Measurement of the Charge of an Electron - 2112

Measurement of the Charge of an Electron - 2112

Measurement of the Charge of an Electron Presented by John Cole Experiment Conducted by John Cole, Sarmadi Almecki, and Pirouz Shamszad Abstract T h e m e a s u re m e n t o f t h e c h a r g e o f a n e le c t r o n w a s c a r r ie d o u t . A n a ly z e d u s in g E b e r - M o lz E q u a t io n Ic = A [e q V b /k T 1 ]

C o n s ta n t T e m p e ra tu re V a r y in g V o lt a g e C o n s ta n t V o lta g e V a ry in g T e m p e ra tu re Theory Fundamental Charge Townsend Millikans Oil Drop Experiment Transistor Theory Ic = A[eqVb/kT 1]

Ic = collector current q = charge (eV) Vb = base voltage of the transistor K = Boltzmans Constant (8.617 342 x 10-5 eV K-1) T = temperature in Kelvins Ohms 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 Voltage Across Collector Resistor -- Vrc 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 Vrc -- Collector Volatge 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 Voltage Across Collector Resistor -- Vrc 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 Voltage Across Collector Resistor -- Vrc 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

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