Any constant in physics or chemistry comes from experimental design and consistency in measurements. For example, if you divide multiple of pressure and volume with the multiple of moles and temperature, you will get the constant R for any ideal gas.
However, given how small planck’s constant is, how can we assume its accuracy?
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Many constants, including Planck’s, are not based upon physical measurements. They are derived mathematically. Just like we don’t need to physically measure a circle to the nth degree to derive the value of pi.
The value of Planck’s constant was initially based on a statistical model, that was supposed to explain the emission of light by hot bodies. Planck never measured a single quantum of light, but his model was the only one to make sense when measuring how the light spectrums looked like.
There are many experiments that can be employed to determine Planck’s constant. A historic one is Milikan’s oil drop experiment. However, nowadays Planck’s constant has a fixed value the same way the speed of light does. Of course, this value is selected taking into account the available experimental data.
Using formulas, we can substitute in observations we have and solve for the observations that are too small (or too big) to make.
Here’s the *simplified* process for deriving Planck’s Constant:
1. Take a black hole that absorbs ALL radiation that touches it. Classical mechanics couldn’t explain radiation *from* a black hole like this.
2. Planck suggested that light could be emitted or absorbed as a set amount, instead of a wave with continuously varying wave.
3. He then suggests that the energy of a photon (the set amount) is proportional to its frequency. That gives you E = f * h, where “h” is some standard amount you need to modify the frequency.
4. When you observe data from black-hole body radiation, you can mathematically analyze the distribution of energy to give you “h”. This is Planck’s constant.
**Generally, this formula is written as E=hv, but I used “f” for “frequency” to make it easier to follow.*
easy, consider einsteins experiment for the photoelectrical effect. you take a laser and shoot it against a metal, measuring the electrical current from the metal. the energy of the current will be proportional to the energy of your laser light. since E~hf (energy = planck constant * frequency of light), you can measure plancks constant simply be finding the proportional behavior of energy and frequency of light.
Actually we know the exact value of the Planck constant nowadays, without any uncertainty.
That is because the Planck constant is one of the constants which is used to define the base units in the new SI system. So the kilogram is defined the way, that the plank value have this exact value. (Similar how it is with the meter and speed of light).
For how the value was determined historically other people has already explained
Based on our current understanding of physics, light, and quantum mechanics, we have a relationship between the energy of a photon of light, its frequency and the planck constant. Namely E=fh where f is the frequency.
The Planck constant is pretty unique because it shows up in quantum mechanics all over the place (Planck got a Nobel Prize for this for a reason). So, there are actually multiple ways to measure Planck’s constant because it doesn’t only show up when looking at light. For example, it also has a relationship with electron orbitals in an atom. We can be fairly certain the value is accurate because when we use the value with quantum mechanics, it correctly predicts other values that we’ve experimentally confirmed.
So it’s a two step process.
Step 1, measure e/h using a SQUID https://en.m.wikipedia.org/wiki/SQUID . I did this in the lab as an undergrad: it’s fiddly and needs liquid helium, but nowhere near impossible. Your signal to noise ratio is gigantic because of the superconductor involved.
Step 2, measure e using e.g this method https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4914236/#:~:text=The%20charge%20of%20the%20electron,Vs%2C%20across%20the%20capacitor.
This allows you to calculate h directly by dividing the result of step 2 by the result of step 1.
Because it’s been defined as a fixed value. The Planck Constant is EXACTLY 6.62607015×10^−34 J⋅Hz^−1 because thats HOW units like Joule and Hertz are defined. If we can eventually measure something that small, the machines will calibrate themselves by assuming the Plank Constant is correct and adjust the energy/frequency readings until that’s true.
And keep in mind all of these units are made up. They’re a way of understanding and expressing the natural world. There is no reason we couldn’t have made the Planck Constant equal to one, but that would force us to redefine how big a Joule is, how long a second is, change the definition of a Kilogram, and force us to redo and redefine most of physics. Instead, we defined certain naturally occurring phenomenon as set values and based eveything off of that
Probably the easiest example is the speed of light. Instead of basing it off of the meter and worrying about how our measurement techniques will change in the future, we flipped it around. The speed of light is EXACTLY 299792458 m/s, and a meter is defined as EXACTLY 1/299792458 of that. This ratio is the same no matter the situation, no matter the conditions, no matter how you measure it. Same as the Planck Constant.
Not sure how familier you are with the prototype kilogram, but that’s probably the best example of why we WANT to fix certain values instead of relying strictly on measurements. The kilogram was originally defined as the mass of a particular object. There were several identical copies made and shipped all over the world, but the one in Paris was considered THE kilogram. But over time the mass of these objects diverged. Oxidation, dust, small bits flaking off, weird quantum stuff…. According to the most accurate measurements in the world, the Prototype Kilogram “changed” it’s mass. But since the Kilogram was defined as EXACTLY that object it still weighted 1kg, even though it’s mass was different than the last time. So every time the prototype kilogram was weighed, the “value” of the kilogram had to be updated.
The value of planck’s constant can be measured easily by employing a really simple photoelectric effect setup. You shine light on some photometal which has electrodes across it to generate potential difference and hence an electric field of desired strength, then you measure the current passing through the photometal. You increase the potential difference up until you see the current flowing through the material go to zero. This is the point where all the energy the photons have passed onto the photoelectrons has been “absorbed” by the field and they just can’t make it to the other electrode(they have no energy left at this point). Now you see the PD you’re at and multiply this by e because this is how much energy the electron had right before all of it got “eaten” up. The energy this electron had is equal to the energy the photon that hit it was. And you also know the frequency of the light you were shining on the photometal.
Now using E = h*f you can simply do h = E/f and congrats you’ve just calculated the value of planck’s constant!
The purpose of this whole thing was to just express that planck’s constant isn’t exactly “made up” but is a constant that can be experimentally verified. We also did Millikan’s oil drop experiment for it but I missed that lab so…
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