!tan"e *the initial )al%e being 00/ a! a

f%n"tion of the magneti" fiel$ B *in @a%!!/ :


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B #$gass% Inner ring #& of initial 'istance% Oter ring #& of initial 'istance%

.60 08.8

2. 0.

.60 . 0.

6 .8 0.76.26 7.6 .2

6.76 8. .

8.2 6.2 8

8.76 .2 7.

7 2. .

7.6 . .

7.7 20.

.6 7. 20.

. 7. 22.

.6 78.2 22.

0.8 78 2.2

7.7 2.7

2.8 72.2 27

O%ter ring

2 4 6 8 10 12

90

100

110

120

130

Be!t fit : 2.7724=00

Central ring -no graph-

O!"illate! beteen 7. an$ 02..

! it !ho%l$ be "on!tant' e

get )ery E%i"@ly an i$ea of

o%r e4perimental %n"ertainty*F2.M/

#nner ring

2 4 6 8 10 12

70

80

90

100

Be!t fit : -2.774=00

Theory tell! %! that the to !lope!' in ab!ol%te )al%e' !ho%l$ a$$ %p t% .870-6 "m->a%!!.

The !lope! here are per"entage an$ in @a%!!-' !o :

*2.772M=2.7M/0- < 4.()* 1)+, cm+1/-assith a 2.M %n"ertainty on that re!%lt.


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/ iolet lines

I!ing another filter' it i! po!!ible to ma@e mea!%rment! for other ring! than the green one :

B #$gass% Inner ring #& of initial 'istance% Oter ring #& of initial 'istance%

.60 0 7

6 2

7 77 27

.6 76 2

7 0

O%ter ring

2 4 6 8 10 12

110

120

130

140

150

Be!t fit : 2.6624=00

Central ring -no graph-

O!"illate! beteen an$ 08..

! it !ho%l$ be "on!tant' e

get )ery E%i"@ly an i$ea of

o%r e4perimental %n"ertainty

*F7M/

#nner ring

2 4 6 8 10 12

60

70

80

90

100

Be!t fit : -2.604=00

The !lope! here are per"entage an$ in @a%!!-' !o :

*2.6M=2.66M/0- < ,.14* 1)+, cm+1/-assith a 7M %n"ertainty on that re!%lt.?e !ho%l$ fin$ .87' hi"h i! at the limit of o%r e4perimental error.


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0mmar an' Conclsion

#n the progre!! report' # ha$ li!te$ the major problem! e ha$ :

The ring! are !till too $im

O%r opti"al !et%p $oe!n3t !eem to be )ery goo$ if e ant a f%ll pi"t%re of the $iffra"tion patter.

?e ha)e tro%ble! fi4ing the !enior lab "amera on the tele!"ope' therefore the eb"am i! really

"on)enient to ha)e imme$iate image! an$ $atapoint!.

?e greatly impro)e$ the brightne!! of the image an$ it! !i,e *!eeing all the ring!/ by "hanging the

eyepie"e an$ p%tting an e4ternal len! $ire"tly in front of the "amera.

The a""%ra"y of o%r mea!%rment! a! of 6M an$ it i! no of 2.M *by ta@ing more $atapoint! an$

ma@ing !harper image! allo! %! to ma@e better mea!%rment! on gimp/ on the green ring!. O%r

mea!%rment! ere in )ery goo$ agreement ith the theory.

?hat e ante$ to $o' b%t t%rne$ o%t to be more $iff%"lt than e4pe"te$' a! to ma@e inten!ity

mea!%rment! 9 a! gimp $i$n3t !eem to or@ )ery ell on that *the re!%lt! # got $i$ not ma@e any

!en!e 9 it !eem! that it $epen$! more on hi"h pi4el yo% !ele"te$ that the a"t%al e)ol%tion of

inten!ity that yo% "an mea!%re.../' e $e"i$e$ to ma@e $i!tan"e mea!%rment! on other ring! : )iolet

ring!.

#t t%rne$ o%t to be a $iffi"%lt ta!@ : the ba"@gro%n$ noi!e i! !tronger than for the green line!' an$

they are $immer 9 hoe)er' o%r re!%lt! ere !till in agreement ith theory.


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2ore !ictres

1%ll fing! ith no filter 9 B


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3eferences

http:>>en.i@ipe$ia.org>i@i>(eemanJeffe"t

http:>>galileo.phy!.)irginia.e$%>"la!!e!>7>,eeman>,eeman.html

#ntro$%"tion to N%ant%m e"hani"! - Da)i$ P. riffith!

&re)io%! lab report!

ZeemanError.pdf

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