The remarkable thing about our universe is that it’s possible to explore at least some of its inner workings with very simple tools. Gravity is one example, to which [Galileo]’s inclined planes and balls bear witness. But that’s classical mechanics: surely the weirdness that is quantum mechanics requires far more sophisticated instrumentation to explore, right?
That’s true enough — if you consider a voltmeter and a Mark 1 eyeball to be sophisticated. That’s pretty much all you need for instruments to determine Planck’s constant to a decent degree of precision, the way that [poblocki1982]’s did. There’s a little more to it, of course; the method is based on measuring the voltage at which LEDs of various wavelengths start shining, so a simple circuit was built to select an LED from the somewhat grandly named “photon energy array” and provide a way to adjust and monitor the voltage and current.
By performing the experiment in a dark room with adapted eyes, or by using an opaque tube to block out stray light, it’s possible to slowly ramp the voltage up until the first glimmer of light is seen from each LED. Recording the voltage and the wavelength gives you the raw numbers to calculate the Planck constant h, as well as the Planck error Δh, with the help of a handy spreadsheet. [poblocki1982] managed to get within 11% of the published value — not too shabby at all.
Does this all still sound too complicated for you? Maybe a Watt balance made from Lego is more your speed.
21 thoughts on “Measuring Planck’s Constant With LEDs And A DMM”
Optimal results would probably be had by using a darkened room and covering one eye until it dark-adjusts, and using that eye to spot the LED’s light.
Of course you already said that. Reading skills: I’ve heard of them.
So how do you measure the charge on an electron as 1.6 x 10^-19 C, which is a prerequisite to measuring Planck’s constant with only only an LED’s and a Digital Multi-Meter ?
Do not get me wrong I think the above is very neat, but by assuming the value of one universal constant as known, it feels like a cheat.
Just have to carry out Millikan oil drop experiment 1st – https://en.wikipedia.org/wiki/Oil_drop_experiment
In the mid-1960s, while at school in Glasgow, we measured the charge on an electron using oil drops in a static field, and an gold foil electrometer! Multiple measurements produced a graph and error bars. I can’t remember exactly how well we did other than that it was well within an order of magnitude. The mass of the oil drops can be estimated by measuring the time the take to drop a calibrated distance.
We called that “Millidrop’s Oil Kan experiment”.
What’s astonishing is that Millikan did it in 1909. Such determination and patience.
As far as I’m aware, this experiment is still being carried out. I did the Millikan oil drop experiment, and the above mentioned Planck’s constant experiment in school physics class in the early 2000s.
Planck constant in eV/Hz is also useful.
As is eV-μm, where it’s close to 1. (with implied constant c)
I wonder how the value obtained varies depending on wavelength, which I’d expect due to the varying sensitivity of the retina.
LED’s have quite a spread of spectrum, but this might be narrower at lower powers (who knows, I’ve never tried it).
So as an improvement, view the LED through a spectroscope, and simultaneously measure the observed wavelength.
It is not as simple as just measuring the voltage and knowing the wavelength. Take a simple silicon diode. You all might agree that the forward bias voltage of this diode is about V = 0.7 V, but the bandgap energy is Egap ~ 1.1 eV, so you would have to give an 1 (e)lektron “1.1 Volts” of energy (-> 1.1eV) to be excited across the bandgap. Many LEDs have some sort of localised states which make them emit light, so the emitted wavelength is smaller than the bandgap energy. For high energy (blueish LEDs) the main loss might for example be a Schottky barrier at the metal semiconductor interface. I think it might be pure coincidence that you get close value. Also see doi.org/10.1088/1361-6552/ab525d .
“Take a simple silicon diode. You all might agree that the forward bias voltage of this diode is about V = 0.7 V, but the bandgap energy is Egap ~ 1.1 eV, so you would have to give an 1 (e)lektron “1.1 Volts” of energy (-> 1.1eV) to be excited across the bandgap.”
Um. The forward bias voltage is lower than the bandgap energy because at zero current, the voltage formed across the diode comes from a balance between drift and diffusion. It’s typically around 0.3V-0.4V lower, as you’ve just noted. You can ballpark it based on rough doping amounts. In other words, they’re pretty much straight related, which means pretending it’s perfect means you’ll just end up with a rough overall error.
The paper you pointed to is a bigger concern, though, which is why with most setups like this you have to be careful to pick LEDs that aren’t wavelength-shifting.
I’ll be impressed when I see someone measure Plancks Constant with some ball bearings and an inclined plane…
That is simple you just need to place the inclined plane very close to the event horizon of a black hole, and the ball bearings will be emitting light in hardly anytime at at all. But because YOU have constrained the test equipment, of course the the initial configuration will be more difficult than usual.
I remember doing this experiment as part of my Physics A level exams, here in the UK That was nearly 40 years ago :-)
This reminds me of the experiment where you measure the speed of light using a microwave and some marshmallows
I usually use grated cheese. :)
I’ve been mostly using chocolate to measure the speed of light in a microwave.
Anything this simple I had to try. On the plus side it’s pretty cool to estimate planck’s constant using an LED and a voltmeter. On the other hand, it’s frustrating because all the estimates are 10-20% low. The reason seems to be the estimate E=eV, where V is the activation voltage. Rewriting gives V=E/e. Apparently, this should be V=E/e + phi/c, where phi/c “relates to the energy losses in the semiconductors p/n junction”. (I’m just a signal processor so this is all Greek to me, a-hem…). Fyi here’s a link describing this, along with a procedure that accounts for the extra constant. They get good results, but it’s no longer simple. https://www.scienceinschool.org/2014/issue28/planck
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