planck_constant_apparatus.docx - froehlich

Apparatus for Determining Planck’s Constant with LEDs Glenbrook North High School February 11, 2015 Bob Froehlich Introduction Light emitting diodes have been used in the classroom to determine Planck’s constant for decades1. The general setup is extremely simple, requiring a power supply, resistor and LEDs of different wavelengths. Several experimental procedures have been documented, however they all require measurement of the threshold voltage across the diode performed under steady state conditions2 or plotted against time3. Although other techniques have involved finding the tangent to a current vs. voltage curve for the diode4, they have raised some controversy5. The discussion that follows and the preferred apparatus embodiment focus on determining the threshold voltage. The actual laboratory procedure is left to the instructor.

Theory The experiment relates the energy gap, Eg, between conduction and valence bands to the frequency of the emitted light through

Eg = hν = hcλ

, (1)

assuming a quantum number of 1. The energy is related to the threshold voltage by Eg = qVT (2) where q is the fundamental charge. When rearranged and solved for VT, this results in the relationship

VT =hcq1λ

. (3)

Plotting VT vs. 1/λ will yield a linear graph, the slope of which is Planck’s constant multiplied by c/q, 1.875 × 1027 m s-2 A-1. Preferred Embodiment The apparatus of figure 1 has been modified so it can be used without an ammeter, as students notoriously destroy ammeters.

In this circuit, the current is measured as a voltage across a 1k Ω, 1% resistor. Therefore, the indicated voltage represents the current in milliamperes. Four such circuits are built into the apparatus, selectable with a jumper. LED

Fig. 1. Basic experimental setup allowing measurement of LED voltage and current

Fig. 2. Modified circuit configuration illustrating a single LED selected

planck_constant_apparatus.docx - froehlich

wavelengths are 470 nm, 527 nm, 591 nm and 624 nm. In addition, a fifth jumper location will illuminate all the LEDs for spectrum analysis.

Circuit Board The CadSoft Eagle source document for board layout and schematic diagram is available at devices.froehlichsphysics.com. Eagle Light

circuit board layout software is freeware that performs the same functions as CadSoft’s professional package, with the following limitations:

• The useable board area is limited to 100 x 80 mm (4 x 3.2 inches).

• Only two signal layers can be used (top and bottom).

• The schematic editor can only create one sheet.

• Support is only available via email or through the Eagle forum

• Use is limited to non-profit applications or evaluation purposes.

The freeware version of Eagle is downloadable from the CadSoft website: cadsoftusa.com. Eagle is available for Windows, Linux and Mac. Fabrication Board files with a .brd extension may be uploaded to a number of circuit board fabricators. OSH Park (oshpark.com) is one such house that specializes in short-run projects at a cost of $5 per square inch with no setup fees. Turnaround is dependent on quantities, but short runs take about two weeks and include silkscreen and solder mask. Note: The board layout is a shared file at OSH Park. To order more of the same, search for froehlichsphysics on the OSH Park website, or go to: oshpark.com/shared_projects/6LbttgAb.

Fig. 3. Schematic diagram

Fig. 4. External connections

Fig. 5. Printed wiring board

planck_constant_apparatus.docx - froehlich

1O'Connor, Patrick, and Leah O'Connor. "Measuring Planck's Constant Using a Light Emitting Diode." The Physics Teacher 12 (1974): 423. Web 2 Steady state measurements typically test when the LED turns on by either observing emitted light or measuring the current. The apparatus described herein was designed for steady state measurement. See: Hackworth, Martin. "Measuring Planck’s Constant." Web. 4 Feb. 2015. <http://www2.cose.isu.edu/~hackmart/planck's.PDF> "Determination of Planck’s Constant Using LEDs." Web. 7 Feb. 2015. <https://web.phys.ksu.edu/vqm/tutorials/planck/>. 3 Discharging a capacitor and plotting the voltage across the diode has been described in several papers. See: Zhou, Feng, and Todd Cloninger. "Computer-Based Experiment for Determining Planck's Constant Using LEDs." The Physics Teacher 46 (2008): 413-15. Web. Thurman, Zechariah. "Determining Planck's Constant Using LEDs." Web. 4 Feb. 2015. <http://works.bepress.com/cgi/viewcontent.cgi?article=1002&context=zechariah_thurman>.

4 Nieves, L., G. Spavieri, B. Frenanzez, and R. A. Guevara. "Measuring the Planck Constant with LEDs." The Physics Teacher 35 (1997): 108-09. Web. 5 Hermann, Friedrich, and Georg Job. "Historical Burdens on Physics." Web. 4 Feb. 2015. <http://www.physikdidaktik.uni-karlsruhe.de/publication/Historical_Burdens.pdf>. Hermann, F., and D. Schatzle. "Question #53. Measuring Planck's Constant by Means of an LED." American Journal of Physics 64.12 (1996): 1448. Web. Morehouse, Roger. "Answer to Question #53. Measuring Planck's Constant by Means of an LED." American Journal of Physics 66.1 (1998). Web.