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CONTENTS

Experiment objectives: ................................................... 4

 Abstract: ........................................................................ 4

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History: .......................................................................... 4

Historical importance of this experiment:..............................................4

Technological importance of this experiment:........................................4

Introduction: .................................................................. 4

What are cathode rays? .................................................. 5

Properties of cathode rays:..................................................................5

Theory: .......................................................................... 5

Experimenta detais: ...................................................... !

The mean and its standard error:..........................................................7

"e#ections o$ Eectrons in an Eectric %ied: .................... &

e'm Apparatus: ............................................................... &

E(uipment: .................................................................... &

The e/m T!e:......................................................................................"

The Helmholt# $oils:............................................................................"

The $ontrols:......................................................................................."

$loth Hood:........................................................................................."

%irrored &cale:...................................................................................."

&olenoid:............................................................................................."

'heostat:............................................................................................"

(oltmeter:...........................................................................................")mmeter:............................................................................................"

)*ometer+mltimeter:........................................................................10

 Additiona E(uipment )eeded: ...................................... *+

Experimenta ,rocedure ................................................ *+

,-ipment needed:............................................................................10

&et p:..............................................................................................10

arning:...........................................................................................10ata ac-isition.................................................................................10

$alclations and )nalysis:..................................................................11

-bservations and cacuations: ...................................... **

)t (oltage1"0*olts..........................................................................11

)t (oltage200*olts:.........................................................................11

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)t (oltage210*olts:.........................................................................12

)t (oltage220*olts:.........................................................................12

)t (oltage20*olts:.........................................................................1

)t $onstant crrent 1 ):...................................................................1

)t $rrent1.1 ):..............................................................................14

)t $rrent1.2 ):..............................................................................15

)t $rrent1. ):..............................................................................1

)t $rrent1.4 ):..............................................................................17

The %ean (ale 3or $onstant (oltage:................................................1

The %ean (ale 3or $onstant $rrent:................................................1

%ean (ale:.......................................................................................1

)ctal (ale f e/m:...........................................................................1

Percentage ,rror:...............................................................................1"

oncusion: ................................................................... */T0o 1impe "emonstrations: ......................................... */

Improvin2 Experimenta 3esuts: ................................... */

%easrement of e/m..........................................................................1"

Notes.............................................................................................................................. 19

,recautions: ................................................................. +

 Appendix: ..................................................................... +

EXPERIMENT OBJECTIVES:

Measure the ratio of the eletro! harge"to"#ass ratio e$# %& stu'&i!g t

eletro! tra(etories i! a u!ifor# #ag!eti )el'.

*BSTR*CT:

I! this e+,eri#e!t the e-et of %oth eletro!i a!' #ag!eti )el'

eletro! is o%sere' a!' %& #a/i!g use of these )el's o! eletro!0 harge

#ass ratio e$#2 of eletro! a! also %e alulate'. The harge o! eletro! a! %e #easure' %& usi!g oth

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Charge

to

#ass

ratio

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#etho's0 3Milli/a! oil 'ro, #etho'40 %ut #ass of eletro! a!!ot %e #easure' usi!g other #etho's. So 5e u

this e+,eri#e!t. The alulate' alue of e$#0 5hih is 1.67 8 111 $/g.

ISTOR;:

ISTORIC*< IMPORT*NCE O= TIS EXPERIMENT:

I! 1>96 J. J. Tho#so! ,erfor#e' a series of 5i'e"ra!gi!g e+,eri#e!ts 5ith far"reahi!g o!se?ue!es t

@'isoer& of the eletro!@2. These results 5ere ruial to the 'eelo,#e!t of the u!'ersta!'i!g of t

eletrial ,ro,erties of #atter. is e+,eri#e!ts o!)r#e' that the s,ee' of the eletro!s is sig!i)a!tl& le

tha! that of eletro#ag!eti 5aes0 A a!' gae a! e$#2 of a%out ti#es larger tha! that of a &'rog

ato# io!ie' i! a! eletrol&sis e+,eri#e!t. It 5as !ot o%ious at the ti#e 5hether the large harge to #a

ratio 5as a o!se?ue!e of a s#all #ass0 5ith the sa#e u!it of harge that 5as i!stru#e!tal i! eletrol&sis0

5hether it 5as o5i!g to a large i!tri!si harge. Dhat he 5as a%le to sho5 5as that this !e5 ,artile0 5ith

harateristi harge"to"#ass ratio 5as a o!stitue!t of eer& #aterial that he 5as a%le to utilie as a atho'

This i!'e,e!'e!e sho5e' that the ,artiles of the %ea# are a o##o! o!stitue!t of #atter0 5hih 5e !

all the eletro!.

TECNO

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D*T *RE C*TOFE R*;SL

If a gas sa#,le is i!tro'ue' i!to the regio! %et5ee! t5o harge' ,lates0 a urre!t o5 a! %e o%sere

suggesti!g that the ato#s hae %ee! %ro/e! 'o5! i!to harge' o!stitue!ts. The soure of these harg

,artiles is a heate' atho'e that0 i! fat0 auses the ato#s of the sa#,le to io!ie. These 5ere /!o5!

atho'e ra&s. I! 1>960 Tho#so! set out to ,roe that the atho'e ra&s ,ro'ue' fro# the atho'e 5e

atuall& a strea# of !egatiel& harge' ,artiles alle' eletro!s. See =igure 1.> i! the te+t%oo/ for Tho#so

e+,eri#e!tal setu,2. =ro# Ma+5ellGs theor&0 he /!e5 that harge' ,artiles oul' %e 'eete' i! a #ag!e

)el'.

PROPERTIES O= C*TOFE R*;S:

There 5ere a !u#%er of results gathere' oer the &ears %& atho'e ra& tu%e researhers.

a. If a! o%(et is ,lae' i! the ,ath of the atho'e ra&0 a sha'o5 of the o%(et is ast o! the glo5i!g tu

5all at the e!'. This sho5e' that the atho'e ra&s traele' i! straight li!es.%. The atho'e ra& a! ,ush a s#all ,a''le 5heel u, a! i!li!e0 agai!st the fore of grait&. This sho5

that the atho'e ra& arrie' e!erg& a!' oul' 'o 5or/.. The atho'e ra& is 'eete' fro# a straight li!e ,ath %& a #ag!eti )el'0 suggesti!g that the t5o 5e

relate' i! so#e 5a&. The 'isoer& of this e-et i! 1> ,re'ates %& so#e te! &ears the u!i)atio!

eletriit& a!' #ag!etis# %& Ja#es Cler/ Ma+5ell.'. *lthough there 5as so#e s,eulatio! that the atho'e ra&s 5ere !egatiel& harge'0 it is !ot sho5! to

true %& e+,eri#e!t u!til 1>90 (ust t5o &ears %efore Tho#so! a!!ou!es the eletro!.e. J.J. Tho#so! is the )rst i!'ii'ual to suee' i! 'eeti!g the atho'e ra& 5ith a! eletrial )el'. e '

so i! 1>96. The atho'e ra&s %e!' to5ar' the ,ositie ,ole0 o!)r#i!g that atho'e ra&s is !egati

harge'.

TEOR;:

  If a !arro5 %ea# of eletro!s #oi!g 5ith o!sta!t s,ee' %e ,ro(ete' i!to a #ag!eti )el'

'irete'0 sa&0 i!to the ,la!e of the ,a,er20 a o!sta!t fore = !or#all& o! eah eletro! a!' #a/es the %ea#

#oi!g i! a irular ,ath of ra'ius r. the fore = ,roi'es the !eessar& e!tri,etal fore a!' is gie! %&:

= Be..12

Ce!tri,etal fore mv

..2

Dhere0 0 # a!' e are res,etiel& the eloit&0 #ass a!' the harge of the eletro!A B is the #ag!eti )el'

a!' r0 the ra'ius of the irular ,ath. E?uatio! 12 a!' 2 5e get :

Bev=m v

e=

  v………………………(3)

No5 i! this e+,eri#e!t the eletro! %ea# is o%tai!e' %& heati!g a atho'e eletriall&2 a!' aelerati!g the

eletro!s gie! of %& it through a ,ote!tial 'i-ere!e of V olts a,,lie' %et5ee! the atho'e a!' a! a!o'e

o!tai!i!g a s#all ori)e through 5hih the eletro! %ea# issues out. The %ea# is #a'e isi%le %& the

,rese!e of a gas i! the tu%e at lo5 ,ressure. as ato#s are e+ite' %& the olli'i!g eletro!s a!' e#it light

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e!a%li!g us to see the ,ath of the %ea#2. The /i!eti e!erg& gai! %& the eletro!s i! falli!g through the

,ote!tial V is gie! %&:

eV =   m v2 … … … … … … …..(4)

*ssu#i!g0 of ourse0 that eletro!s o#e out of the atho'e 5ith ero eloit& atuall& the eloit& 'istri%ut

is #a+ 5ellia!2.

=ro# e?uatio! 2 5e hae:

v2=

  e

v =  2 eV 

… … … … … … … … .(5)

Su%stituti!g the alue of fro# 2 i!to 20 5e get

e=

2eV 

m

e2

2=

2  e

m.V 

2 2

e

m=

2 2

This is the relatio! that 5e i!te!' to use to alulate e$#.

EXPERIMENT*< FET*I

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Curre!t I2 fro# a %atter& is ,asse' through the oils o!!ete' i! series2 a!' a! %e o!trolle' %& a rheos

a!' #easure' %& a! a##eter. The #a+i#u# allo5e' urre!t is a#,eres.

The oltage V2 a!' the urre!t I2 shoul' %e so a'(uste' that the ,ath of the %ea# %eo#es a irle. This 5

%e ,ossi%le o!l& 5he! the #ag!eti )el' is set e+atl& ,er,e!'iular to the i!itial 'iretio! of the %ea# i.e.0

it o#es out of the a!o'e. The 5iri!g o!!etio!s are !ot 'iQult to lear! a!' &ou shoul' o!sult the i!stru

for this ,ur,ose.

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σ =  ( x i− ́ x)

The sta!'ar' error of the #ea! is the!0

S . E ( ́ x )=  σ 

;ou shoul' also ,lot a gra,h %et5ee! a!' r /ee,i!g I o!sta!t2 a!' see that it is li!ear.

FE=96. * %ea# of eletro!s is aelerate' through a /!o

,ote!tial0 so the eloit& of the eletro!s is /!o5!. * ,air of el#holt oils ,ro'ues a u!ifor# a

#easura%le #ag!eti )el' at right a!gles to the eletro! %ea#. This #ag!eti )el' 'eets the eletro! %eai! a irular ,ath. B& #easuri!g the aelerati!g ,ote!tial V20 the urre!t to the el#holt oils I20 a!' t

ra'ius of the irular ,ath of the eletro! %ea# r20 e$# is easil& alulate': e$# V$Br. The e$# a,,arat

also has 'eetio! ,lates that a! %e use' to 'e#o!strate the e-et of a! eletri )el' o! the eletro! %ea

This a! %e use' as a o!)r#atio! of the !egatie harge of the eletro!0 a!' also to 'e#o!strate ho5

osilloso,e 5or/s. * u!i?ue feature of the e$# tu%e is that the so/et rotates0 allo5i!g the eletro! %ea# to

orie!te' at a!& a!gle fro# "9 'egrees2 5ith res,et to the #ag!eti )el' fro# the el#holt oils. ;ou

therefore rotate the tu%e a!' e+a#i!e the etor !ature of the #ag!eti fores o! #oi!g harge' ,artil

Other e+,eri#e!ts are also ,ossi%le 5ith the e$# tu%e. =or e+a#,le0 &ou a! use a s#all ,er#a!e!t #ag!

i!stea' of the el#holt oils to i!estigate the e-et of a #ag!eti )el' o! the eletro! %ea#.

EHIPMENT:

TE E$M THBE:

The e$# tu%e is )lle' 5ith heliu# at a ,ressure of 1" ## g0 a!' o!tai!s a! eletro! gu! a!' 'eet

,lates. The eletro! %ea# leaes a isi%le trail i! the tu%e0 %eause so#e of the eletro!s olli'e 5ith heliu

ato#s0 5hih are e+ite' a!' the! ra'iate isi%le light. The heater heats the atho'e0 5hih e#its eletro!

The eletro!s are aelerate' %& a ,ote!tial a,,lie' %et5ee! the atho'e a!' the a!o'e. The gri' is h

,ositie 5ith res,et to the atho'e a!' !egatie 5ith res,et to the a!o'e. It hel,s to fous the eletr

%ea#.

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TE E + 1" tesla$a#,ere.

TE CONTRO

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Po5er Su,,lies: 7"9 VFC U * ri,,le 1W2 for el#holt oils.

7. VFC or V*C for )la#e!t 1"

VFC aelerati!g ,ote!tial

Meters: *##eter 5ith " * ra!ge to #easure urre!t i! el#holt oils.

Volt#eter 5ith " V ra!ge to #easure aelerati!g ,ote!tial.

EXPERIMENT*< PROCEFHRE

EHIPMENT NEEFEF:

e$# a,,aratus0 igh Voltage Po5er su,,l& for the aelerati!g oltage a!' the )la#e!t heater20 D ,o5

su,,l& for the el#holt oils20 t5o 'igital #ulti #eters.

SET HP:

The 5iri!g 'iagra# for the a,,aratus is sho5! i! =ig. I#,orta!t: Fo !ot tur! a!& e?ui,#e!t u!til a! i!stru

hae he/e' &our 5iri!g.

*e,ta%le ,o5er su,,lies setti!gs: Eletro! u!$)la#e!t eater 7 V *C.

Eletro'es 1 to V FC

el#holt Coils 79 V FC ri,,le shoul' %e less tha! 1W2

D*RNIN:

The oltage for a )la#e!t heater shoul' !eer e+ee' 7. V*C. igher alues a! %ur! out )la#e!t. T

el#holt urre!t shoul' NOT e+ee' a#,s. To aoi' ai'e!tal oershoot ru! the ,o5er su,,l& at a 3lo

setti!g i! a o!sta!t urre!t #o'e.

F*T* *CHISITION

Slo5l& tur! the urre!t a'(ust /!o% for the el#holt oils lo/5ise. Dath the a##eter a!' ta/e a

that the urre!t is less tha! *. Dait seeral #i!utes for the atho'e to heat u,. Dhe! it 'oes0 &ou 5ill see the eletro! %ea# e#er

fro# the eletro! gu!. Its tra(etor& %e ure' %& the #ag!eti )el'. Rotate the tu%e slightl& if &ou see a!& s,irali!g of the %ea#. Che/ that the eletro! %ea# is ,aralle

the el#holt oils. If it is !ot0 tur! the tu%e u!til it is. Fo!Yt ta/e it out of its so/et. *s &ou rotate t

tu%e0 the so/et 5ill tur!. Measure#e!t ,roe'ure for the ra'ius of the eletro! %ea# r: =or eah #easure#e!t reo

*elerati!g oltage V Curre!t through the el#holt oils

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=or eah of the four V setti!gs alulate the #ea! e$# Z0 the sta!'ar' 'eiatio! [ a!' the sta!'a

error. *re these #ea!s o!siste!t 5ith o!e a!other suQie!tl& that &ou a! o#%i!e the# L Calulate the #ea! for all e$# rea'i!gs0 its sta!'ar' 'eiatio! [ a!' the sta!'ar' error..

S,eif& ho5 this #ea! o#,ares to the ae,te' alue.

=i!all&0 ,lot the 'ata i! the follo5i!g 5a& 5hih shoul'0 reeal a li!ear relatio!shi,: ,lot V o! t

or'i!ate \&"a+is] ersus rB$ o! the a%sissa \+"a+is]. The o,ti#al slo,e of this o!)guratio! of 'a

shoul' %e e$# Z. Feter#i!e the slo,e fro# &our ,lot a!' its error. Fo &ou hae a!& alue

i!tere,tL Dhat 'o &ou e+,etL

OBSERV*TIONS *NF C* .7 1.1 1.>+1" 1.177+1"

7

1.6+111

.6> .9 1. 1.>+1" 1.7>+1"

7

1.+111

.6 .66 1. 1.+1" .6+1"

7

1.>+111

.61 .6 1. 1.7+1" .79+1"7 1.17+11

1

*erage Value of e$# 1.9+111 C$Kg

*T VO .6 1 9.>+1" 9.7+1"

6

.6+11

1

.>6 . 1.1 1.7+1" 1.1+1"

7

1.1>+11

1

.>1 .> 1. 1.+1" 1.1+1"

7

1.6+11

1

.66 .>> 1. 1.6+1"

1.9>+1"

7

1.7+11

1

.61 .> 1. 1.7+1"

.79+1"

7

1.17+11

1

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*erage Value of e$#1.>>+111 C$Kg

*T VO.+1"

7.>9+1"

6

.>+111

.9> .9 1.1 9.91+1"

>.>7+1"

6

1.96+111

.>9 . 1. 1.11+1"

1.9+1"

7

1.77+111

.>> . 1. 1.+1" 1.+1"

7

1.1+111

.6 .6 1. 1.7+1" .+1"

7

1.+111

*erage Value of e$#1.69+111 C$Kg

*T VO.+1"

7.+1"

6

.+111

.9 .6 1.1 9.61+1" 9.+1"

6

.7+111

.>6 .6 1. 1.1+1" 1.+1"

7

1.6+111

.> .6 1. 1.6+1

"

1.7+1

"

7 1.>+1

11

.> .1 1. 1.+1" .+1"

7

1.6+111

*erage Value of e$# 1.>1+111 C$Kg

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*T VO 1.1 .7+1

".>+1

"6.17+111

.9 . 1. 1.1>+1

"1.+1

"71.>+111

.> . 1. 1.>+1

"1.7+1

"71.9+111

.6 .76

1. 1.9+1

".+1

"71.+111

.66 .> 1. 1.77+1

"

.67+1

"7

1.17+1

11

*erage Value of e$# 1.91+111 C$Kg

*T CONST*NT CHRRENT 1 *:

No 'ia#eter#2

ra'ius#2

Volts2 BT2 B e$#

1 .>1 .6 16 1.9+1"7

1.1+1"

1

1.9+11

1

.91 .6 1> 9.177+1"

>.+1"

6

.6+11

1

.9 .6 >.>+1" 6.6>+1"

6

.+111

.9 .6 1 >.+1" 6.7+1"

9

.6+111

.9> .9 6.9+1" 7.+1"6

.1+111

*erage Value of e$# .176X111 C$Kg

Page 1 of 20

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17J 16J 1>J 19J BJ B1J BBJ1.7

1.6

1.>

1.9

B

B.1

B.B

B.I

B.P

B.J

s?uare of ra'ius &"a+is

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17J 16J 1>J 19J BJ B1J1.7

1.>

B

B.B

B.P

B.7

B.>

I

Era,h %$5 rB a!' oltage

*T CHRRENT1. *:

No 'ia#eter#

2

ra'ius

#2

Volts2 BT2 B e$#

1 .> . 16 1.166+1"

1.>+1"7 1.+11

1

.> . 1> 1.+1" 1.+1"7 1.+11

1

.> . 19 1.19+1" 1.1>+1

"7

1.+11

1

.>7 . 1.16+1" 1.6+1"7 1.>+11

1

.97 .7 1 1.>+1" 1.19+1"7 1.77+11

1

*erage Value of e$# 1.7+111 C$Kg

Page 15 of 20

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17J 16J 1>J 19J BJ B1J1.P

1.7

1.>

B

B.B

B.P

Era,h %$5 rB a!' oltage

*T CHRRENT1. *:

No 'ia#eter

#2

ra'ius

#2

Volts

2

BT2 B e$#

1 .6 .6 1> 1.6+1

".17+1

"71.1+111

.66 .> 19 1.+1

".+1

"71.6+111

.> .1

1.+1"

1.6+1"7

1.+111

.> .

1 1.9+1

"1.76+1

"71.1+111

.> . 1.9+1

"107>+1

"71.>+111

 

*erage Value of e$# 1.+111 C$Kg

Page 1 of 20

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16J 1> 1>J 19 19J B BJ B1 B1J BB BBJ1.IJ

1.PJ

1.JJ

1.7J

1.6J

1.>J

1.9J

Era,h %$5 rB a!' oltage

*T CHRRENT1. *:

No 'ia#eter

#2

ra'ius

#2

Volts

2

BT2 B e$#

1 .6 .

1> 1.77+1

".6+1

"71.+111

.61 .6 19 1.7+1

".79+1

"71.11+111

.69 .9 1.69+1"

.1+1"7

1.16+111

.67 .> 1 1.+1

".>+1

"71.+111

.>1 . 1.9+1

".+1

"71.+111

*erage Value1.7+111 C$Kg

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16J 1> 1>J 19 19J B BJ B1 B1J BB1.B

1.I

1.P

1.J

1.7

1.6

Era,h %$5 rB a!' oltage

TE ME*N V*

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  *tual alue 1.6+111C$/g

PERCENT*E ERROR:

*tual alue of e$# 1.6+111C$/g

O%sere' alue of e$# 1.7 X111C$Kg

Pere!tage error c ua va ue−   serve va ue  8 1

  6.>W

CONCW #ista/e. I 'eli%eratel& ,erfor#e' this test0 &et there is #ista/

there are 'isti!tie 5ells,ri!gs of %lu!'ers roo# is!Gt o#,letel& 'ar/0 ali%ratio!0 #easuri

'isa,,oi!t#e!t i! #easuri!g the 'ia#eter a!' so o!2. Su%se?ue!t to ,erfor#i!g this e+a#i!atio! 5e

'isoer the harge to #ass ,ro,ortio! of the eletro!. This is #ost i#,eratie i!estigatio! to 'isoer har

to #ass ratio of eletro!.

TDO SIMP

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PREC*HTIONS:

 The #ag!eti )el' shoul' %e set e+atl& ,er,e!'iular to the eletro! %ea#.

 The high oltage su,,l& shoul' !ot %e s5ithe' o! u!til all the o!!etio!s hae %ee! he/e' %& t

i!strutor.  The #eters shoul' %e set o! their a,,ro,riate ra!ges %efore 5iri!g the# i! the iruit.

 The oltage to the heater of the eletro! gu! shoul' NEVER e+ee' 7. olts0 u!less !ote' other5ise

tu%e. igher oltages 5ill %ur! out the )la#e!t a!' 'estro& the e$# tu%e.  ;ou 5ill %e 5or/i!g 5ith high oltage. Ma/e all o!!etio!s 5he! ,o5er is o-. Tur! ,o5er o- %efo

ha!gi!g$re#oi!g o!!etio!s. Ma/e sure that there is !o loose or o,e! o!tats.

*PPENFIX:

,lectric 6eld:

The s,ae arou!' a harge' ,artile 5here a!other test harge feels attratio! or re,ulsio! suh )el' is al

eletri )el'.

%agnetic 6eld:

The regio! surrou!'i!g a urre!t arr&i!g o!'utor suh regio! is sai' to %e #ag!eti )el'.

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. 6sman usta$a 7roup 5 89eader

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