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  • Author Author: fmilburn
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Today I learned something new about LEDs

fmilburn

Introduction

 

I ran into this interesting post today: https://www.thingiverse.com/thing:2592741

 

What a cool device!  I am waiting on delivery of a board for my current project and had some time so decided to look into the determination of Plank's Constant with LEDs myself.  Judging by the number of hits in an internet search this is a common experiment now in undergraduate physics labs.  See for example this link: http://home.sandiego.edu/~rskelton/phys197lab/Plancks_Constant_Red_Tide.pdf

 

The derivations are in the link and a search will find much more material.  But briefly, if the wavelength of an LED is known and if the turn on voltage of the LED can be determined (where photons are first emitted) then the energy of the photons released can be determined.  The Planck-Einstein equation is:

 

E = h f

 

where E is the energy of a photon, h is Plank's constant, and f is the frequency of the light which is the inverse of the wavelength times the speed of light.  By measuring different LEDs with different wavelengths we can see that the energy is indeed proportional to frequency, and estimate Planck's Constant.

 

Equipment

 

  • Multimeter to measure voltage across the LED
  • Multimeter to measure current through the LED
  • Bunch of different LEDs with known wavelengths
  • Variable voltage source - can be a variable power supply like I used or a potentiometer set up as a voltage divider across a fixed voltage

 

Below is my collection of 5 mm LEDs.  The top row has LEDs from a well known manufacturer with datasheets showing wavelength.  The others are a mix of things I pulled out of old equipment and cheap stuff from the usual internet locations and no data.

image

And here is my test setup.  Please don't look too closely, there is a photo with better organization and equipment in the link above :-)

 

image

In the photo above the voltage is cranked way up to show the yellow LED lit in the small breadboard.  The current is 389.3 uA which is way higher than what we will be measuring.  A limiting issue here is the range of my multimeter but we work with what we have.  My voltage source is kind of rough too.  Oh well...

 

Test Procedure

  1. Insert a LED into the breadboard
  2. Turn off the room lights and adjust the voltage down until the LED just turns off
  3. Record the voltage (V) and current (uA) from the meters
  4. Take additional measurements at increasing voltages so that the slope of the curve around the turn on voltage for the LED can be examined (as noted above, my current measurements are very rough - no more than +/- 10% at best)
  5. Return to step 1. until all LEDs are measured

 

Data

image

Click to make larger if it is hard to read.  This table above shows the data for LEDs where I have a datasheet.  Starting at the top and going down there are blue, green, yellow, red, and IR LEDs.  I chose to call the point for each LED with the lowest current reading the turn on voltage.  Some observations:

 

  • The eye is an amazing instrument.  The lowest current for most of these LEDs is the one I judged where the LED just turned off in a darkened room.  One source I saw used this method and I decided to record it at first just to see how sensitive my eyes were.  Turns out they can easily see the emissions from a current of just a couple of uA.  And my multimeter can't go any lower than that.
  • The green LED sticks out in that I could see down to 1 uA as measured on my meter.  For those who aren't color blind, green cones in the eye are the most sensitive.

 

I also decided to look at some LEDs where I did not have a datasheet and these are shown on the table below:

image

In order, from top to bottom, they are orange, pink, RGB red, RGB green, and RGB blue LEDs.  The RGB LED is a common cathode RGB 5 mm LED with a somewhat diffused case.  The individual pins were stuck in one at a time and measured.  Some observations:

 

  • Orange doesn't look too surprising.  It is falling between the wavelength of red and yellow for the known LEDs.  There is a table in the link above that shows the kind of overlap that can occur.
  • Pink is surprising.  Note that the voltages look like blue more than anything else.  What is happening?  From an internet search I found that pink LEDs are frequently made from one or two phosphor layers over a blue LCD:  LED types by Color, Brightness, and Chemistry
  • The RGB looks about right although for some reason although blue is a bit of a flier.  By eye the blue was detected at a very high current relative to the other LEDs.  To get the turn on Voltage I relied on turning the voltage down to 0.2 uA as read from the multimeter.  Blue is the lowest response cone in the human eye and this LED had a diffused case.  But it still seems a bit of an outlier.

 

Determination of Planck's Constant

 

image

Now it is time to see how well I did.  In the table at top left and in the plot on the right the turn on voltage is plotted as a function of the inverse wavelength of the LED.  The LEDs without datasheets are omitted.  A least squares fit was then made and the slope calculated.  The data is very highly correlated with an offset from the origin.  This offset is expected due to the way the experiment was conducted but the slope should be OK.  We can now calculate Planck's Constant from the following formula:

 

Planck's Constant = (Experimental Slope) x 10-9 x electron charge * speed of light,  or

h = m * 1E-9 * e / c

 

The constant 1E-9 is needed since wavelength here is in nanometers and speed of light is in meters.  The values for other constants are shown in the table.

 

And the calculated value is 7.37 E-34 Js Vs. an accepted value of 6.63E-34 Js.  The error is 11%.

 

I think this is reasonable given the equipment and methods used.   I hypothesize that the error could be reduced by:

  • Better definition in the procedure on what constitutes the turn on voltage.  Just where does it occur exactly?
  • More accurate measurement of current for determining the turn on voltage.  Maybe use my oscilloscope and a low value resistor.  Or ask for a new multimeter for Christmas.
  • Measurement of wavelength at turn on rather than using the datasheet which is measured at 20 mA.  Don't have the equipment for that.
  • More accurate voltage measurement (this is probably second order)
  • Steadier voltage source (second order again)

 

If you made it this far, thanks for reading image

 

Update:  The Wikipedia article is pretty good also https://en.wikipedia.org/wiki/Light-emitting_diode  

  • in reply to jw0752

    Thanks John,

    I'd love to see what kind of results others could achieve with an improved approach to the method.  I did a quick internet search after completing the experiment and found one student who claimed on the order of 3-4% if I remember correctly.

    Frank

  • Hi Frank,

    What a neat experiment and a great post. I always appreciate a mixture of electronics and physics in the blog posts. I will have to give this one a try myself.

    John

  • I have to point out that both Planck's constant and the energy formula you presented are probably not correct.

     

    In my research, I discovered that Planck's constant has only been validated for wavelengths between 1 and 3 microns.

     

    The energy formula E = hf is incorrect.

     

    The energy of photons is determined by their mass, which decreases with frequency.  It was this wrong interpretation that makes people assume that high frequency photons have more energy.

    In fact, the lower frequency photons have much more energy, which is why IR is the main component of energy transfer.

     

    Planck created his fudge factor h when he was trying to fit his data to the formula.  He needed a way to account for what he thought was an anomaly when he ran into UV light.  His factor h fixed his data and Planck himself worried that it was wrong.  Unfortunately, the Quantum Mechanics mafia grabbed hold of the constant and declared it valid and immutable.  So now everyone uses the constant everywhere, even though it has never been verified.

     

    The experiments you ran fit his rough data, but it misses the real issue of understanding what photons are and how they really work.

     

    DAB

  • A great and interesting write up with clear explanations of what you are doing - thank you. I think your initial 11% error is very good considering your home-made approach.