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![Page 1: Measurement of the Charge of an Electron Presented by John Cole Experiment Conducted by John Cole, Sarmadi Almecki, and Pirouz Shamszad.](https://reader036.fdocuments.us/reader036/viewer/2022083009/5697c0301a28abf838cda9c9/html5/thumbnails/1.jpg)
Measurement of the Charge of an
Electron
Presented by John Cole
Experiment Conducted by John Cole, Sarmadi Almecki, and Pirouz Shamszad
![Page 2: Measurement of the Charge of an Electron Presented by John Cole Experiment Conducted by John Cole, Sarmadi Almecki, and Pirouz Shamszad.](https://reader036.fdocuments.us/reader036/viewer/2022083009/5697c0301a28abf838cda9c9/html5/thumbnails/2.jpg)
Abstract
C on s tan t Tem p era tu reV aryin g V o ltag e
C on stan t Vo ltageVaryin g T em p era tu re
A n a lyzed u s in gE b er-M o lz E q u a tionIc = A [eq V b /kT – 1 ]
Th e m easu rem en t o fth e ch arg e o f an e lec tron
w as ca rried ou t.
![Page 3: Measurement of the Charge of an Electron Presented by John Cole Experiment Conducted by John Cole, Sarmadi Almecki, and Pirouz Shamszad.](https://reader036.fdocuments.us/reader036/viewer/2022083009/5697c0301a28abf838cda9c9/html5/thumbnails/3.jpg)
Theory
• Fundamental Charge
• Townsend
• Millikan’s Oil Drop Experiment
![Page 4: Measurement of the Charge of an Electron Presented by John Cole Experiment Conducted by John Cole, Sarmadi Almecki, and Pirouz Shamszad.](https://reader036.fdocuments.us/reader036/viewer/2022083009/5697c0301a28abf838cda9c9/html5/thumbnails/4.jpg)
Transistor Theory
• Ic = A[eqVb/kT –1] • Ic = collector current
• q = charge (eV)
• Vb = base voltage of the transistor
• K = Boltzman’s Constant
(8.617 342 x 10-5 eV K-1)
• T = temperature in Kelvins
![Page 5: Measurement of the Charge of an Electron Presented by John Cole Experiment Conducted by John Cole, Sarmadi Almecki, and Pirouz Shamszad.](https://reader036.fdocuments.us/reader036/viewer/2022083009/5697c0301a28abf838cda9c9/html5/thumbnails/5.jpg)
Ohm’s Law
V = I R • V = voltage (eV)• I = current (amps)• R = resistance (ohms)
![Page 6: Measurement of the Charge of an Electron Presented by John Cole Experiment Conducted by John Cole, Sarmadi Almecki, and Pirouz Shamszad.](https://reader036.fdocuments.us/reader036/viewer/2022083009/5697c0301a28abf838cda9c9/html5/thumbnails/6.jpg)
Combining the Equations
Vrc = BeqVb/kT • Approximates for the specific voltage greater than 1/40 V
![Page 7: Measurement of the Charge of an Electron Presented by John Cole Experiment Conducted by John Cole, Sarmadi Almecki, and Pirouz Shamszad.](https://reader036.fdocuments.us/reader036/viewer/2022083009/5697c0301a28abf838cda9c9/html5/thumbnails/7.jpg)
Experimental Setup
• NPN transistor 2N3904
• 2 10 turn potentiometer
• Voltage source
• Voltmeter (base)
• Voltmeter (rc)
• Resistors
![Page 8: Measurement of the Charge of an Electron Presented by John Cole Experiment Conducted by John Cole, Sarmadi Almecki, and Pirouz Shamszad.](https://reader036.fdocuments.us/reader036/viewer/2022083009/5697c0301a28abf838cda9c9/html5/thumbnails/8.jpg)
Experimental Setup
•Temperature was varied in the second part using a heat pump & refrigeration device.
•Transistor leads were extended so that it could be remotely placed in the temperature controlling device.
•Mercury thermometer monitored temperature
![Page 9: Measurement of the Charge of an Electron Presented by John Cole Experiment Conducted by John Cole, Sarmadi Almecki, and Pirouz Shamszad.](https://reader036.fdocuments.us/reader036/viewer/2022083009/5697c0301a28abf838cda9c9/html5/thumbnails/9.jpg)
Procedure Part I
• Voltage was varied using the potentiometerConstant Temperature, Varying Voltage
• Data was recorded at 294.15K
![Page 10: Measurement of the Charge of an Electron Presented by John Cole Experiment Conducted by John Cole, Sarmadi Almecki, and Pirouz Shamszad.](https://reader036.fdocuments.us/reader036/viewer/2022083009/5697c0301a28abf838cda9c9/html5/thumbnails/10.jpg)
Procedure Part IIConstant Voltage, Varying Temperature
• Temperature was adjusted via heat pump / refrigerator
• Data was recorded
T
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Part I: Varying Potential Log Scale
0.0497872
0.135335
0.36788
1
2.71828
7.38905
20.0855
54.598
0.5 0.52 0.54 0.56 0.58 0.6 0.62 0.64 0.66
Vol
tage
Acr
oss
Col
lect
or R
esis
tor
-- V
rc
Vb -- Base to Emitter Voltage
Vrc vs. Vb
e/kT = 31.1452 +/- 1.03
'lab3_electron.dat'
• Logarithmic Scale plotted using gnuplot software
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Part I: Non Log Scale
0
5
10
15
20
25
0.5 0.52 0.54 0.56 0.58 0.6 0.62 0.64 0.66
Vrc
--
Col
lect
or V
olat
ge
Vb -- Base to Emitter Voltage
Vrc vs. Vb
e/kT = 31.1452 +/- 1.03
'lab3_electron.dat'f(x)
![Page 13: Measurement of the Charge of an Electron Presented by John Cole Experiment Conducted by John Cole, Sarmadi Almecki, and Pirouz Shamszad.](https://reader036.fdocuments.us/reader036/viewer/2022083009/5697c0301a28abf838cda9c9/html5/thumbnails/13.jpg)
Interpretation: Part I
• Slope = q/kt
• Slope value found using method of least squares
• Slop value = 31.1452 +/- 1.03
• Using the equation Vrc = BeqVb/kT
• k and t are constants, solved for q
Fundamental Charge of an Electron 1.2648 e-19 C +/- 4.18 e-21 C
![Page 14: Measurement of the Charge of an Electron Presented by John Cole Experiment Conducted by John Cole, Sarmadi Almecki, and Pirouz Shamszad.](https://reader036.fdocuments.us/reader036/viewer/2022083009/5697c0301a28abf838cda9c9/html5/thumbnails/14.jpg)
Part II: Log Scale
0
10
20
30
40
50
60
70
0.0029 0.003 0.0031 0.0032 0.0033 0.0034 0.0035 0.0036 0.0037
Vol
tage
Acr
oss
Col
lect
or R
esis
tor
-- V
rc
1/T (K -̂1)
Vrc vs. 1/T
'lab3_electron_temp.dat' using 5:3
![Page 15: Measurement of the Charge of an Electron Presented by John Cole Experiment Conducted by John Cole, Sarmadi Almecki, and Pirouz Shamszad.](https://reader036.fdocuments.us/reader036/viewer/2022083009/5697c0301a28abf838cda9c9/html5/thumbnails/15.jpg)
Part II: Non Log Scale
0
2
4
6
8
10
12
14
16
18
20
0.0029 0.003 0.0031 0.0032 0.0033 0.0034 0.0035 0.0036 0.0037
Vol
tage
Acr
oss
Col
lect
or R
esis
tor
-- V
rc
1/T (K -̂1)
Vrc vs. 1/T
qV(b)/k = -6411.11 +/- 247.8
'lab3_electron_temp.dat' using 5:1f(x)
![Page 16: Measurement of the Charge of an Electron Presented by John Cole Experiment Conducted by John Cole, Sarmadi Almecki, and Pirouz Shamszad.](https://reader036.fdocuments.us/reader036/viewer/2022083009/5697c0301a28abf838cda9c9/html5/thumbnails/16.jpg)
Interpretation: Part II
• Slope found using method of least squares
• Value of 6411.11 +/- 247.8
• slope = qVb/k
Fundamental Charge of an Electron 1.7703 e-19 C +/- 6.842 e-21 C
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Error
• Voltmeters » Vc = 1/100 V» Vb = 1/1000 V
• Statistical Limitationslimited data
• ThermometerSingle Degree Accuracy
•Resistor }} accurate to only 2%
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Conclusion
1.7703 e-19 C +/- 6.842 e-21 C
1.2648 e-19 C +/- 4.18 e-21 CPart I :
Part II:
Average 1.3175 e-19C +/- 5.511e-21C
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Improvement
• More Accurate Equipment
• More independent sets of data for statistical improvement
• Attention to detail in circuit construction
• Different Transistors
![Page 20: Measurement of the Charge of an Electron Presented by John Cole Experiment Conducted by John Cole, Sarmadi Almecki, and Pirouz Shamszad.](https://reader036.fdocuments.us/reader036/viewer/2022083009/5697c0301a28abf838cda9c9/html5/thumbnails/20.jpg)