Planck's Constant using LEDs

A Simple Experiment With Which You Can Derive The Value of The Planck’s Constant At Home.

In 1900, Max Planck presented one of the most revolutionary papers in humankind’s history, the paper that gave birth to the Planck’s constant and the theory of Quantum Mechanics. Max Planck presented his paper titled Zur Theorie des Gesetzes der Energieverteilung im Normalspektrum that explained the Law of Energy Distribution theory in Normal Spectrum and changed our perception of the observed universe at the microscale. Planck explained the blackbody radiation spectrum in the most unerring manner by putting forward his revolutionary Planck’s law. (A detailed explanation of what Planck did can be found in this video)

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Max Planck, the father of quantum physics

Planck assumed that the standing waves in a blackbody could only have a particular energy, in the multiples of hν where h is the Planck’s constant and ν is the frequency. Thereby, Planck unknowingly introduced one of the most important fundamental constant in physics, the Planck’s constant, while trying to explain the blackbody spectrum. So in simple words, Planck’s constant is a quantum of electromagnetic action that relates a photon’s energy to its frequency. When the Planck constant is multiplied by a photon’s frequency, the resultant product corresponds to its energy. 

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When Planck calculated the value of Planck’s constant from experimental data on black-body radiation,  he found it to be 6.55×10-34J⋅s. By definition, the most precise value of the Planck constant calculated to date is 6.62607004 × 10-34 J.s. Whenever we think of how the fundamental constants’ values are calculated, we generally create an image of very extensive, elaborated, and advanced experimental setups in our minds. No doubt that some of the fundamental constants’ precise experimental measurements really need some huge complicated setups. But you know what, the case with the measurement of the Planck’s constant is somewhat different.

There are some simple experiments with which even a high school student can deduce the value of Planck’s constant with minimal setup and apparatus requirements. And one of the easiest methods is the one utilizing LEDs. How? Let’s have a look!

Determination of Planck’s constant with LEDs (Light emitting diodes):

To understand how the LEDs can be used to evaluate Planck’s constant value, we first need to know how a Light Emitting Diode actually works.

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As the name says, a Light Emitting Diode(LED) is a two-terminal semiconductor device that emits light of frequencies characteristic of the material. In the unbiased condition, a potential barrier gets developed across the LED’s p-n junction. However, when the LED is connected to an external voltage in the forward-biased direction, the potential barrier’s height across the p-n junction gets reduced. At a particular voltage, the potential barrier’s height eventually becomes very low such that the electrons’ energy becomes sufficient to let them start crossing the junction.

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As the electrons start crossing the junction, they are in an excited state. And when they return to their normal state, energy is emitted in the form of photons, and the LED starts glowing. This particular voltage at which the LED begins to glow is called the knee voltage or the threshold voltage. Once the knee voltage is reached, the current may increase, but the voltage does not change and almost remains constant.

Now, the light energy that gets emitted during forward biasing is given as E=hc/λ where c is the velocity of light, h is the Planck’s constant, and λ is the wavelength of light being emitted by the LED (like λ for a blue LED is near about 450nm while λ for a red LED is near about 625 nm and so on)

Furthermore, if V is the forward-biased voltage at which the LED starts glowing, which means if V is the knee or the threshold voltage, then the energy acquired by electrons crossing the junction is related to V as E=eV where e is the charge carried by each electron(1.6 × 10-19 C). As this energy corresponds to the light energy being emitted by the LED, so by comparing the last two equations for E, we arrive at the relation:

V=(hc/e)(1/λ)

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The graph between V and 1/λ. The slope of the graph gives the value of hc/e

Here, h,c, and e are the constants, which means that V and λ are inversely proportional to each other. This equation says that if we plot a graph between the knee voltage (V) and the inverse of wavelength (1/λ) for different LED lights, we will obtain a straight line, and the slope of that line will correspond to the value of the constant hc/e. Let’s say, if the slope of the line obtained is m, then m=hc/e. Finally, by employing this relation, we can find the value of Planck’s constant to be:

h = em/c

In this way, only with the aid of a few different LEDs of known wavelength, a power supply (0-10V), a resistor, and multimeters (to measure voltage and current) we can derive the value of the Planck’s constant at home. However, while experimenting, we need to take care of a few things. First of all, LED is a susceptible device. So while increasing the voltage, it must be increased in small intervals to save the LED from any damage. Moreover, to get a precise value of h, the value of threshold voltage must be noted as soon as the LED just starts glowing.

A reference circuit to calculate the value of the Planck's constant
A reference circuit to calculate the value of the Planck’s constant

I hope this article helped give you an idea of how you can derive the value of Planck’s constant with the simple apparatus at your school’s/college’s physics lab or even at your home. If you give it a try, share your derived value of Planck’s constant in the comments section.

Happy Learning!

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