There are (probably) less than two dozen fundemental constants that define the physics of our universe. Determining the value of them might seem like the sort of thing for large, well funded University labs, but many can be determined to reasonable accuracy on the benchtop, as [Marb’s Lab] proves with this experiment to find the value of Planck’s Constant.
[Marv’s Lab] setup is on a nice PCB that uses a rotary switch to select between 5 LEDs of different wavelengths, with banana plugs for the multi-meter so he can perform a linear regression on the relation between energy and frequency to find the constant. He’s also thoughtfully put connectors in place for current measurement, so the volt-current relationship of the LEDs can be characterized in a second experiment. Overall, this is a piece of kit that would not be out of place in any high school or undergraduate physics lab.
To use this to determine Planck’s constant, you need to use Planck’s relation for the energy of a photon: get some energies (E), plug in the frequency (f), and bam! You can generate a value for h, Planck’s constant. The energies? Well, that’s a very easy measurement, but it requires some understanding of how LEDs work. [Marb] is simply measuring the voltage needed to just barely light the LED of a given frequency. For frequency, he’s relying on the LED datasheets.
That translates to the energy of the photon because it corresponds to the energy (in electron volts) required to jump electrons over the bandgap of the semiconductor in the LED — that’s how the light is generated. Those photons will have the energy of the gap, in theory.
In practice, the LEDs do not emit perfectly monochromatic light; there’s a normal distribution centered on the color they’re “supposed” to be, but it is fairly tight. That’s probably why is able to [Marv] get to within 5% of the canonical value, which is better than we’d expect.
This isn’t the first time we’ve determined plank’s constant; it’s quite possible to get to much higher accuracy. The last time we featured this particular technique, the error was 11%.
Seems like cheap equipment can get you 95% of the way there but it’s expensive equipment that gets you the last 5%.
The last five percent doubles the difficulty, the last one percent 10x, the last 0.1% 1000x
The old (software) joke is the first 90% of a project takes 90% of the time, and that last !0% takes the other 90%.
But yeah, cheap stuff gets you mostly there, which is often good enough.
at 5% accuracy, pi = 3.
Cool experiment, though
“at 5% accuracy, pi = 3…”
There is basic, basic philosophical difference between physics and mathematics.
Hint: ever hear of anyone winning ‘The Nobel Prize for Mathematics”?…
You haven’t.
You never will.
Some are able to get a Nobel prize.
Some, the Abel.
The prize was irreversibly tarnished back in 2009 when it diminished the work of legitimate canidates by demeaning their work and putting a career “community organizer” on a pedestal above them. A person who has done absolutely nothing constructive for humanity.
which is awesome, no more pesky decimals… I’ll go live in a 5% world I think
No it’s not. It’s 3.14 +/- 0.16
Pi could be 3.3 just as well.
that’s cool though… like wrapping some string around a cylinder and then measuring it with my hands, i’d be pleased if i got 3 as the answer. when you’re doing measurements with tools that are primitive relative to the task, 5% isn’t bad. a first stab at it.
I remember blowing someone’s mind pointing this out two decades ago. That was fun. (“this” = That the energy of a photon matches fairly nicely to the voltage needed to drive an LED for that wavelength of light.)
That’s pretty neat. Question though, is the value of h used anywhere by the multimeter or datasheet? I just want to be sure we’re not using h to calculate h.
It probably depends how the manufacturer of the LED determines the wavelength to advertise. If they’re re-arranging the formula to f = E/h and then doing the same experiment, then we’re really just comparing multi-meters.