Measuring the value of Planck’s Constant with LEDs
Kuan Yew Khang, Deon Foo, Ong Haozhi
School of Science and Technology, Singapore
Abstract
Calculating Planck’s constant allows us to understand the behaviour of matter at subatomic level. It can help us learn more about how to describe blackbody radiation, something that is very close to the radiation we receive from the sun. With that information, we could find out the amount of radiation we receive from the sun and find ways to lessen the radiation. We aim to use LED bulbs to calculate Planck’s constant by changing the amount of volts and milliamperes and using the results to plot a graph of current (mA) against voltage. Using these results, we would be able to find the activation voltage and use this information to find planck constant as accurate as possible, which is our goal. However, our results were not as accurate as we thought. We chose this topic as it gives us a chance to learn about something beyond our current syllabus and enhance our knowledge on the topic.
1.Introduction
Our project is measure a value with experimental research. The category of our project is Mechanics, Physics and Astronomy.
1.1. Research Questions
What is Planck’s constant?
“Planck's constant relates the energy of a photon with the frequency of light. It allows the precise calculation of the energy of light emitted or absorbed and thereby permits the determination of the actual energy of the photon. Along with constant for the speed of light, Planck's constant (h = 6.626 1034 joulesecond in the meterkilogramsecond system of measurements) is a fundamental constant of nature.” (Lerner, K. L., 2004)
During the twentieth century, German physicist, Maxwell Planck, “proposed that atoms absorb or emit electromagnetic radiation only in certain units or bundles of energy termed quanta.” (Lerner, K. L. ,2004) Planck developed a quantum theory that account for a wide range of physical phenomena with acceptance of his experimental results regarding radiation emitted by an object and its temperature increases.
Electromagnetic radiation was thought to travel in waves with a never ending number of frequencies and wavelengths. “Planck determined that energy of light was proportional to its frequency. As the frequency of light increases, so does the energy of the light.” (Lerner, K. L. ,2004)
How to accurately measure Planck’s constant?
Use a moving coil watt balance and electric power measured in terms of Josephson and quantum Hall effect is compared with mechanical power measured in terms of meters, kilograms and seconds. We find the Planck constant h=6.62606891(58)×10−34Js. The quoted standard uncertainty (1 standard deviation estimate) corresponds to (8.7×10−8)h. Comparing this measurement to an earlier measurement places an upper limit of 2×10−8/yr on the drift rate of the SI unit of mass, the kilogram.”( Edwin R. Williams, Richard L. Steiner, David B. Newell, and Paul T. Olsen. ,1998 ,September 21)
Why do we use LEDS to measure Planck’s constant?
Planck’s constant is the relation between the energy of a photon and the frequency of light. It is a constant value that should not change, therefore allows the calculation of the actual energy of a photon.
When an electric current runs through a LED (LightEmitting Diode), energy is released in the form of photons. A LED can produce different colours. The colour of the light is determined by the energy in the photons. The colours can be altered by the chemical composition of the semiconductor materials.
The colour of light is determined by the wavelength. We use LEDs in this experiment because each colour of LED has a different threshold voltage at which electrons start being produced. Measuring this voltage, together with known values for the emission wavelengths, provides a path to finding a value for the Planck constant.
What is Quantum?
“Quantum is the Latin word for amount and, in modern understanding, means the smallest possible discrete unit of any physical property, such as energy or matter.” (Rouse,M. ,2006, July) Planck wanted to discover why radiation “from a glowing body changes in color from red, to orange, and, finally, to blue as its temperature rises. He found that by making the assumption that radiation existed in discrete units in the same way that matter does, rather than just as a constant electromagnetic wave, as had been formerly assumed, and was therefore quantifiable, he could find the answer to his question.”(Rouse,M. ,2006, July)
Planck wrote a mathematical equation that involves a figure used to represent individual units of energy and called these units quanta. “Planck assumed there was a theory yet to emerge from the discovery of quanta, but in fact, their very existence defined a completely new and fundamental law of nature. Einstein's theory of relativity and quantum theory, together, explain the nature and behavior of all matter and energy on earth and form the basis for modern physics.” ( Rouse,M. ,2006, July)
Why is Planck’s constant important?
“Planck’s Constant defines the quanta (minimum amount) for the energy of light, and therefore also the energies of electrons in atoms. It also factors into something called the Uncertainty Principle, discovered by Werner Heisenberg in 1927.” (Clear, S,2010 September 7)
A particle is located somewhere and has a position given by x, and is moving with a certain velocity which is given by p (momentum and the velocity multiplied by mass). “The Uncertainty Principle shows that one cannot know the x and p values to a precision greater than hbar/2. The value hbar is just Planck’s constant divided by 2π, or h/2π. (The “uncertainty” is shown by a Δ.)” (Clear, S,2010 September 7)
1.2.Hypotheses
The value of planck’s constant is 6.6704 × 1034 m2 kg / s and has a percentage error of less than 10%.
2. Methods
2.1. Equipment list
 Five LEDs emitting coloured light – one each of red, orange, green, blue, and yellow. Choose LEDs with a clear, colourless casing surrounding the LED, so that the colour of the light comes from the device itself, not from the coloured casing.
 Six 9 V batteries
 Two multimeters (one to be used as a voltmeter and the other as an ammeter)
 10 kΩ potentiometer or rheostat.
 Six Alligator clip Wires
2.2 Diagram of experimental setup
Figure 1:Experimental setup used to find the Voltage and Ampere
2.3. Procedures
1.Connect the ammeter in series with the LED to measure the current through it, and connect the voltmeter in parallel to the LED to measure the voltage across it. The applied voltage can be changed by using the potentiometer or rheostat.
2.Change the voltage in steps of 0.05 V from the lowest volts to light up the led to the highest voltge the led can take and measure the resulting electrical current. Note that when the current flowing through the LED is small, the LED might not light up, but the ammeter can still measure the current. To protect the LED, take note to keep the current below 5mA
3.Repeat experiment for each LED twice to calculate average.
4.For each LED, plot a graph of current against voltage. On each graph, find the straight line of ‘best fit’ to join up the points that slope up from the xaxis. If the points lie close to the line, this shows that a linear relationship holds between the applied voltage and the current in this region of the graph.
5.Finally, determine the activation voltage (Va) from the collected data. This is the point at which the current begins to increase linearly with voltage. It can be read off the graph by extrapolating the straight line representing the linear response region backwards
2.4. Risk Assessment and Management
Risk

Risk chance

Management

Shocked by the electricity

Medium

Don’t touch the wires when electricity is transmitting

LED lights shine in your eyes, causing temporary blindness

Low

Don’t stand in front of the LEDs

Breakage of glass covering LED, cutting yourself on the glass shards

Low

Be careful not to drop the LED or hold it with a lot of force

Burnt by Heat from battery

Low

Do not touch battery when in use

2.5 Data Analysis
With the results obtained, we will use them to calculate Planck’s Constant and see how accurate our results are.
E=hc/λ
3. Results
The results of our experiment are as shown below:
Table 1:Table of warm/yellow LED milliamperes and voltage
Warm/yellow

Volts

miliamperes result 1

milliamperes result 2

Mean milliampere

Activation

2.47

0.02

0.02

0.020

2.55

0.14

0.11

0.125
 
2.6

0.44

0.28

0.360
 
2.65

1.12

0.57

0.845
 
2.7

2.24

1.05

1.645
 
2.75

3.38

1.65

2.515

Table 2:Table of blue LED milliamperes and voltage
Blue

Volts

milliamperes result 1

miliamperes result 2

Mean milliampere

Activation

2.40

0.03

0.03

0.030

2.45

0.09

0.07

0.08
 
2.5

0.27

0.22

0.245
 
2.55

0.67

0.66

0.665
 
2.6

1.47

1.39

1.430
 
2.65

2.63

2.58

2.605

Table 3:Table of green LED milliamperes and voltage
Green

Volts

milliamperes result 1

milliamperes result 2

Mean milliampere

Activation

2.17

0.05

0.05

0.050

2.2

0.09

0.08

0.085
 
2.25

0.23

0.20

0.215
 
2.3

0.45

0.42

0.435
 
2.35

0.77

0.73

0.750
 
2.4

1.16

1.08

1.120

Table 4:Table of red LED milliamperes and voltage
Red

Volts

milliamperes result 1

milliamperes result 2

Mean milliampere

Activation

1.7

0.09

0.09

0.090

1.75

0.43

0.35

0.390
 
1.8

1.35

1.20

1.275
 
1.85

3.23

2.73

2.980
 
1.9

6.32

6.02

6.170
 
1.95

10.80

10.23

10.515

Table 5:Table of orange/amber LED milliamperes and voltage
Orange/amber

Volts

milliamperes

Mean milliampere

Activation

1.735

0.08 and 0.09

0.085

1.8

0.40 and 0.34

0.370
 
1.85

1.35 and 1.08

1.215
 
1.9

3.80 and 3.65

3.725
 
1.95

8.90 and 7.54

8.220
 
2

16.90 and 16.73

16.815

Table 6:Table of 1/λ (typical wavelength)
LED Colour

Typical wavelength, λ (nM)

Activation voltage(V)

1/λ(m^1)

Red

623

1.700

1.60514 x 10^6

Orange

586

1.735

1.70648 x 10^6

Green

567

2.170

1.76367 x 10^6

Blue

467

2.400

2.14133 x 10^6

Yellow

590

2.470

1.69492 x 10^6

Graph 1:Graph of activation voltage (yaxis) against 1/λ (xaxis)
Graph 2:Graph of voltage (xaxis) against milliampere (yaxis) for tables 15
4. Discussion
4.1 Analysis of result
This is the equation to calculate Planck’s Constant, where c=the speed of light, e=the charge on an electron and m=gradient of linear regression.
Our result was:
4.2 Key findings
We found out that our value of Planck’s constant had a percentage error of 59.8% when compared with the actual value of Planck’s constant.
4.3 Explanation of key findings
We could not find an accurate result for Planck’s constant. One of these factors could have affected our results:
 Different brand of LEDs used in the experiment
 We used different voltage batteries for different LEDs as different LEDs have different activation voltage
 We used a 10kΩ resistor instead of a 1kΩ resistor suggested by another experiment done by other people.
 We might have set up the circuit wrongly, causing the electricity to flow more in some places and less in others, causing the results to be inaccurate
4.4 Evaluation of hypothesis
We failed to prove our hypothesis that the value of Planck’s constant is 6.6704 × 1034 m2 kg / s and has a percentage error of less than 10%.
4.5 Areas for improvement
 Do our experiments faster so that we do not have to rush when we need to plot our graphs and tables. As we spent most of our first few lessons trying to figure out the best way to set up the circuit, we wasted a lot of time, causing us to rush in the later parts.
 Have a bit more background knowledge on electronics so that we don’t struggle to assemble the circuit and make sure that it is correct. As we did not know much about electronics, we struggled to figure out how to set up the circuit.
 Plan ahead to get equipment and resources. We took very long to get all our equipment and resources and because of that, we started our experiment late.
5. Conclusions
5.1 Practical Applications
Using the Planck’s constant and a few other terms (gravitational constant and speed of light), we are able to calculate the Planck length, which is the shortest unit of measurement. It is the smallest length anything can be. And this is not the only application. Another use for Planck’s constant is that it relates the energy of a single photon in electromagnetic radiation to the frequency of the radiation.
5.2 Areas for further study
What does Planck’s constant have to do with other topics? Does Planck’s constant depend on temperature? Is Planck’s constant affected by any factors?
5.3 Comparison with previous research
 In a study done in July 25, 2011, by one of the students in the Pennsylvania State University, he managed to find the value of Planck’s constant as 6.180x1034 , with a percentage error of 6.7%. We found that the way he set up the experiment was different from ours. Therefore, there is a possibility that the way the circuit is setup has an impact on the results of the experiment.
 In a study found in the World Journal of Chemical Education, the results for the value of Planck’s constant was 6.28x1034
 In a study done by students from Indiana University of Pennsylvania and Cleveland Community College, the results for the value of Planck’s constant was 6.625 x 1034 . We found that they measured the discharge voltage of the capacitor in the LED circuit to accurately determine the threshold value to turn on the LED. As they used a capacitor to take their readings which we did not use, could affect the accuracy of the results.
6. References
Book references
Lerner, K. L. (2004). Planck's Constant. In K. L. Lerner & B. W. Lerner (Eds.), The Gale Encyclopedia of Science (3rd ed., Vol. 5, pp. 30963097). Detroit: Gale. Retrieved from http://go.galegroup.com.proxy.lib.sg/ps/i.do?id=GALE%7CCX3418501773&v=2.1&u=sgnlb&it=r&p=GVRL&sw=w&asid=5f57185dd60642b4bbd414d0ed55a5e7
Journal references
Checchetti, A. , & Fantini, A. (2015). Experimental Determination of Planck’s constant using Light Emitting Diodes (LEDs) and Photoelectric Effect. World Journal of Chemical Education, 3(4), 8792.
David B. Newell, Edwin R. Williams, Paul T. Olsen, and Richard L. Steiner. (1998 September 21). Accurate Measurement of the Planck Constant, Retrieved from http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.81.2404
Zhou, F., Cloninger, T. (2008, October) ComputerBased Experiment for determining Planck’s Constant Using LEDs. Retrieved from: http://users.wpi.edu/~physics/Labs/CTerm%20Current/PH1130/Lab%20Insructions/Photoelectic%20Effect%20%20Tuzel/ledexperimentPlanck's%20constant.pdf
Website references
Clear, S. (2010, September 7) Clear Science The Uncertainty Principle. Retrieved from http://clearscience.tumblr.com/tagged/quantum_mechanics
Eagan, R. (2011, July 25) Experimental Determination of Planck’s Constant
Maria Rute de Amorim e Sá Ferreira André (2014 February 20) Classroom Fundamentals: measuring the Planck’s constant Retrieved from http://www.scienceinschool.org/2014/issue28/planck
Rouse,M. (2006, July) Definition Quantum. Retrieved from http://whatis.techtarget.com/definition/quantum
7. Bibliography
(a) Books
Lerner, K. L. (2004). Planck's Constant. In K. L. Lerner & B. W. Lerner (Eds.), The Gale Encyclopedia of Science (3rd ed., Vol. 5, pp. 30963097). Detroit: Gale. Retrieved from http://go.galegroup.com.proxy.lib.sg/ps/i.do?id=GALE%7CCX3418501773&v=2.1&u=sgnlb&it=r&p=GVRL&sw=w&asid=5f57185dd60642b4bbd414d0ed55a5e7
(b) Journals
Checchetti, A. , & Fantini, A. (2015). Experimental Determination of Planck’s constant using Light Emitting Diodes (LEDs) and Photoelectric Effect. World Journal of Chemical Education, 3(4), 8792.
David B. Newell, Edwin R. Williams, Paul T. Olsen, and Richard L. Steiner. (1998 September 21). Accurate Measurement of the Planck Constant, Retrieved from http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.81.2404
Eagan, R. (2011, July 25) Experimental Determination of Planck’s Constant
Zhou, F., Cloninger, T. (2008, October) ComputerBased Experiment for determining Planck’s Constant Using LEDs. Retrieved from: http://users.wpi.edu/~physics/Labs/CTerm%20Current/PH1130/Lab%20Insructions/Photoelectic%20Effect%20%20Tuzel/ledexperimentPlanck's%20constant.pdf
(c) Websites
Clear, S. (2010 September 7) Clear Science The Uncertainty Principle. Retrieved from http://clearscience.tumblr.com/tagged/quantum_mechanics
Erickson, J. (2005) Planck’s Equation. Retrieved from
Maria Rute de Amorim e Sá Ferreira André (2014 February 20) Classroom Fundamentals: measuring the Planck’s constant Retrieved from http://www.scienceinschool.org/2014/issue28/planck
Rouse,M. (2006, July) Definition Quantum. Retrieved from http://whatis.techtarget.com/definition/quantum
8. Acknowledgements
We would like to thank Mr Teng and Mr Tan for guiding us throughout the entire project. We would also like to thank the lab staff for providing us with the resources we needed to do our experiments.
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