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Syllabus 021-025Physics for Science and Engineering Students

Laboratory III

Instructor: TBAOffice Hours:TBA

TA: TBAOffice Hours:TBA

Description: 021-023, 024, 025. General Physics for Science and Engineering Students1, 2, & 3. Lab. 1 cr. ea. Laboratory courses to accompany introductoryphysics courses 021-013, 014 and Introduction to Modern Physics 021-015 respectively.

Physics 025 is the third semester of the calculus based introductorylaboratory physics course intended for science and engineering majors.The course provides laboratory work on experiments dealing withconcepts in modern physics.

Co-Requisite: Students should also be enrolled in Introduction to Modern Physics (021-015)

Goals: The overall goal of this course is to provide the student with theappropriate experimental evidence to reinforce concepts learned inelementary modern physics. Specific objectives are as follows:

1. To develop introductory concepts in modern physics, relativity andquantum mechanics.

2. To develop an understanding of standard techniques of data reductionand error analysis commonly used by introductory physics students.

3. To develop quantitative reasoning skills and analytical thinking asrelated to problem solving in modern physics.

4. To learn proper techniques that are useful for experimental design.

5. To learn proper methods for presentation of scientific results.

Text: Handouts will be provided for each laboratory exercise. No particular textwill be required. Many experimental write-ups will also be availableelectronically.

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References: Theory of Errors, Robert Taylor

Modern Physics by Serway (Required text for 021-015)

Attendance: Attendance is required for all laboratories exercises. Students may notsubmit reports for exercises for which they were not in attendance.Students who arrive to class late will be required to complete the entirelaboratory exercise. Such students will not be permitted to join a groupthat has already started on the laboratory exercise.

Grading: Laboratory Reports 85%Final Exam 15%

A penalty of 5 points per day will be imposed for all late reports. Latereports will not be accepted after 1 week. Students required to make uplaboratories will be required to do so within one week of the date thelaboratory was missed.

Letter Grade:A 90-100%B 80-89.9%C 70-79.9%D 60-69.9%F Below 60%

GENERAL INSTRUCTIONS

Laboratories offer an ideal opportunity to learn and strengthen, by means of actualobservations, some of the principles and laws of physics that are taught to you in physicslectures. You will also become familiar with modern measuring equipment and learn thefundamentals of preparing a report of the results.

1. You are expected to arrive on time since instructions are given and announcementsare made at the start of class.

2. A work station and lab partners will be assigned to you in the first lab meeting. Youwill do experiments in a group but you are expected to bear your share ofresponsibility in doing the experiments. You must actively participate in obtainingthe data and not merely watch your partners do it for you.

3. The assigned work station must be kept neat and clean at all times. Coats/jacketsmust be hung at the appropriate place, and all personal possessions other than thoseneeded for the lab should be kept in the table drawers or under the table.

4. The data must be recorded neatly with a sharp pencil and presented in a logical way.You may want to record the data values, with units, in columns and identify the

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quantity that is being measured at the top of each column.

5. If a mistake is made in recording a datum item, cancel the wrong value by drawing afine line through it and record the correct value legibly.

6. Have your data sheet signed by the instructor before you leave the laboratory. Thiswill be the only acceptable proof that you actually performed the experiment. Acopy of the signed data sheet must be attached to the written report as an Appendix.

7. Each student, even though working in a group, will have his or her own data sheetand submit his or her own written report, typed, for grading to the instructor on thenext scheduled lab session. No late reports will be accepted.

8. Actual data must be used in preparing the report. Use of fabricated, altered, and otherstudents' data in your report will be considered as cheating. No credit will be givenfor that particular lab and the matter will be reported to the Dean of Students.

9. Be honest and report your results truthfully. If there is an unreasonable discrepancyfrom the expected results, give the best possible explanation.

10. If you must be absent, let your instructor know as soon as possible. A missed lab canbe made up only if a written valid excuse is brought to the attention of yourinstructor within a week of the missed lab.

11. You should bring your calculator, a straight-edge scale and other accessories to class.It might be advantageous to do some quick calculations on your data to make surethat there are no gross errors.

12. Eating, drinking, and smoking in the laboratory are not permitted.

13. Refrain from making undue noise and disturbance.

Report Format

Each report should include the following information:

0. Cover sheet - The cover sheer should contain the name of the experiment andyour name as well as the identification of any laboratory partners. Include thedate, the name of the class and the section, the name of the instructor, the name ofthe Teaching Assistant, and your student ID.

1. Introduction - Describe the general nature of the experiment to be performed anddiscuss the objectives of the experiment.

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2. Theory - Review the theoretical basis for the measurements and the calculationsthat you will be making. Present and discuss appropriate formulas.

3. Data Presentation - Present the data that you measured in appropriate data table.Discuss how you obtained the data (The Procedure) as needed.

4. Discussion - Discuss your findings. Describe any pertinent calculation that youmade. Present the results of your calculation in Data Table and in Graphs.Discuss each table and graph presented.

5. Summary - Provide a summary of your findings. Discuss how these findingdeviated from or conformed with your expected results. Discuss the physicsprinciples that were reinforced by the results of your experiment.

6. Questions - Answer the questions presented at the end of the laboratory report.

7. Appendix - Include a copy of the data sheet obtained in the laboratory. This sheetmust have an instructor signature. (That is, a copy of the signed data sheet mustbe attached to the written report as an Appendix.)

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Schedule of Experiments for Fall 1998

Dates Laboratory Exercises025 Section 1025 Section 2 Group A

Mondays Tuesdays

8/24/98 8/25/98 Introduction – Measurements, Statistics andSpreadsheets

8/31/98 9/01/98 Microwave Optics – Double Slit9/07/98 9/08/98 Labor Day9/14/98 9/15/98 Microwave Optics – Bragg Diffraction9/21/98 9/22/98 Precision Interferometer – Wavelength9/28/98 9/29/98 Precision Interferometer – Index of Refraction

10/05/98 10/06/98 Nuclear Radiation I10/12/98 10/13/98 Columbus Day10/19/98 10/20/98 Nuclear Radiation II10/26/98 10/27/98 Planck’s Constant - h/e11/02/98 11/03/98 The Ratio – e/m11/09/98 11/10/98 Critical Potential11/16/98 11/17/98 Superconductivity11/23/98 11/24/98 Optional Experiments*11/30/98 12/01/98 Lab Test

Note: All experiments are due the first class meeting following the completion of theexperiment.

*Optional ExperimentsElectron Spin ResonanceLight Emitting Diode

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Statistical Analysis & Spread Sheets

Background

No physical measurement is exact. One must in general indicate to what degreethe experimenter has confidence in the measurement. Usually this is done by the numberof significant digits. For example, the lengths of 2.76 cm and 3.54x103 cm both havethree significant digits. As a common practice the significant digits will include thosenumbers taken directly from the scale and one estimated place. Additions andsubtractions use only the smallest number of significant figures that is common to all themeasurements, so that the sum of 6.86 + 9.376 + 8.3782 would be 24.62. Formultiplication and division the result should have only as many significant digits as theleast accurate of the factors. The product of 18.76 by 9.57 = 179 since the less accuratefactor has 3 significant digits.

Regardless of how carefully a measurement is made there is some uncertainty inthe measurement. This uncertainty is called an error. Errors are not necessarily mistakes,blunders or accidents. There are two classes of errors, systematic and random. Theyoccur because of problems with the reading of the instrument or because some externalfactor such as temperature, humidity, etc. These errors can be corrected if they areknown to be present. Calibration techniques, attention to conditions surrounding themeasurements, and changing operators are used to reduced system error. The randomerrors are by nature, erratic. They are subject to the laws of probability or chance. It isto such errors that experimental statistics is applied.

The effect of random errors may be lessened by taking a large number ofmeasurements. For a large number of measurement the most probable value of thequantity (the average or mean) is obtained by adding all the readings and dividing by thenumber of readings, taking the mean. The average derivation (a.d.) is obtained by addingthe absolute value of the difference between each reading and the mean and dividing bythe number of readings. The average deviation of the mean (A.D.), sometimes referred toas the “experimental error”, is the average derivation divided by the square root of thenumber of observations (A.D.). The standard deviation is also measure of the uncertaintyof a measurement. When values are quoted for measurements as a value ± anothernumber, the second number is usually the A.D., the average derivation of the mean, e.g. x± A.D., or the standard deviation, e.g. x ± σ

The usual experimental procedure is to make a large number of measurements.For this course you will normally make several measurement of each quantity andcalculate an average and A.D. or σ. Frequently you will compare your measurements toknown values or the a value calculated from a straight forward derivation. The lattercomparison is made by calculating the percentage error. The percentage error is thedifference between the “standard value” and the “experimental value” divided by the“standard value” and multiplied by 100%.

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Data Tables

All data tables should be properly labeled with a title for the table, headings foreach column and description of the information in the table..

Title of Table Here

Calculated Quantity Formula

average deviation a.d . =1

Nx i − x

i =1

N

∑ , for N measurements of the quantity xi

average deviation of the mean A.D. =a.d.

N

average or mean x =1

Nxi

i=1

N

∑

standard deviation

σ =xi − x( )2

i=1

N

∑N −1

=x i

2 −x i

i =1

N

∑

2

Ni =1

N

∑N − 1

percentage error %error =x − xa

xa

• 100% , where xa is the accepted value

Least Squares Fit:(y = a + bx) b =

N xiyii =1

N

∑ − xi =1

N

∑ yii =1

N

∑

N x i2 − x i

i =1

N

∑

2

i =1

N

∑; a =

xi2

i=1

N

∑ yii =1

N

∑ − xii =1

N

∑ xiyii =1

N

∑

N xi2 − x i

i =1

N

∑

2

i =1

N

∑= y − bx

Least Squares Fit:(y = bx), i.e. the origin is (0,0) b =

xiyii =1

N

∑xi

2

i= 1

N

∑; a = 0

Table 1. (Place a description of the information in the table here.)

Graphs

All graphs should follow the format given below. A description of the graph should beplaced immediately after the graph.

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10864200

10

20

30

Graph Title

X Axis Lable (units)

Y A

xis

Lab

le (

unit

s)

y = - 1.5 + 2.6x

Plot Symbols

Error Bars

Equation of Least Squares Fit Line Y=Intercept +Slope*X

Least Squares Fit Line

Graph 1: (Place a statement here that describes the graph and its corresponding dataimmediately after the graph.)

Note: These simulations we have developed are written using EXCEL. The student mayuse other spreadsheets or computer graphics programs to complete these exercises ifhe/she so chooses.

Exercise # 1 for 021-025 Experiment I

The student should run Simulation #1 on the worksheet named SIMULATION in theExcel Program PHYIIIEXPI. The program is for a black box that generates numbers andshows the value of the number and its corresponding index (sequence) on displays in thesimulation. The number are selected randomly from a known parent distribution with amean of ten (10) and a standard deviation of two (2).

1. Generate a minimum of 30 numbers by clicking on the NEXT READING button.

2. Record the INDEX and each corresponding VALUE in the worksheet namedANALYSIS.

3. Using EXCEL Spreadsheet FUNCTIONS, determine the following:(a) average

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(b) average deviation(c) average deviation of the mean(d) standard deviation(e) median(f) range of data

4. Compute the percentage error from the known value for the mean

5. Present the data and results in appropriately labeled tables on your EXCELSpreadsheet.

Excel Worksheet for Simulation #1

Exercise for 021-025 Introductory Laboratory

The student should run Simulation #2 on the worksheet named SIMULATION in theExcel Program PHYIIIEXPI. The program is for a simulated counting experiment inwhich the SAMPLE (a point source) is located at a variable distance from theDETECTOR. The operator controls the distance between the SAMPLE PLATFORMand the DETECTOR by clicking the UP or DOWN buttons. The distance (in cm)between the SAMPLE PLATFORM and the DETECTOR is displayed on a button in thesimulation. The simulated signal is given as counts per second received by theDETECTOR and are displayed on a button in the simulation. The simulated signals areselected randomly from a Gaussian distribution with a known mean and standarddeviation. These numbers are corrected so that the signal is inversely proportional to thesquare of the distance between the DETECTOR and the SOURCE. A small offset isapplied to this correction to account for the typical situation where there is someunknown distance between the front of the detector housing and its active elements. Asmall background count is also accounted for in the simulation.

1. Generate a DETECTOR reading in Counts/s for every cm from 1 to 20 cm.Control the separation by using the UP and DOWN buttons.

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2. Record the SEPARATION and each corresponding DETECTOR READING inthe worksheet named ANALYSIS.

3. Using EXCEL graphics, graph a log-log plot of DETECTOR READINGS vs.SEPARATION. Be sure to properly label your graph.

4. Plot the best fit straight line to your graphical data using Least Squares Analysistechniques. Built in Functions in EXCEL can do this.

5. Verify the 1/r2 relationship by comparing the value of the slope for your straightline to the expected value of two (2).

6. Compute the percentage error from the known value for the mean

7. Present the data, graph and results in appropriately labeled tables and graphs onyour EXCEL Spreadsheet.

Excel Worksheet for Simulation #2

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INTERFEROMETRY: MEASUREMENT OF WAVELENGTH∗

INTRODUCTION

In general, an interferometer can be used in two (2) ways. If thecharacteristics of the light source are accurately known (wavelength,polarization, intensity), changes in the beam path can be introduced andthe effects on the interference pattern can be analyzed. On the otherhand, by introducing specific changes in the beam path, information canbe obtained about the light source that is being used. In this experiment,you will use the interferometer to measure the wavelength of your lightsource (laser).

In the interferometer arrangement, the distance that the movablemirror moved toward the beam-splitter is given by dm. If N fringetransitions are observed in the diffraction pattern, as the position of the“movable” mirror is changed, then the wavelength of the light source isgiven by

λ = 2dm/N (1)

PROCEDURE

1. Align the laser and interferometer in the Michelson mode, so aninterference pattern is clearly visible on your viewing screen. SeeFigure 1.

2. Adjust the micrometer knob to a medium (approximately 50 µm).In this position, the relationship between the micrometer readingand the mirror movement is most nearly linear.

3. Turn the micrometer knob one full turn counterclockwise. Continueturning counterclockwise until the zero on the knob is aligned withthe index mark. Record the micrometer reading.

NOTE: When you reverse the direction in which you turn themicrometer knob, there is a small amount of give before the mirror

∗ Taken from PASCO Scientific laboratory write-ups

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begins to move. This is called mechanical backlash, and is presentin all mechanical systems involving reversals in direction ofmovement. By beginning with a full counterclockwise turn, andthen turning only counterclockwise when counting fringes, you caneliminate errors due to backlash.

4. Adjust the position of the viewing screen so that one of the markson the millimeter scale is aligned with one of the fringes in yourinterference pattern. You will find it easier to count the fringes ifthe reference mark is one or two fringes out from the center of thepattern.

5. Rotate the micrometer knob slowly counterclockwise. Count thefringes as they pass your reference mark. Continue until somepredetermined number of fringes have passed your mark. (Count20 fringes for your first trial.). As you finish your count, the fringesshould be in the same position with respect to your reference markas they were when you started to count. Record the final readingof the micrometer dial.

6. Record dm, the distance that the movable mirror moved toward thebeam-splitter according to your readings of the micrometer knob.Each small division on the micrometer knob corresponds to one µm(10-6 meters) of mirror movement.

7. Record N, the number of fringe transitions that you counted.

8. Repeat steps 3 through 7 five times, increasing N by 5 counts eachtime.

Analysis

For each trial, calculate the wavelength of the light, using equation (1),then average your results. Complete the data table below. Determinethe Average and standard deviation of the data. Compare your resultsfor the wavelength to the known wavelength for the laser used in theexperiment.

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Table 1. Wavelength Determination

Trail N dm (µm) λ (µm)

1

2

3

4

5

Average

Standard

Deviation

% error

Questions

1. In the calculation to determine the value of λ based on themicrometer movement, why was dm multiplied by two?

2. Why move the mirror through many fringe transitions instead ofjust one? Why take several measurements and average the results?

3. If the wavelength of your light source is accurately known,compare your results with the known value. If there is a difference, towhat do you attribute it?

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4. When measuring mirror movement using the micrometer dial onthe interferometer, what factors limit the accuracy of your measurement?

Viewing Screen

BeamSplitter

Adjustable Mirror

AdjustmentScrews

MovableMi r ror

Compensator(optional)18 mm Lens

Laser

Micrometer Knob

Figure 1. Experimental Layout

Figure 2. Experimental Setup

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THE INDEX OF REFRACTION OF GLASS∗

INTRODUCTION

One method to measure the index of refraction of glass is to slowlyvary the length of glass through which the interferometer beam passes.This experiment introduces a technique for making such a measurement.

In principle, the method for calculating the index of refraction isrelatively straight forward. The light passes through a greater length ofglass as the plate is rotated. One thus determines the change in pathlength of the light beam as the glass plate is rotated. Then determinehow much of this change in path length is through glass dg(θ) and howmuch is through air da(θ). The relationship between the measured fringetransitions (N) and the change in path length is given by

N =2na da(θ) + 2ngdg (θ )

λo

(1),

where na = index of refraction of air,ng = index of refraction of glass plate, andλo = wavelength of the light source in vacuum.

It can then be shown that for a plate of thickness t, the index ofrefraction is given by

ng =

2t − Nλo( ) 1− cosθ ( )2t 1− cosθ ( ) − Nλo

(2),

Light Principles and Measurements, Monk,McGraw-Hill, 1937.

PROCEDURE

1 Align the laser and interferometer in the Michelson mode. SeeFigure 1.

2. Place the rotating table between the beam-splitter and movablemirror, perpendicular to the optical path.

∗ Taken from PASCO Scientific laboratory write-ups

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NOTE: if the movable mirror is too far forward, the rotating table won’tfit. You may need to loosen the thumbscrew and slide themirror farther back.

3. Mount the glass plate on the magnetic backing of the rotationalpointer.

4. Position the pointer so that its “0” edge on the Vernier scale islined up with the zero on the degree scale on the interferometerbase.

5. Remove the lens from in front of the laser. Hold the viewing screenbetween the glass plate and the movable mirror. If there is onebright dot and some secondary dots on the viewing screen, adjustthe angle of the rotating table until there is one bright dot only.Then realign the pointer scale. The plate should now beperpendicular to the optical path.

6. Replace the viewing screen and the lens and make any minoradjustments that are necessary to get a clear set of fringes on theviewing screen.

7. Slowly rotate the table by moving the lever arm. Count the numberof fringe transitions that occur as you rotate the table from 0degrees to an angel θ = 5 degrees.

8. Repeat the procedure above for rotations of θ through 0 to 10degrees, 0 through 15 degrees and 0 through 20 degrees.

DATA ANALYSIS

Complete Table 1 below. Determine the average value of the indexof refraction for the glass plate and the standard deviation in this value.

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Table 1: Experiment Results for Index of Glass Plate

Trial θ max (degrees) N ng

1

2

3

4

Average

Standard Deviation

QUESTIONS:

1. Explain any trends or differences for the four differencemeasurements you made, i.e. 0<θ<5, 0<θ<10, 0<θ<15, and 0<θ<20. Is itbetter to use a small angle or a large angle of this experiment? Why?

2. Starting with equation 1, derive equation 2.

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Viewing Screen

BeamSplitter

AdjustmentScrews

MovableMi r ror

18 mm Lens

Laser

Micrometer Knob

Adjustable Mirror

-5

30

0

Rotational Pointer

Glass plate

Figure 1. Experimental Layout

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DOUBLE SLIT INTERFERENCE∗

INTRODUCTION:

When an electromagnetic wave passes through a two-slit aperturethe wave diffracts into two waves which superpose in the space beyondthe apertures. Similar to a standing wave pattern, there are points inspace where maxima are formed and others where minima are formed.With a double slit aperture, the intensity of the wave beyond the aperturewill vary depending on the angle of detection. For two thin slitsseparated by a distance d, maxima will be found at angles such that

d sinθ = nλ (1)

and minima will be found at angles such that

d sinθ = nλ/2, (2)

where θ = the angle of detection, λ = the wavelength of the incidentradiation, and n is any integer. See Figure 1. Refer to a textbook formore information about the nature of the double-slit diffraction patternand the derivations of equations (1) and (2).

PROCEDURE:

1. Arrange the equipment as shown in Figure 2. Use the Slit ExtenderArm, two Reflectors, and the Narrow Slit Spacer to construct the doubleslit. (Use a slit width of about 1.5 cm.) Be precise with the alignment ofthe slit and make the setup as symmetrical as possible.

2. Adjust the Transmitter and Receiver for vertical polarization (0°)and adjust the Receiver controls to give a full-scale reading at the lowestpossible amplification.

3. Rotate the Goniometer arm, on which the Receiver rests, slowlyabout its axis. Observe the meter readings.

∗ taken from PASCO Scientific laboratory write-ups

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4. Reset the Goniometer arm so the Receiver directly faces theTransmitter. Adjust the Receiver controls to obtain a meter reading of1.0. Vary the angle θ for every two degrees from 0 to 80 degrees. Ateach setting record the meter reading. (In places where the meterreading changes significantly between angle settings, you may find ituseful to investigate the signal level at intermediate angles.)

5. Keep the slit widths the same, but change the distance betweenthe slits by using the Wide Slit Spacer instead of the Narrow Slit Spacer.Because the Wide Slit Space is 50% wider than the Narrow Slit Spacer (90mm vs. 60 mm) move the Transmitter back 50% so that the microwaveradiation at the slits will have the same relative intensity. Repeat themeasurements.

ANALYSIS:

1. Present your data in an appropriate data. From your data, plot agraph of meter reading versus θ. Identify the angles at which the maximaand minima of the interference pattern occur. Be certain to label yourgraph properly.

2. Calculate the angles at which you would expect the maxima andminima to occur in a standard two-slit diffraction pattern. Refer toequations (1) and (2). Determine the percentage error between thecalculated maxima and minima and the locations of your observed maximaand minima

3. Plot a graph of sinθ vs. n for your data at each maximum observed.Determine the best fit straight line for your data with the constraint thatthe intercept is located at the origin. Given this constrain the slope ofthe best fit line is given by

b =xiyi

i =1

N

∑xi

2

i =1

N

∑. (3)

QUESTIONS:

1. What assumptions are made in the derivation of equation (1) andto what extent are these assumptions met in this experiment?

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2. Derive equation (1).

Transmitter

d θ

Receiver

Figure 1. Double Slit Interference

Transmitter

Receiver

Double Slit

Figure 2. Equipment Setup.

NOTES:1. Wavelength at 10.525 GHz = 2.85 cm2. The experimenter’s body position may affect the results.

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Figure 3. Photo of Setup

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Ratio of e/m

Introduction

The Specific Charge of Electron Apparatus is used in conjunction with theElectron Tube to measure the ratio of electron charge e to electron mass m. Anelectron stream is accelerated through a measured potential difference. Thestream is projected through, and perpendicular to, a magnetic field of sufficientstrength to cause it to bend in a circular path. The value of e/m can be computedfrom the relationships that exist among the acceleration potential, the strength ofthe magnetic field, and the diameter of the circular path that the electron beamdescribes.

From the definition of the magnetic induction B in a magnetic field, the force Facting upon a charge e that is moving with velocity v perpendicular to thedirection of the field is given by

F = BeV. (1)

Since the direction of this force is always perpendicular to the velocity vector, itfollows that the force is a centripetal one. Such a force causes the electron withmass m to move in a circular path. Hence,

mv2

r= BeV, (2)

where r is the radius of the circular path of the electron. The kinetic energyacquired by an electron that falls through a potential difference V is given by

eV =

mv2

r. (3)

From equations (2) and (3)

em

=2V

B2r2(4)

Note that since the cathode “gun” is located about 0.254 cm below the anodeplate opening the part of the equation involving the radius has a constantnumerical factor added.

em

=2V

B2 r2 + 0.00254 2( ) . (5)

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The apparatus used in this experiment makes it possible to determine the ratioe/m. The magnitude of the flux density B, caused by the Helmholtz coils at thecentral point is given by

B =

8µoNI

125R, (6)

where N is the number of turns per coil, I the current in the coils and R the coilradius and µo the permeability of free space.

Procedure

6. Explore the area around the Helmholtz coils to see that there is no seriousinterference from stray magnetic fields. This can be done with a compassor a gaussmeter.

7. Connect the apparatus as shown in Figure 1. Check that the anodes ofthe grid and plate are referenced to the cathode of filament. HAVEINSTRUCTOR CHECK SETUP!

8. Adjust the filament current to about 0.9 amps. The e/m base is designedsuch that 0.9 amperes supplied to the base yields 0.6 amps to the tubefilament. After allowing the cathode to heat for about 1 minute, apply theplate potential and grid potential and notice the blue stream of electronsthat rises from the hole in the center of the disk. Then reduce the filamentcurrent to the minimum level that still yields a visible beam. Adjust theplate potential to 80-200 volts and vary the grid potential to bring the beaminto sharp focus. The electron stream should have a diameter of about2 mm or less.

9. Energize the circuit to the field coils and then increase the current until thebeam bends into a complete semicircle. Adjust the plate voltage to varythe accelerating potential and change the field current until the beam fallson one of the marked circles. (The grid potential may need to be adjustedwhen the plate potential is changed in order to keep the beam in focus.)Record the plate potential, the field current, and the radius of thedescribed circle(.5, 1.0, 1.5, 2.0 cm). Measure the mean radius of theHelmholtz coils and record the number of turns per coil (119).

10. Repeat the observations by switching the field current polarity to obtainseveral sets of data for each of the circles on the disk. Depending on theanode plate voltage applied, it may be impossible to focus the beam onthe innermost circle.

Analysis

Using the data recorded from the experiment and the working equation, calculatethe values of e/m obtained from the sets of observations. Record the percentagedifference between the standard value of e/m and the mean of the values

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calculated from the observations. Do there seem to be sources of systematicerror? Try to identify some of the sources of error.

Data Table for e/m Experiment

Number of Turns per Coil (N) =Radius of Coil (R) = m

Positive Polarity

Radius of Inscribed Circle(cm)

0.5 1.0 1.5 2.0

Radius of electron beam,r (cm

Field Coil Current, I(amps)

Plate Potential, V (volts)

Magnetic Field, B (tesla)

e/m (coulombs/meter)

Reversed Polarity

Radius of Inscribed Circle(cm)

0.5 1.0 1.5 2.0

Radius of electron beam,r (cm

Field Coil Current, I(amps)

Plate Potential, V (volts)

Magnetic Field, B (tesla)

e/m (coulombs/meter)

Average value for e/m(coulombs/meter)

Percentage Error

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Figure 1. Box Diagram for wiring the e/m tube.

E&M Apparatus

Filament Cathode

Plate

Grid

6.3 VAC 0-80VDC

80-200VDC

Field Coils0-20VDC

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Photoelectric Effect Using the h/e Apparatus

Introduction

In photoelectric emission, light strikes a material, causing electrons to be emitted.The classical wave model predicted that as the intensity of incident light wasincreased, the amplitude and thus the energy of the wave would increase. Thiswould then cause more energetic photoelectrons to be emitted.

The new quantum model, however, predicted that higher frequency light wouldproduce higher energy photoelectrons, independent of intensity, while increasedintensity would only increase the number of electrons emitted(or photoelectriccurrent).

In the early 1900s several investigators found that the kinetic energy of thephotoelectrons was dependent on the wavelength, or frequency, andindependent of intensity, while the magnitude of the photoelectric current, ornumber of electrons was dependent on the intensity as predicted by the quantummodel.

Explaining the photoelectric effect in terms of the quantum model, we see that

Where E is the energy of the photon, h is Planck’s constant, ν is the frequency,KEmax is the maximum kinetic energy of the emitted photoelectrons and Wo is theenergy needed to remove the electrons from a material’s surface.

Experiment 1.

According to the photon theory of light, the maximum kinetic energy, KE, ofphotoelectrons depends only on the frequency of the incident light, and isindependent of the intensity. Thus the higher the frequency of the light, thegreater its energy.

In contrast, the classical wave model of light predicted that KE would depend onlight intensity. In other words, the brighter the light, the greater its energy.

This lab investigates both of these assertions. Part A selects two spectral linesfrom a mercury light source and investigates the maximum energy of thephotoelectrons as a function of the intensity. Part B selects different spectrallines and investigates the maximum energy of the photoelectrons as a function ofthe frequency of the light.

E = hν = KEmax + W0

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Part A

11. Adjust the h/e Apparatus so that only one of the spectral colors falls uponthe opening of the mask of the photodiode. If you select the green oryellow spectral line, place the corresponding colored filter over the whitereflective mask on the apparatus.

12. Place the Variable Transmission Filter in front of the White Reflectivemask so that the light passes through the section marked 100% andreaches the photodiode. Record the DVM voltage reading.

13. Press the instrument discharge button, release it and observeapproximately how much time is required to return to the recorded voltage.

14. Move the variable Transmission Filter so that the next section is directly infront of the incoming light. Record the new DVM reading, andapproximate the time to recharge after the discharge button has beenpressed and released.

15. Repeat step 4 until you have tested all five sections of the filter.16. Repeat the procedure using a second color from the spectrum.

Part B

(g) You can easily see five colors in the mercury light spectrum. Adjust the h/eApparatus so that only one of the yellow colored bands falls upon theopening of the mask of the photodiode. Place the yellow colored filter overthe White Reflective Mask on the h/e Apparatus.

(h) Record the DVM voltage reading(stopping potential).(i) Repeat the process for each color in the spectrum. Be sure to use green

filter when measuring the green spectrum.

Experiment 2.

According to the quantum model of light, the energy of light is directlyproportional to its frequency. Thus, the higher the frequency, the more energy ithas. With careful experimentation, the constant of proportionality, Planck’sconstant, can be determined.In this lab you will select different spectral lines from mercury and investigate themaximum energy of the photoelectrons as a function of the wavelength andfrequency of the light.

Procedure

1. You can see five colors in two orders of the mercury light spectrum.Adjust the h/e Apparatus carefully so that only one color from the firstorder falls on the opening of the mask of the photodiode.

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2. For each color in the first order, measure the stopping potential with theDVM and record that measurement. Use the yellow and green coloredfilters on the Reflective mask of the h/e Apparatus when you measure theyellow and green spectral lines.

3. Move to the second order and repeat the process.

Analysis

After graphing stopping potential vs. frequency can you get a result for h/e andW/e? Also can you calculate h and W?

Questions

8. Describe the effect that passing different amounts of the same coloredlight through the variable Transmission Filter has on the stopping potentialand thus the maximum energy of the photoelectrons, as well as thecharging time after pressing the discharge button.

9. Describe the effect that different colors of light had on the stoppingpotential and thus the maximum energy of the photoelectrons.

10. Defend whether this experiment supports a wave or a quantum model oflight based on your results.

11. Explain why there is a slight drop in the measured stopping potential asthe light intensity is decreased.

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The Photoelectric Effect Using Light Emitting Diodes

The photoelectric effect is the emission of electrons from a metallic surface bythe incidence of a beam of light. The maximum kinetic energy of the ejectedphotoelectrons depends only on the frequency of the light and the kind of metalused. For a particular metal, there is a definite cutoff frequency υo below whichno photoelectric effect occurs.

Theory:

Light can be viewed as a series of discontinuous, concentrated packages ofenergy, called photons. The energy of a single photon is given by E = hυ, whereE is the quantum energy, υ is the frequency and h is Planck's constant. In thephotoelectric process a whole quantum of radiant energy is absorbed by a singleelectron. In addition, a certain amount of energy is required to liberate theelectron from the metal; and any extra energy that the electron absorbs goes toincrease the kinetic energy of the photoelectron. Applying the principle of energyconservation, Einstein arrived at the photoelectric equation:

hυ = W + (1/2) mv2

where W is the work function of the metal and (1/2) mv2 is the kinetic energy of theejected electron. Here m is the mass of the electron and v is the maximumvelocity of the photoelectron.

When an electron is accelerated by a potential difference V, the kinetic energy ofthe electron is given by:

(1/2) mv2 = eV

where e is the charge on the electron. A large enough negative potential differencewill stop the flow of the fastest-moving electrons between electrodes and isknown as the stopping potential. In terms of the stopping potential V, thephotoelectric equation can be written as:

hυ = W + eV

For V = 0, W = hυo, where υo is the photoelectric threshold frequency. Thus,the frequency υ must be equal to or greater than υo for the photocathode to emitany electrons at all.

Apparatus:

The photoelectric unit consists of a rod-mounted panel featuring six LightEmitting Diodes (LEDS) and a saddle base. In addition you will need an AC

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power supply capable of delivering 0 - 5 V, a digital voltmeter , and a digitalammeter.

Procedure:

An LED begins to emit light when the voltage applied to it creates a largeenough energy difference between two electronic states in the parts of the diodefor an electron transition to release one quantum of light at the wavelength of theLED. When the diode's characteristic curve is is obtained by plotting Diodecurrent versus voltage, a “knee” on the curve is clearly seen. The appliedvoltage at the "knee" is proportional to the minimum emission voltage for thelight. Measuring this voltage for several LEDs of known emission wavelengthenables Planck’s constant, h, to be found to within 10% reliability.

Let Vo be the applied voltage at the "knee", Then

eVo = h(c/λ)

where c = 3x108 m/s and λ is the known emission wavelength. A plot of Voversus 1/λ will yield a straight line. Planck's constant can be determined from theslope of this straight line.

(1) Graph at least one current vs. voltage curve for each diode given in the tablebelow.

Diode Emission Wavelength(nm)

480 560 590 635 650 950

(2) Determine the stopping potential (“knee” of the curve) for each curve obtainedin step (1) above.

(3) From a plot of Vo vs. 1/λ, determine your experimental value of h.

(4) Discuss your results. Compare your findings to the accepted value for h.

---------------------------------------------------------------------------------------------------------------

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Cur

rent

Voltage"knee"

Typical Current Vs. Voltage Curve Wiring Diagram

100 Ω

LED

VA

+

0 - 5 V

***WARNING*** Do Not Exceed 5 Volts on the Diodes

+ -

20 mA

50 mA

I max480 nm

560 nm

590 nm

635 nm

665 nm

950 nm100 mA

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Critical Potential Tube1

Introduction

Collisions between electrons and gas atoms can be studied in some detailwith the gas triode tubes. The luminous discharge produced, when viewed with aspectroscope, reveals a line spectrum indicating exchanges of discrete amountsof energy due to collision when atoms are “excited”. Introductory laboratoryexperiments have confirmed that the exchange is made by non-elastic collisionsbut the resolution of such experiments is typically not sufficient to show existenceof any individual energy levels. In this experiment we utilized a tube whichproduces a beam of electrons with a relatively narrow spread in energy.

The critical Potential Tube is of standard size and fits in the UniversalStand for TelAtomic tubes. The inside surface of the bulb is coated with atransparent conducting layer connected to the anode of a simple diode gun. Atungsten cathode emits electrons in a narrow cone determined by the exitaperture in the anode. The collector is a wire ring that is positioned so that itcannot receive electrons directly from the cathode. The tube contains helium atlow pressure.

Electrical connections are made to plugs on the neck and the bulb of thetube, and sockets in the base cap of the tube. Filament voltage should be 3.0 V,1.5 A d. c., ripple free. Built in diode protection in the tube permits safeapplication of 6.3 V a. c., but results are not so demonstrative when using a. c.as opposed to d .c. voltage for the filament.

The anode voltage should range from 0 - 35 V d. c. with a current of 10mA. The collector should be maintained at a voltage of 1 - 3 V d. c. above(positive) with respect to the anode. Dry cells are convenient for this purpose.

Discussion

The onset of excitation of atoms occurs when the colliding electrons havecertain “critical energies” measured by the potential drop between the anode andcathode through which they are accelerated. An electron with just sufficientenergy to excite an atom will, after collision, have little or no residual energy andin the field-free region of the bulb will diffuse eventually to the walls and bereturned to the cathode. By making the collector a few volts more positive thanthe anode such an electron will be attracted to the wire collector.

Thus when the average energy of the electron stream is sufficient to excitethe helium gas atoms, the population of the low energy electrons will increasesignificantly to produce in the collector a measurable current which has little or nocontribution from the main beam. As the accelerating potential voltage isincreased, the collector current at first increases and then falls away until

1 Taken from TelAtomic Experiment 2533

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another, higher energy, excitation occurs. The principal excitations potentials forHelium is given in Table 1.

Table 1. Average Values of the Critical Potentials for the Principal Energy Levelsof Helium

Level Ground State 1st 2nd 3rd Ionization

Energy (eV) 0 19.8 20.9 22.9 24.6

The collector current is typically a few microamps and can be measuredwith a sensitive ammeter or galvanometer. The circuit is shown in Figure 1.

Figure 1. Wiring Schematic

C5

F4

F3

A1

VF

-

+

TEL. 2501

TEL 2533

Grounded Screen

TEL 2533.01

1.5 - 3.0 V

0.75/1.5 V

Battery Unit

TEL. 2355.06

- +

VC 1

2

1

2

ChannelChannel 0-1 VSlow Fast

OscilloscopeDataRecorder

Hertz Control ConsoleTEL.2812

0-60 Va.c. amplifier

VA

I C

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Figure 2. Ramp Signal

min

max

Y1

Y2

VA

VM

Procedure

17. Set up the equipment in the correct configuration as in figure 1.

18. Set channel 2 FAST on the Hertz Control Console to the signal of theoscilloscope and channel 1 on the Hertz Control Console as theoscilloscope trigger. (Remember for the BNC connectors, the black clipsshould go to the common ground.)

19. Set the filament voltage, Vf (Vf is the round steel knob on top of theDIGIRAMP) to zero and adjust the Oscilloscope trigger level control andthe channel 1 shift control to obtain a stable trace as shown in figure 2.

20. Use the oscilloscope controls to invert channel 2 and move the trace tothe lower edge of the screen.

21. Slowly increase Vf in the region 1.5 to 3.0 volts using the fine controls onthe top surface of LOVOLT DIGIRAMP.

22. Set Vm to 10 V and carefully adjust Vf to obtain a trace with several peaksand adjust the trace to fill the oscilloscope screen.

Analysis

1. Graph the collector current as a function of accelerating voltage andobtain the characteristic curve for the helium filled tube. Use a resolutionof 0.1 volt for the accelerating voltage on the x-axis. It should be sufficientto take the data for the graph in the range of 18 to 29 volts on the anode.

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A typical curve is shown in figure 2. Note the locations of each transitionas shown in the figure. Label each transition level observed on yourgraph.

2. Obtain a correction for the ionization potential by comparing the ionizationvoltage measured from your curve to the known value of 24.6 eV. Use thedifference in the measured valued and the known value as a correctionfactor for your measurements.

3. From the characteristic current versus voltage curve that you obtained,determine the average value of the critical potentials for each principalenergy level of helium.

(j) Determine the corrected values for these potentials using the correctionfactor that you obtained in # 3 above.

5. Compare your results to the expected results. Discuss any differencesand the possible sources of error in the experiment.

Figure 3. Typical Graph

Leve

l 1

Leve

l 2

Leve

l 3

Ioniz

ati

on

Colle

ctor

Curr

ent

Anode Voltage (eV)

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Table 2: Data Table

Excitation Level Peak Voltage (eV) Correction Factor(eV)

Corrected Voltage(eV)

1

2

3

Ionization

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BRAGG DIFFRACTION(Taken from PASCO Scientific laboratory write-ups)

INTRODUCTION:

Bragg’s Law provides a powerful tool for investigating crystalstructure by relating the interplanar spacings in the crystal to thescattering angles of incident x-rays. In this experiment, Bragg’s Law isdemonstrated on a macroscopic scale using a cubic “Crystal” consistingof 10-mm metal spheres embedded in an ethafoam cube.

Before performing this experiment, you should understand thetheory behind Bragg Diffraction. In particular, you should understand thetwo criteria that must be met for a wave to be diffracted from a crystalinto a particular angle. Namely, there is a plane of atoms in the crystaloriented with respect to the incident wave, such that:

1. The angle of incidence equals the angle of reflection, and

2. Bragg’s equation, 2d sinθ = nλ., is satisfied; where d is the spacingbetween the diffracting planes, θ is the grazing angle of the incidentwave, n is an integer, and λ is the wavelength of the radiation.

PROCEDURE:

1. Arrange the equipment as shown in Figure 1.

2. Notice the three families of planes indicated in Figure 2. (Thedesignations (100), (110), and (210) are the Miller indices for these setsof planes.) Adjust the Transmitter and Receiver so that they directly faceeach other. Align the crystal so that the (100) planes are parallel to theincident microwave beam. Adjust the Receiver controls to provide areadable signal. Record the meter reading.

3. Rotate the crystal (with the rotating table) one degree clockwiseand the Rotatable Goniometer arm two degrees clockwise. Record thegrazing angle of the incident beam and the meter reading. (The grazingangle is the complement of the angle of incidence. It is measured withrespect to the plane under investigation, NOT the face of the cube; seeFigure 3.)

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4. Continue in this manner, rotating the Goniometer arm two degreesfor every one degree rotation of the crystal. Record the angle and meterreading at each position. (If you need to adjust the INTENSITY setting onthe Receiver, be sure to indicate that in your data.)

5. Repeat the steps above for the (110) family of planes.

ANALYSIS

1. Graph the relative intensity of the diffracted signal as a function ofthe grazing angle of the incident beam for each of the family of planes.At what angles do definite peaks for the diffracted intensity occur?

2 Use your data, the known wavelength of the microwave radiation(2.85 cm), and Bragg’s Law to determine the spacing between the (100)planes of the Bragg Crystal. Measure the spacing between the planesdirectly, and compare with your experimental determination. Presentyour findings in an appropriately labeled table.

QUESTIONS:

1. What other families of planes might you expect to show diffractionin a cubic crystal? Would you expect the diffraction to be observablewith this apparatus? Why?

2. Suppose you did not know beforehand the orientation of the “inter-atomic planes” in the crystal. How would this affect the complexity ofthe experiment? How would you go about locating the planes?

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n

Cubic Lattice

Rotating Table

Figure 1: Experimental Set-up

Photograph of Experimental Setup

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(100)

(110)(210)

Figure 2: Definition of Families of planes.

Grazing Angle

Figure 3: The Grazing angle, measured with respect to the crystal planefor (100) orientation.

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Nuclear Radiation 1: Radiation Shielding∗

Introduction

The purpose of this laboratory activity is to investigate the penetratingability of three common types of nuclear radiation and the ability of differentmaterials to absorb the energy associated with nuclear radiation.

Radioactive decay is strange and mysterious for several reasons.Besides the obvious fact that none of our senses can detect individual decayevents, the nuclear decay process seems at the same time to be random yetpredictable. It is impossible to say which nucleus will become unstable enough todecay next; however, it is fairly easy to use a Geiger counter to count the numberof nuclei which do decay per second.

The statistical nature of radiation decay is clearly demonstrated when onetakes a repeated readings of counts for a specific number of time units, (forexample counts per second) and then plot the histogram of these data. Theresulting plots shows that the data approximates a Gaussian Distribution.

0

10

20

30

40

50

60

1 2 3 4 5 6 7 8 9 10

Counts (Arbitrary Units)

Distribution of Radiation Counts

Figure 1. Approximation of Gaussian distribution by random nuclear radiation

Absorption of radiation is governed by the equation

N = Noe− µx , (1)

where, N is the measured number of counts per second, No is an arbitraryconstant, µ is the absorption coefficient for the material being tested, and x is the

∗ Lab write up based on PASCO Scientific Workshop Lab Manual.

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thickness of the material. The value of µ depends on both the material and thetype of radiation.

Procedure

Background Radiation

23. The setup should include a Macintosh computer, signal interface, Nuclearsensor, sources and assorted cables and stands. The software programtitled P59 Radiation Shielding should be running.

24. Move all radiation sources at least 10 feet from the Nuclear Sensor.25. Click the REC button to begin collecting data. (Data collecting will

automatically stop after 60 seconds. The Table display will show thenumber of counts for each 15 second interval.)

26. Click on the Table to make it active. Record the MEAN as the averagebackground radiation count (per 15 second interval ) .

27. After you record the MEAN, delete RUN #1. Click on RUN #1 in the DataList in the Experiment Window.

Radiation Shielding

(k) Use the same setup as in the background radiation procedure.(l) Position the alpha source under the Geiger-Muller tube at the bottom end of

the Nuclear sensor.(m) Click the REC button to collect counts for 60 seconds.(n) Record the MEAN as the unshielded alpha source radiation count .(o) After recording the mean, delete RUN #1.(p) Place 1 small square of paper on top of the alpha source.(q) Click the REC button to collect counts for 60 seconds.(r) Record the MEAN as the one layer shielded alpha source radiation count.(s) After recording the mean, delete the data.(t) Repeat steps 6-9 until you have 5 pieces of paper over the source.(u) Repeat steps 1-10 for the beta and gamma sources.(v) Now repeat the entire process with the alpha, beta and gamma sources only

use plastic squares to shield the sources.(w) Repeat the entire process with the alpha, beta, and gamma sources but use

LEAD squares to shield the sources.

By measuring the thickness of each absorber you will have sufficient datato graph the number of counts as a function of absorber thickness for each of theabsorbers. Make a semi-log plot of these data and determine µ for eachabsorbing material from the slope of your graphs.

Data Table For Paper Shielding

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Layers of ShieldingMaterials

zero one two three four five

Thickness ofMaterial (mm)

Source Counts µ (mm-1)

Alapa

Beta

Gamma

Data Table For Plastic ShieldingLayers of Shielding

Materialszero one two three four five

Thickness ofMaterial (mm)

Source Counts µ (mm-1)

Alapa

Beta

Gamma

Data Table For Lead ShieldingLayers of Shielding

Materialszero one two three four five

Thickness ofMaterial (mm)

Source Counts µ (mm-1)

Alapa

Beta

Gamma

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Questions

4. Which type of radiation is the most penetrating?5. Which type of radiation is the least penetrating?6. What generalization can you make about the effect of the thickness of the

shielding material on the count rate?7. What generalization can you make about the effect of the density of the

shielding material on the count rate?

Lab write up based on PASCO Scientific Workshop Lab Manual.

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Nuclear Radiation II: Inverse Square Law∗

Introduction

The purpose of this laboratory activity is to investigate the relationship betweenthe distance to a radioactive source and the measured activity from the source.

One of the most common natural laws is the inverse square law. As one famousscientist put it, “the inverse square law is characteristic of anything which startsout from a point source and travels in straight lines without getting lost.” Lightand sound intensity both behave according to an inverse square law when theyspread out from a point source. Your intuition says that as you move away froma point source of light like a light bulb, the light intensity becomes smaller as thedistance from the bulb becomes larger. The same is true for sound intensity asyou move away from a small radio speaker. What may not be as obvious is thatif you move twice as far from either of these sources, the intensity becomes onefourth as great, not half as great. In a similar way, if you are at the back of anauditorium listening to music and you decide to move three times closer, thesound intensity becomes nine times greater. This is why the law is called theinverse square law.

Nuclear radiation behaves this way as well. If you measure the counts persecond at a distance of 1 centimeter, the counts per second at 2 centimeters orat 4 centimeters should vary inversely as the square of the distance. If N is thenumber of counts measured at a distance r from the detector, N is given by

N =

N0

r2 (1)

where No is an arbitrary constant.

Procedure

The equipment and software should be setup beforehand. The setup shouldinclude a computer, Pasco interface, Geiger-Muller counter, adjustable stand andradioactive sources.

28. Remove the plastic cap from the counter.29. Place the beta source on the adjustable stand.30. Move the stand and source as close as possible to the sensor.31. Click the record button for ten different counts. Record average and

standard deviation.32. Move the stand down one centimeter.33. Repeat steps 4 and 5 until the source is 7 centimeters away from the

counter. ∗taken from PASCO scientific Science Workshop

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34. Repeat the entire procedure for the alpha and gamma sources.

Data Analysis

Using your data discuss the relationship between distance and activity. Usegraphs and any statistical techniques that may be appropriate to this laboratory.

Questions

(x) Dose nuclear radiation follow the inverse square law? Justify you answer.(y) What first action would be important to protect yourself from the radiation

released from a broken container of radioactive material?(z) Does alpha and gamma radiation have the same relationship to distance

from the source as beta radiation?(aa) How would the risk of exposure to radioactive substances be different if

nuclear radiation followed an inverse cube law?

Figure 1. Experimental Layout

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