Developing Research and Experimentation Skills: Demonstrated

using a Black Body Radiation Experiment.

Abstract

Traditionally undergraduate labs are taught by having a student carry out a number of steps to set up equipment and take specific data to achieve a

certain aim. With this approach there is little opportunity to develop many of the skills important in experimentation and research. With this in

mind, various labs have been developed at an intermediate and advanced lab level to offer the student an open learning opportunity, involving the

student follow their own ideas to research and solve a number of problems before obtaining the set goal. An example of this approach is

demonstrated here, using the black body radiation approximation for a tungsten filament of a common light bulb, to obtain the ratio of Planck’s to

Boltzmann’s constants (h/k). The propagation of error gives an expected error of about 2%, and it will be shown that only when a number of

systematic errors are resolved is this level of accuracy obtained

M.J.Pearson and J.D.White,

Physics Department, Juniata College, 1700 Moore Street, Huntingdon, PA 16652

Conclusions

Common problems found with this experiment, both in technique and with the equipment, that gave less than optimal results include:

• Not adjusting the equipment to optimize the light received by the photodetector.

• Not collecting a sufficient number of data points (~15) for an exponential curve fit (equation 1).

• Using photodetector values that are either too high or too low.

• Using a less than optimal model for temperature vs. resistivity; the power fit produces the best results.

• Inaccurate measurements for the resistance of the tungsten filament.

• Not calibrating the monochromator correctly.

• Only using normal tungsten light bulbs; other types of bulb don’t work with the approach outlined here.

• Using a badly calibrated multimeter.

The experiment is presented to the students with some of the pitfalls and various things to consider. Whether they are performing this experiment in Modern or Advanced Lab depends on what they are told, and what is expected from

them.

With all of these problems noted, this becomes an excellent experiment for students to carry out to test and develop their experimental and research skills. It allows them to apply statistics to predict how accurately h/k should be

measured, and then when numbers beyond this are found, further investigations can be carried out to figure out why. At the end the students are given the whole picture and thus see how well they did, and learn what they may have done

differently. They learn the benefits of undertaking short preliminary studies to iron out problems, before collecting substantial data for a good pilot study.

There are many directions this experiment could take in the future, such as comparing different methods (6, 7) for determining temperature of the filament or the wavelengths over which the experiment can be performed for Planck’s

theory to be applied. With this, and other similarly orientated experiments, students develop many skills not normally obtained until they have spent substantial time out on their own doing research.

References

(1) Crandall, R.E., Delord, J.F. Minimal apparatus for determination of Planck’s constant. Am. J. Phys. 51, 90-91 (1983)

(2) Dryzek, J., Ruebenbauer, K. Planck’s constant determination from black body radiation. Am. J. Phys. 60, 251-253 (1991)

(3) Brizuela, G., Juan, A. Planck’s constant determination using a light bulb. Am. J. Phys. 64, 819-821 (1996)

(4) Handbook of Chemistry and Physics, 54th Ed, CRC Press, E-110 (1973)

(5) Handbook of Chemistry and Physics, 75th Ed, CRC Press, 12 (1995)

(5) Zanetti, V. Sun and lamps. Am. J. Phys. 52, 1127-1130 (1978)

(6) Zanetti, V. Temperature of incandescent lamps. Am. J. Phys. 53, 546-548 (1985)

Acknowledgments

We would like to thank the many students that have helped develop the various aspects of this experiment.

Introduction

Tungsten bulbs have been used in laboratories for a number of years as excellent sources of black body radiation allowing Panck’s radiation law to

be explored. There have been a number of studies that have investigated the black body properties of tungsten light bulbs, and have usually been

associated with determining Planck’s constant (1-3). The method applied here has modified (simplified) previous techniques to accommodate the

equipment used and address the specific aims.

This method was used to obtain the Planck/Boltzmann constant ratio (h/k) by students at Juniata College for a number of years, and always

produced higher errors (as much as 50%), whereas propagation of errors stated a value of h/k to within 2% should be possible. A number of

important factors (systematic errors) were discovered that led to the high error, and once resolved led to an accurate (within 2%) measurement of

h/k.

This experiment now acts as an exercise for the students to carry out to gain some valuable experimental and research skills. This poster summarizes

the considerations that need to be made for a successful experiment; these considerations are either passed directly on to the students as a teaching

point, or hints are given to allow the students to work things out for themselves.

Theory

Planck’s Law of Radiation, P = (2phc2)/(l5(ehc/lkT -1), describes the power output (P) of radiation from a black body, where l is wavelength, c is the

speed of light, and h/k are Planck/Boltzmann constants (6.62559x10-34Js/1.38054x10-23 JK-1). By applying the approximation ehc/lkT>>1 it can

simply be shown that:

P=De-(hc/lk)(1/T) – equation 1

where D=2phc2/l5. In this study D was not investigated and P was assumed to be proportional to the signal received by the photodetector (see

methods). Results

How this experiment (study) is presented to the students is crucial. Give them too much information (tips) and they don’t learn to think, problem solve & research for themselves. Give the students too little, and they are left wasting

their time floundering and frustrated. Of course this does give them a real insight into research, but not one that is particularly constructive. Running the experiment as a competition between two groups has worked well. When all of

the systematic errors are ironed out, summarized in figure 1, an accuracy of less than 2%, as predicted by propagation of error, is obtained for wavelengths of 400-800nm. Wavelengths higher than 800nm have been studied, but have

generally yielded less accurate results.

Use the full range of voltages (0-143V)

Figure 1: Shows the apparatus setup and associated problems, learning points or necessary precautions, to collect suitable data in order to measure h/k to within ~2% as given by the propagation of error. It is crucial to optimize

the light transmission through the monochromator for low wattage bulbs and/or short wavelengths as expected from the bulb transmission and photodetector properties.

W1

W2

or

PHOTODETECTOR VOLTAGE

PHOTODETECTOR

MONOCHROMATOR

TUNGSTEN BULB

VARIAC

(0-142.6V AC)

BULB VOLTAGE

BULB CURRENT

Calibrate accurately using a HeNe

Stay within the range of the device.

Correctly set up circuit

Accurately measure the bulb (filament)

resistance. (Systematic Error)

Consider bulb type - Clear/Frosted/Long

life/Daylight (Preliminary Studies)

Research intensity vs. wavelength properties

Can’t use values too low (<0.015V)

Can’t use values at, or approaching, the

maximum (12.5V) (Curve Fit Errors)

Use wavelength response chart to

understand what wavelengths are possible

with this detector.

Uncalibrated multimeter makes things

interesting…. (systematic error)y = 4380e

-17269x

R2 = 0.9994

0

2

4

6

8

10

12

0.0003 0.0004 0.0005 0.0006 0.0007

1/Temperature (/K)

Rel

ativ

e In

ten

sity

(V

)

Excel - Use with Care

To the inexperienced user, Excel can cause a number of errors in an experiment. For instance the general equation exp(-(x)^2) yields the wrong

answer if entered this way. For the correct answer exp(-((x)^2) ) is needed. For this study, the equations for the curve fits generally, by default,

don’t give enough significant figures to represent the curve. Statistical tests can be carried out without any thought to what type of data is being

worked with. The students learn the valuable lesson that even software can lead to systematic errors.

Methods

The equipment setup is shown schematically in figure 1. A variac autotransformer (General Radio Co), supplying voltages up to 142.6V, controlled

the intensity of tungsten light bulbs (GE & Sylvania: 25-100W). Light was passed through one of two high intensity monochromators (Bausch &

Lomb, l=400-1200nm), into a photodetector (Thor Labs, DET110). Photodetector values were measured by a multimeter (Craftsman Professional

8T59 or Hewlett Packard 34401A). Resistance of the bulb at different voltages was calculated from the measured (Keithley 169 multimeter) voltage

across, and current through, the bulb.

Room temperature resistance (R0) of the tungsten filament of resistivity (r0), length (l) and area (A) was given by R0=r0A/l and more generally

filament resistance (R) and resistivity (r) was given by R=rA/l. Combining these equations produces r=Rr0/R0, thus removing the need to know A

or l (assuming these properties don’t significantly change). Initially an estimate of R0 was measured directly across the terminals of the bulb (W1)

and finally, when all the data had been collected and the bulb was no longer needed, across the filament (W2) (see figure 1).

The student has to decide the best way to calculate the filament temperature, as calculated from a CRC (4, 5). Figure 2 summarizes the

considerations here. They also have to work out, through preliminary studies, a good number of data points to test Planck’s model (equation 1).

The propagation or errors was calculated using equation 1 and the above information. This is fairly involved and particularly rewarding to the

student.

Figure 2: Shows the resistivity vs. temperature data from a CRC (4) along with a power or 3rd order polynomial fit. Students have to decide on the

best model for this data, and usually end up with either the power or 3rd order polynomial fit. Which do you think would be the best fit? Or would

the relationship r = 48.0 (1 + 4.8297 × 10-3 T + 1.663 × 10-6 T2 (5) be better?

POWER FIT

T = 305135855.67760r0.82984

R2 = 0.99992

3rd ORDER POLYNOMIAL FIT

T = 239963075796022000000r3 - 938006202006370r

2 + 3804035980r + 104

R2 = 0.99998

0

500

1000

1500

2000

2500

3000

3500

4000

0.0E+00 2.0E-07 4.0E-07 6.0E-07 8.0E-07 1.0E-06 1.2E-06 1.4E-06

Resistivity {r} (Ohm.m)

Tem

per

atur

e {T

} (

K)