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Measurement of the Charge
of an Electron
Presented by John Cole
Experiment Conducted by John Cole, Sarmadi
Almecki, and Pirouz Shamszad
Abstract
The measurement of
the charge of an electron
was carried out.
Analyzed using
Eber-Molz Equation
Ic = A[eqVb/kT –1]
Constant Temperature
Varying Voltage
Constant Voltage
Varying Temperature
Theory
• Fundamental Charge
• Townsend
• Millikan’s Oil Drop Experiment
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
Ohm’s Law
V=IR
• V = voltage (eV)
• I = current (amps)
• R = resistance (ohms)
Combining the Equations
Vrc = BeqVb/kT
• Approximates for the
specific voltage
greater than 1/40 V
Experimental Setup
• NPN transistor 2N3904
• 2 10 turn potentiometer
• Voltage source
• Voltmeter (base)
• Voltmeter (rc)
• Resistors
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
Procedure Part I
Constant Temperature, Varying Voltage
• Voltage was varied using the potentiometer
• Data was recorded at 294.15K
Procedure Part II
Constant Voltage, Varying Temperature
• Temperature was adjusted via heat pump / refrigerator
• Data was recorded
T
Part I: Varying Potential Log Scale
Vrc vs. Vb
54.598
20.0855
'lab3_electron.dat'
e/kT = 31.1452 +/- 1.03
7.38905
2.71828
1
0.36788
0.135335
0.0497872
0.5
0.52
0.54 0.56 0.58
0.6
0.62
Vb -- Base to Emitter Voltage
• Logarithmic Scale plotted using gnuplot software
0.64
0.66
Part I: Non Log Scale
Vrc vs. Vb
25
20
'lab3_electron.dat'
f(x)
e/kT = 31.1452 +/- 1.03
15
10
5
0
0.5
0.52
0.54
0.56
0.58
0.6
0.62
Vb -- Base to Emitter Voltage
0.64
0.66
Interpretation: Part I
•
Slope value found using method of least squares
•
Slop value = 31.1452 +/- 1.03
• Using the equation Vrc = BeqVb/kT
•
Slope = q/kt
•
k and t are constants, solved for q
Fundamental Charge of an Electron
1.2648 e-19 C +/- 4.18 e-21 C
Part II: Log Scale
Vrc vs. 1/T
70
'lab3_electron_temp.dat' using 5:3
60
50
40
30
20
10
0
0.0029
0.003
0.0031 0.0032 0.0033 0.0034 0.0035 0.0036 0.0037
1/T (K^-1)
Part II: Non Log Scale
Vrc vs. 1/T
20
'lab3_electron_temp.dat' using 5:1
f(x)
18
16
14
12
qV(b)/k = -6411.11 +/- 247.8
10
8
6
4
2
0
0.0029
0.003
0.0031 0.0032 0.0033 0.0034 0.0035 0.0036 0.0037
1/T (K^-1)
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
Error
• Voltmeters
» Vc = 1/100 V
» Vb = 1/1000 V
• Thermometer
Single Degree Accuracy
•Resistor
}}
•
accurate to only 2%
Statistical Limitations
limited data
Conclusion
Part I :
1.2648 e-19 C +/- 4.18 e-21 C
Part II:
1.7703 e-19 C +/- 6.842 e-21 C
Average
1.3175 e-19C +/- 5.511e-21C
Improvement
• More Accurate Equipment
• More independent sets of data for statistical improvement
•
Different Transistors
• Attention to detail in circuit construction