Measurement of the Charge of an Electron

Measurement of the Charge of an

Electron

Presented by John Cole

Experiment Conducted by John Cole, Sarmadi Almecki, and Pirouz Shamszad

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.

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 = I R • 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

• Voltage was varied using the potentiometerConstant Temperature, Varying Voltage

• Data was recorded at 294.15K

Procedure Part IIConstant Voltage, Varying Temperature

• Temperature was adjusted via heat pump / refrigerator

• Data was recorded

T

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

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)

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

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

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)

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

• Statistical Limitationslimited data

• ThermometerSingle Degree Accuracy

•Resistor }} accurate to only 2%

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

Improvement

• More Accurate Equipment

• More independent sets of data for statistical improvement

• Attention to detail in circuit construction

• Different Transistors