Determination of Planck’s constant using LEDs
Determining Planck’s constant from I-V characteristics of LEDs
March 8, 2016
 This is the Final Exam for the Laboratory component of the Modern Physics course.
 Each student will conduct this experiment independently. You are not supposed to
discuss this experiment with other students in the class or anybody else.
 Each student must schedule a two hour time slot with the instructor to conduct this
experiment.
 You are allowed a 3” x 5 ” notecard for the exam. This may contain notes that help
you operate the equipment or use the software. You are required to attach the
notecard to your answer sheet at the end of the exam.
Table of Contents
0.
1.
2.
3.
4.
5.
6.
Preliminaries 1
Introduction 2
Equipment 3
Initial setup 3
Activity #1: Analyzing the LED spectra 4
Activity #2: Determining the I-V characteristics of the LEDs 5
Data Analysis. 7
0. Preliminaries
0.1 Fundamental constants:
Fundamenta l unit of charge e  1.6  10 19 C
Speed of light c  3  108 m/s
0.2 The aim of this experiment is to determine Planck’s constant from the I-V characteristic
curves of an LED.
0.3 To understand the electrical properties of LEDs (Light Emitting Diodes) read the following
topics before proceeding any further.
0.3.1
General Physics Lab Manual: PN Junctions (available on the Blackboard).
0.3.2
Tipler, Physics, Section 27-4: Band Theory of Solids
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Determination of Planck’s constant using LEDs
1. Introduction
1.1 In this section we summarize the results that will help you conduct the experiment to
determine Planck’s constant from the I-V characteristics of an LED. Your reading of the material
mentioned in Item 0.3 should help you understand these results.
1.2 Figure 1 shows a circuit consisting of an LED connected in series to a resistance R and a
variable power supply such that the LED is forward biased. Let VD be a voltmeter measuring the
voltage across the LED and VR a voltmeter measuring the voltage across the resistance R.
Measuring the voltage VR is equivalent to measuring the current in the circuit.
VD
-
+
R
VR
V
Figure 1: Forward biased LED
1.3 Forward biasing the LED results in a flow of electrons across the pn junction in the LED
that causes a current to flow in the circuit.
1.4 As electrons flow across the pn junction they loose energy. In the process the electrons emit
photons and the diode lights up.
1.4.1 The energy lost by the electrons is approximately equal to the band gap energy of
the LED which is the energy difference between the valence band and the conduction
band.
1.5 Conservation of energy implies that the relation between the potential difference across the
LED (VD) and the energy of the emitted photon is given by
eV D 
hc

,
where  is the wavelength of the light emitted by the LED.
1.6 To determine Planck’s constant:
1.6.1 Obtain a set of LEDs that emit light of different known wavelengths . These
LEDs will be made available to you in the lab.
1.6.2 Proceed to connect each LED one at a time in the circuit shown in Figure 1 and
for a common reference current in the circuit (the same as a common value of VR as
mentioned in Item 1.2), determine the voltage VD across each LED.
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Determination of Planck’s constant using LEDs
1.6.3
Analyze the data based on equation (1) and determine Planck’s constant h.
2. Equipment
 Spectrometer
 Circuit board containing LEDs of known wavelengths (Klinger)
 Science Workshop 750 Interface with a built-in Signal Generator (PASCO).
 Two Voltage probes that plug directly into the Science Workshop 750 Interface
 Connecting wires
 PC with Data Studio and MS Excel softwares
3. Initial setup
3.1 Examine the circuit board containing the LEDs. It contains 6 LEDs with wavelengths
ranging from 465 nm to 950 nm. One terminal of each LED is connected to a 100  resistor.
3.2 Switch on the SW 750 first and then the computer and monitor.
3.3 Run the software DataStudio on the computer.
3.3.1
This should open
3.3.1.1. a window that prominently displays a picture of SW 750,
3.3.1.2. a Sensors window listing all the sensors that may be connected to the SW
750,
3.3.1.3. a Signal Output window that displays an icon for the signal generator ( the
Output icon),
3.3.1.4. a Data window and
3.3.1.5. a Displays window.
3.4 For help with any of the DataStudio menus/items select that particular component and
hit F1.
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Determination of Planck’s constant using LEDs
4. Activity #1: Analyzing the LED spectra
4.1 In this activity you will observe the spectra of each LED by observing the light emitted by
the LED through the spectrometer.
4.2 Connect the circuit shown in Figure 2.
-
+
R
V
Figure 2: Circuit to analyze the LED spectra
4.3 Use the built-in signal generator on SW750 (the Output terminals) as the power supply.
4.3.1 Connect the positive of the Output terminals on SW750 (the terminal with
the sine wave symbol below it) to the + terminal of one of the LEDs (the free
terminal of the LED). Start with the 465 nm LED.
4.3.2 The ground terminal on SW750 must be connected to the – terminal on the
circuit board (the free terminal of the resistor).
4.3.3
These connections ensure that the LED is forward biased.
4.4 On the DataStudio window on the computer:
4.4.1 Click on the Output icon and drag and drop it in the SW 750 icon window. This
should place a Sine Wave icon in the SW750 window and should open the Signal
Generator settings window. Initialize the signal generator as follows:
4.4.1.1. Mode: On/Off. This can be done by clicking on the Auto button. This allows
you to manually operate the signal generator by clicking on the ON and OFF
buttons
4.4.1.2. Signal generator waveform: DC Voltage. This allows you to supply a
constant DC voltage to the LED.
4.4.1.3. Amplitude: 4.000 V
4.4.2
Switch on the signal generator by clicking the ON button. The LED should light
up. The +/- buttons below the Amplitude display allows you to increase the DC voltage
in increments shown on the left. To change the value of the increments use the arrow
buttons below the Amplitude display. Do not exceed an amplitude of 5.0 V.
4.4.3 View the light emitted by the LED through the spectrometer. Make a note of
what you observe.
4.4.4
Repeat for the remaining LEDs.
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Determination of Planck’s constant using LEDs
4.4.5 You will notice that the 950 nm LED does not emit any light and so its spectrum
cannot be observed.
4.4.6 When you are done switch off the signal generator. You do not have to
disconnect the circuit since you will need it for the next activity.
4.4.7
Answer all the questions pertaining to this Activity on the Question sheet.
5. Activity #2: Determining the I-V characteristics of the LEDs
5.1 The I-V characteristic curve of an LED is a graph of the current flowing through the LED as
a function of the voltage across the LED. This is equivalent to plotting the voltage across the
resistor VR versus the voltage across the LED VD.
5.2 In this activity you will not be using the Blue LED (465 nm LED).
5.3 Make the connections shown in Figure 1.
5.3.1 Connections from the signal generator have already been made. Start with the 560
nm LED.
5.3.2 Connect one of the voltage sensors to Analog Channel A and the other to Analog
Channel C on SW750.
5.3.3 Connect the leads from the Channel A voltage sensor across the LED with the
positive lead (red) connected to the + terminal of the LED and the negative lead (black)
connected to the other terminal of the LED.
5.3.4 Connect the leads from the Channel C voltage sensor across the resistor with the
negative lead (black) connected to the - terminal on the circuit board (the terminal which
is connected to the ground of the signal generator).
5.4 On Data studio:
5.4.1
Initialize the Signal generator with the following settings:
5.4.1.1. Mode: Auto
5.4.1.2. Signal generator waveform: Positive Up Ramp wave.
5.4.1.3. Amplitude: 5.000 V
5.4.1.4. Frequency: 1.00 Hz
5.4.1.5. Measurements and Sample Rates: Place a check mark on the Measure Output
Voltage box and uncheck the Measure Output Current box. Change the Sample
Rate to 500 Hz
5.4.1.6. The signal generator supplies a voltage that varies linearly from 0 to 5.0 V in
1.0 s.
5.4.2 Click, drag and drop the Voltage Sensor icon from the Sensors window in the
SW 750 icon window. This should place a Voltage sensor icon in the SW 750 icon
window connected to Channel A.
5.4.3
Repeat step 5.4.3 again and another voltage probe is connected to Channel C.
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Determination of Planck’s constant using LEDs
5.4.4
Double-click the Channel A Voltage sensor icon. In the window that opens
5.4.4.1. Make sure the sample rate is 500 Hz. This fixes the rate at which DataStudio
measures voltages across the LED
5.4.4.2. Set the sensitivity to Low (1x). Click OK.
5.4.5
Double-click the Channel C Voltage sensor icon. In the window that opens
5.4.5.1. Make sure the sample rate is 500 Hz. This fixes the rate at which DataStudio
measures voltages across the resistor
5.4.6
Set the sensitivity to Med (10x). Click OK.
5.4.7 From the Displays window on DataStudio open a Graph window to display and
plot a graph of VR vs. VD.
5.4.7.1. Notice that by default DataStudio can create a graph of VR vs. Time. To
change the x-axis from Time to VD refer to the Online Help. On the main
menu follow the link:
Help  Contents  Graph display 
displaying quantities other than time on the X axis
5.4.8
Double-click on the Graph window and the Graph settings window pops open.
Make the following changes to your settings:
5.4.8.1. In the Appearance tab, uncheck Connected Data Points and Show Legend
Symbol.
5.4.8.2. In the Tools tab change the Data Point Gravity to 0.
5.4.8.3. Click OK
5.5 On the main menu, click on Experiment  Set Sampling Options…
5.5.1
For Delayed Start choose None
5.5.2 For Automatic Stop impose the condition that the data collection is stopped when
the voltage across the resistor rises above 0.9 V.
5.6 To obtain the I-V characteristic curve, click on Start.
5.6.1 You should obtain a graph that starts from 0.0 V and increases exponentially till
the voltage across the resistor reaches 0.9 V.
5.7 Use the Graph Tool Scale to Fit located above the graph window to scale your plot.
5.8 Repeat till you obtain I-V characteristic curves for all the LEDs, except the BLUE LED
(465 nm LED).
5.9 Answer all the questions pertaining to this activity in the Question sheet.
5.10 Save your DataStudio worksheet in the folder c:\PHY203. Save it in your name.
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Determination of Planck’s constant using LEDs
6. Activity #3: Data Analysis.
6.1 From the I-V characteristics of the LEDs you need to determine the voltage across the LED
(VD) for a common reference voltage across the resistor (VR).
6.2 Set the reference voltage at VR = 0.8 V.
6.3 Note the corresponding voltages across the five LEDs (VD).
6.3.1 To accurately estimate the LED voltages, you may want to use some of the Graph
Tools available above the graph window. They include: Scale to Fit, Zoom In, Zoom
Out, Zoom Select, Smart Tool etc.
6.4 Use MS Excel for any of the data analysis you wish to perform on your data. Base your
analysis on equation (1) given in the Introduction.
6.5 Complete the data analysis that will enable you to determine Planck’s constant and the
corresponding uncertainty.
6.6 Answer all the questions pertaining to this activity in the Question Sheet.
6.7 Save the Excel spreadsheet in the folder c:\PHY203. Save it in your name.
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