Millikan Plancks Constant Measurement Analysis#10-PHYS442.01

Batuhan Baserdem (2010203105)Department of Physics

Bogazici University, Istanbul, Turkey(Dated: May 30, 2013)

I. ANALYSIS

Millikans data is shown below; This data set was first plotted using ROOT. From the plot functions, a resembling

TABLE I: Measurements of Na

5461 A 4339 A 4047 A 3650 A 3126 A 2535 A

Volts Defl. (mm) Volts Defl. (mm) Volts Defl. (mm) Volts Defl. (mm) Volts Defl. (mm) Volts Defl. (mm)

2.257 28 1.581 44 1.576 82 1.157 67.5 .5812 52 -.0576 68

2.205 14 1.629 20 1.524 55 1.105 36 .5288 29 .0576 38

2.152 7 1.576 10 1.471 36 1.0525 19 .4765 12 .1620 26

2.100 3 1.524 4 1.419 24 1.0002 11 .4242 5 .2670 16.5

1.367 3 .9478 4 .3718 2.5 .3720 8

curve (A(eBx1)+C) was fitted to the results, the C value designed to give the Y-intercept; thus V0. The errors onV values were determined as follows; Millikan states (pg. 365) that the Dolezalek electrometer he has a sensibility of2.5 m per V and the meter can be read to accuracy of .2 mm; which indicates an error on V values is approximately8105 ' 104 V. Due to very high precision (1% on photocurrent deflections and '.0001 on voltage) error bars werenot drawn (they dont display properly anyway) The drawn and fit graphs are in the file. The values and errors ofthe potentials are given as follows. The fit statistics, for convenience; uses peta Hertz (p=1015) as units. Thus whenthe relationship;

E = h (1)

is accepted; plotting V versus pHz allows us to determine the constant h as 1015 times the slope, in terms of eV sec.The data are given below; (Millikan reversed his results for 2532 Awavelength; since he (and we) observed that theapplied voltage was not retarding, but dissociating es. To correct for it; I used the negative value for 2535 Awhen Ifit the line for finding h).

From the slope of the graph (since we are calculating for the retarding potential; the slope is negative;) h isdetermined to be 4.411.035 femto eVsec. (Which is '8 higher than the actual result; 4.135667516(91) but it is stilla very remarkable result) Millikan determined previously in his experiments that the charge of e as 1.59241019C (Actual value being 1.6021764871019 C). If we use this to convert Millikans value to Joule seconds; we get7.0240.056 1034J sec; which is 7 higher that the accepted result with the modern value of e; 6.62606957(29)1034.

The value of h found agrees with modern values certainly; even in a league of 7-8 deviation from the originalresult; there is a great amount of accuracy implied. With statistical analysis tools of today; such calculation caneasily be done on whim; but imagining the difficulty of such practices in the early 20th century certainly is dazzling.Also; the data; although not completely agreed according to ROOTs statistical tools; fits the theory of linear energyrelationship with frequency beautifully.

Appendix A: Coding

The following code was used to analyse the data for the ROOT Framework.

1 f loat Volt5461 [ 4 ] = {2 .257 , 2 . 205 , 2 . 152 , 2 . 1 0 0} ;2 f loat Def l5461 [ 4 ] = { 28 , 14 , 7 , 3} ;34 // f l o a t Volt4339 [ 4 ] = {1.581 , 1.629 , 1.576 , 1 .524} ;5 // f l o a t Def l4339 [ 4 ] = { 44 , 20 , 10 , 4} ;6 f loat Volt4339 [ 3 ] = {1 .581 , 1 . 576 , 1 . 5 2 4} ;

2Deflection (mm)5 10 15 20 25 30

Volta

ge (V

)

2.1

2.12

2.14

2.16

2.18

2.2

2.22

2.24

2.26

Prob 0.973p0

2.152 0.7794 p1

0.01667 -0.006743 Y-Int 0.02885 2.105

Prob 0.973p0

2.152 0.7794 p1

0.01667 -0.006743 Y-Int 0.02885 2.105

5461 Angstroms

(a) 5461 A

Deflection (mm)0 5 10 15 20 25 30 35 40 45

Volta

ge (V

)

1.52

1.53

1.54

1.55

1.56

1.57

1.58

Prob 0.9738p0

0.0282 1.541 p1

0.001078 0.0009893

Prob 0.9738p0

0.0282 1.541 p1

0.001078 0.0009893

4339 Angstroms

(b) 4339 A

Deflection (mm)0 10 20 30 40 50 60 70 80

Volta

ge (V

)

1.35

1.4

1.45

1.5

1.55

Prob 0.9999p0

0.1936 -0.5311 p1

0.003324 0.006786 Y-Int 0.0109 1.352

Prob 0.9999p0

0.1936 -0.5311 p1

0.003324 0.006786 Y-Int 0.0109 1.352

4047 Angstroms

(c) 4047 A

Deflection (mm)0 10 20 30 40 50 60 70

Volta

ge (V

)

0.95

1

1.05

1.1

1.15

Prob 1p0

0.007893 -0.2652 p1

0.003835 0.03868 Y-Int 0.007214 0.9098

Prob 1p0

0.007893 -0.2652 p1

0.003835 0.03868 Y-Int 0.007214 0.9098

3650 Angstroms

(d) 3650 A

Deflection (mm)0 10 20 30 40 50

Volta

ge ( V

)

0.4

0.45

0.5

0.55

0.6

Prob 0.9997p0

0.02495 -0.2331 p1

0.02592 0.05998 Y-Int 0.02569 0.351

Prob 0.9997p0

0.02495 -0.2331 p1

0.02592 0.05998 Y-Int 0.02569 0.351

3126 Angstroms

(e) 3126 A

Deflection (mm)10 20 30 40 50 60 70

Volta

ge (V

)

-0.1

0

0.1

0.2

0.3

0.4Prob 0.9999p0

0.02105 0.6653 p1

0.00315 0.02975 Y-Int 0.01905 0.5175

Prob 0.9999p0

0.02105 0.6653 p1

0.00315 0.02975 Y-Int 0.01905 0.5175

2535 Angstroms

(f) 2535 A

Frequency ( peta Hz)0.5 0.6 0.7 0.8 0.9 1 1.1 1.2

Volta

ge ( V

)

-0.5

0

0.5

1

1.5

2Prob 2.166e-15Slope

0.04248 -4.212 p1

0.03537 4.41

Prob 2.166e-15Slope

0.04248 -4.212 p1

0.03537 4.41

Frequency vs. Voltage

(g) Measuring h

FIG. 1: Graphs of Different Fits

3TABLE II: Stopping potential statistics

Wavelenght (nm) Frequency (pHz) Voltage Error546.1 0.549 2.105 .029

433.9 0.691 1.541 .028

404.7 0.741 1.352 .011

365.0 0.821 .9098 .007

312.6 0.959 .351 .026

253.5 1.183 -.5175 .019

7 f loat Def l4339 [ 3 ] = { 44 , 10 , 4} ;89 f loat Volt4047 [ 5 ] = {1 .576 , 1 . 524 , 1 . 471 , 1 . 419 , 1 . 3 6 7} ;

10 f loat Def l4047 [ 5 ] = { 82 , 55 , 36 , 24 , 3} ;1112 f loat Volt3650 [ 5 ] = {1 .157 , 1 . 105 , 1 .0525 , 1 .0002 , . 9 4 7 8} ;13 f loat Def l3650 [ 5 ] = { 67 . 5 , 36 , 19 , 11 , 4} ;1415 f loat Volt3126 [ 5 ] = { . 5812 , . 5288 , . 4765 , . 4242 , . 3 7 1 8} ;16 f loat Def l3126 [ 5 ] = { 52 , 29 , 12 , 5 , 2 . 5 } ;1718 f loat Volt2535 [ 5 ] = { .0576 , . 0576 , . 1620 , . 2670 , . 3 7 2 0} ;19 f loat Def l2535 [ 5 ] = { 68 , 38 , 26 , 16 . 5 , 8} ;2021 /22 f l o a t Vol tage [ 6 ] = { 2.101 , 1.541 , 1.362 , .9641 , .4396 , .3783} ;23 f l o a t VoltaEr [ 6 ] = { 8.467 e06, 8.573 e6, 8.005 e6, 1.348 e5, 1.846 e5, 8.056 e6};24 /25 f loat Voltage [ 6 ] = { 2 .105 , 1 . 541 , 1 . 352 , . 9098 , . 351 , .5175} ;26 f loat VoltaEr [ 6 ] = { . 02885 , . 0282 , . 0109 , .007214 , . 0257 , . 0 1905} ;27 f loat nanoMet [ 6 ] = { 546 .1 , 433 .9 , 404 .7 , 365 .0 , 312 .6 , 253 .5 } ;2829 int main ( )30 {31 f loat Frequency [ 6 ] ;3233 TGraphErrors graph ;3435 // graph = new TGraphErrors (4 , Defl5461 , Volt5461 ,0 ,0 ) ;36 // graph = new TGraphErrors (3 , Defl4339 , Volt4339 ,0 ,0 ) ;37 // graph = new TGraphErrors (5 , Defl4047 , Volt4047 ,0 ,0 ) ;38 // graph = new TGraphErrors (5 , Defl3650 , Volt3650 ,0 ,0 ) ;39 // graph = new TGraphErrors (5 , Defl3126 , Volt3126 ,0 ,0 ) ;40 //41 graph = new TGraphErrors (5 , Defl2535 , Volt2535 , 0 , 0 ) ;4243 //44 p r i n t f ( \n ) ;4546 for ( int i =0; i S e t T i t l e ( Frequency vs . Voltage ) ;53 graph>GetXaxis ( )>S e t T i t l e ( Frequency ( peta Hz) ) ;54 graph>GetYaxis ( )>S e t T i t l e ( Voltage ( V ) ) ;5556 ///57 /58 graph>Se tT i t l e (2535 Angstroms ) ;59 graph>GetXaxis ( )>Se tT i t l e ( De f l e c t i on (mm) ) ;60 graph>GetYaxis ( )>Se tT i t l e ( Voltage (V) ) ;61 gSty l e>SetOptFit (1011) ;62 TF1 f i t = new TF1(Curve , [ 0 ] (TMath : : Exp(1 [1] x )1)+[2] ,0 ,83) ;

463 f i t >SetParameters ( . 1 , . 0 1 , 2 ) ;64 f i t >SetParName(2 ,YIn t ) ;65 graph>Fi t (Curve ,) ;66 ///6768 TF1 f i t = new TF1( Line , x++1 , 0 , 1 . 3 ) ;69 f i t >SetParName (0 , Slope ) ;70 graph>Draw( A ) ;71 graph>Fit ( Line , R ) ;72 }