You Can Measure This Fundamental Quantum Constant Using LEDs

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Planck’s constant is one of the fundamental constants What sets all the “rules” for how things work in our universe. (It is named after theoretical physicist Max Planck, best known for his work on quantized energy and for winning the 1918 Nobel Prize in Physics.) This letter is represented by. NS.

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You may already be familiar with some other fundamental constants:

  • speed of light (C) is the constant value that all observers measure for all electromagnetic waves.
  • universal gravitational constant (Yes) It is the relation between force, mass and distance for objects involved in gravitational interaction.
  • fundamental electric charge (I) is the charge of the electron and the proton. (They have opposite signs, meaning the electron is negative and the proton is positive.) Every charged object is some integer multiple of this value.
  • Coulomb constant. This is a value in the equation for the interaction between electric charges.

The value of Planck’s constant is 6.626 x 10. Is-34 Joule-second, and it mostly appears in calculations related to quantum mechanics. It turns out that really small things (like atoms) don’t behave like really big things (like baseballs). On this ultra-small scale, our classical view of physics doesn’t work.

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If I throw a baseball, it can have a lot of kinetic energy. I could throw it so it is moving with a speed that gives a kinetic energy of 10 Joules, or 10.1 J, or 10.00001 J. It seems that any value is possible. This is not true at the atomic level.

Let us consider the hydrogen atom. (We’ll choose hydrogen because the simplest atom is the easiest to use.) It has a single electron that interacts with a proton. Electrons Can Have Different Energy—But Not Any energy. It can have an energy of -13.6 eV, or -3.4 eV or -1.5 eV. (eV is an electron-volt, a unit of energy.) But it cannot have an energy of -5 eV—this is not possible. This is because the energy levels of hydrogen are “quantized”, meaning that there are only discrete allowable energies.

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You’ve seen some other examples of quantized things—like stairs. Let each step be 10 cm higher than the step below it. This means that you can stand on the floor with a height of 0 cm, or stand at 10 cm on the first step. However, you cannot stand at a height of 0.5 cm as there is no ladder. The same is true with quantized energies.

Planck’s constant sets the quantization scale for all systems – but it’s only really noticeable for atomic-sized things. Let’s go back to using baseball as an example. you can’t really throw the ball with Any energy. (Remember, I said “too much someone.”) But the difference in the energy of the ball is so small that you will never be able to measure the small jump in energy level. It’s like a set of stairs with each ladder as long as the thickness of a sheet of paper. The levels are so small that you will feel like you are walking on a constant slope.

Planck’s constant is used to measure things that have quantum energy levels that are larger than the object’s energy (as opposed to a baseball). It comes into play to measure the energy level for an atom, or to measure the wavelength of a moving particle, like an electron. It is also used to calculate the distribution of energy for a blackbody (an object that gives off light only because of its temperature), and for the uncertainty principle which gives the relationship between the measurement of position and momentum.

Finally, Planck’s constant appears in the energy-frequency relationship. This means that in order to change the energy level in a quantum system, you have to disturb it at a particular frequency. In this expression, E is the change in energy levels, NS is Planck’s constant and F is the frequency of the disturbance. One way we can disturb a system is with electromagnetic radiation—also known as light.

Illustration: Rhett Allen

If you want to take an electron in a hydrogen atom and excite it from the first energy level to the second, you’ll need a particular frequency of light to hit it. In this case, it is 2.46 x 10 . will lighten with a frequency of15 Hertz.

It also works in reverse order. If you move the electron to the second energy level and it drops to the first energy level, it produces light with a frequency of 2.46 x 10.15 Hertz.

You can’t really see that light, at least not with your mortal eyes – it falls in the ultraviolet region of the electromagnetic spectrum. This change in energy levels to generate electromagnetic radiation is one of the important methods we can use to create light, in particular, with fluorescent lights and LEDs (light-emitting diodes)—which give us a Will get it in a moment.

There is another version of this energy equation. Since disturbance is caused by light, we can describe it with wavelength rather than frequency. All waves have a relationship between wavelength, frequency and speed. light waves travel at a constant speed C. (See, we use these fundamental constants all the time.) This creates the following equation, where is the wavelength:

Illustration: Rhett Allen

(Often, physicists prefer to remain calm. Most of the time, we use the Greek letter (it’s not v) for frequency. It feels more sophisticated to write it that way.)

With this relationship between wavelength and frequency, we get this modified energy equation:

Illustration: Rhett Allen

It turns out that it is easier to think of the interaction between light and matter in terms of wavelength rather than frequency.

Well, all this was just a setup for an experimental method to determine the value of Planck’s constant. The basic idea here is to use the colors of an illuminated LED to demonstrate this energy-wavelength relationship. If I can find out the amount of energy needed to produce the light, as well as the wavelength (in other words, the color) of the light produced, I can determine NS.

There are a few little tricks involved—so let’s figure it out.

Energy and LED

LEDs are everywhere. That flashlight on your smartphone and the new light bulb you have in your home are both LEDs. The red light in front of your television—it’s an LED. Even your remote uses an LED (although it is an infrared one). LEDs come in various colors. You can easily find red, yellow, green, blue, purple and more.

An LED is a semiconductor device with an energy gap, often referred to as a band gap. When the LED is connected to a circuit, it starts the flow of electrons. The energy gap is just like the energy transition in the hydrogen atom. Electrons can be present on either side of the band gap, but not in the middle. If an electron has the right energy, it can jump across the band gap. And since the electron loses energy in the jump, it produces light. The wavelength, or color, of this light depends on the size of that band gap.

If you connect an LED to a single D battery with a voltage of 1.5 volts, nothing happens. In order for the LED to glow you need to increase the voltage to a certain value – this is called forward. The red LED usually requires about 1.8 volts and the blue one takes about 3.2 volts.

Let’s actually measure this value. Here is my experimental setup. I have a variable power supply connected to an LED. I can gradually increase the voltage and measure the electric current. Only when the current starts to rise, will you be able to see visible light.

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