Cherenkov Radiation for lighting

In summary: This is why it is so hard to increase the speed of something travelling close to the speed of light, as the energy required is immense. In summary, the theory is that because the electrons in carbon nanotubes travel closer to the speed of light when under the effects of any potenital difference than most other materials, would it be possible to place two electrodes made of pure nanotubes in a small amount of heavy water (possibly containing an ionic solute to aid conductivity, and to slow light even more) and pass a current across it. The electrons traveling in the nanotubes would enter the water, where the speed
  • #1
Kracatoan
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After writing a physics paper on carbon nanotubes, I've been constantly wondering about a theory I invented and investigated in it, the theory being that because the electrons in carbon nanotubes travel closer to the speed of light when under the effects of any potenital difference than most other materials, would it be possible to place two electrodes made of pure nanotubes in a small amount of heavy water (possibly containing an ionic solute to aid conductivity, and to slow light even more) and pass a current across it. The electrons traveling in the nanotubes would enter the water, where the speed of light is less and then release this light as Cherenkov Radiation, creating a lovely ambient glow.

Just for reference, these extracts are taken from my paper -

The bit about why the electrons move so fast

Unfortunately, AS level (or even A2) physics cannot explain why carbon nanotubes conduct as well as they do, so we will have to delve into the dark and murky realm of quantum mechanics.
Firstly, we must confront the Hall Effect. This is where, under a magnetic field and potential difference through a conductor, another potential difference will be created going perpendicular to the electrical current and magnetic field, as the diagram shows. This applies perfectly well to all 3D conductors, but does not apply to 2D conductors. As strange as it sounds, everything in the 3D world does not need to be 3D, and this is effectively the case with carbon nanotubes. To prove this, we must look at a sheet of graphene. First, we take the plane of the graphene to be x and y, and the plane perpendicular to the graphene to be z. Intuitively, we assume that electrons can move in any way, back, or forwards, left or right, up or down, and this is normally the case. However, in the quantum world of graphene, movement up and away from the plane of graphene is quantised, this means that electrons can only be in certain distances away from the graphene at any time. This would still allow them to move away from the graphene, but for the fact that the quantum levels are almost infinitely small. This allows us to effectively ignore the z axis and so leave us with just x and y – a 2 dimensional object. Remember, 2D conductors are not as rare as you might expect, all that is required is a 2DEG (2 Dimensional Electron Gas), for example, super-cooled helium produces a 2DEG and many transistors nowadays are made from 2DEG containing semi-conductors.
Now, 2D conductors do not abide by the traditional Hall Effect, instead they experience the Quantum Hall Effect. In this, the magnitude of the voltage generated by the Hall Effect takes on quantum values – you can only get certain results which are divided by the Landau energies, as series of quantum energy levels which vary according to the strength of a magnetic field. In most systems which undergo the Quantum Hall Effect, the results create a rather lovely looking fractal. This is a trend that almost every known substance abides to, as it is determined via electrons, whose properties are constant, rather than the properties of the material itself. True for everything, that is, except for one exception - Carbon Nanotubes or Graphene, in which they are different. Normally, in order to create the Quantum Hall Effect, the material in question needs to be at a very low temperature, usually the temperature at which Helium becomes a liquid. In Graphene and CNTs, the effect can be observed at much, much higher temperatures, even room temperature. Also, the quantum values produced are half that of the normal Quantum Hall effect, which isn’t meant to be possible. So, in order to find out what is happening, we need to use the Shubnikov-de Haas Effect. This determines the harmonic oscillation of a particle (in this case the electrons) under the influence of a magnetic field and at low temperatures, and therefore the mass of said particle. This investigation results in the surprising result that, in graphene and carbon nanotubes, electrons have no mass. So, we can now explain the excellent conductivity of graphene and carbon nanotubes using special relativity.
Special Relativity states that as a body approaches the speed of light, space and time become compressed and with them it’s mass. As the mass is compressed, it increases in size and so makes it harder and harder to provide enough energy to increase the speed of the object in question. This is proven by the formula above, as the energy of the object (E) increases with acceleration; m also increases in size because c remains constant. Then, as the second formula shows, when more force (F) is applied to increase the acceleration (a), it is divided by an ever increasing mass and so the acceleration produced gets smaller and smaller. So, this prevents electrons in almost all substances from being able to move very fast because huge amounts of energy are needed to speed them up (in a vacuum, electrons can get very close to the speed of light due to no resistance, but that isn’t relevant). But, as is the case with Carbon Nanotubes and Graphene, the electrons have no mass (seeing as they have no mass, they can be called luxons). This would imply that the electrons can move at the speed of light in a material. Unfortunately, that would be pushing relativity a little too far and they are slowed down by the resistivity of the graphene/carbon nanotube to a more sensible, four-hundredth of the speed of light. This is approximately: 75,000,000 cm/second

and the bit about Cherenkov Radiation, follow this link for a nice picture http://img98.imageshack.us/img98/324/29197750.png"

A highly unusual use of the unusual properties of carbon nanotubes would be as inexpensive sources of lighting. This is due to Cherenkov radiation. This is a peculiar effect produced when electrons traveling near to the speed of light enter a medium, such as water, in which light travels slower than the electron. The electrons entering the water will polarize the atoms in the water molecules (seeing as the electrons carry a negative charge). This means some of the electrons in the energy levels in each atom will be given enough energy to move up to a higher energy shell. However, electrons always want to occupy the lowest energy state and so jump back down to a lower shell (It must be noted that electrons only ‘jump’ up energy levels because those electron energies are quantised, they can only occupy discrete energy levels). As the electrons jump down a shell they need to lose this energy, so they emit a photon. This produces an effect similar to a sonic boom; the electrons out-pace the photons produced by other electron’s entry and so cause them to stack up. This results in a much more concentrated ‘wave’ or ‘cone’ of light in front of the electrons and this is seen as an intense blue light. The light is blue because photons are not particles, they are waves (as proved by Thomas Young’s Double-Slit experiment), as the photons ‘stack up’ the waves are compressed together. The photons produced by the electrons entry usually have a frequency which encompasses the visible light spectra. So, normally the light produced should be white (white light is produced when all the colours in the visible light spectrum mix together), but because they are compressed, we can fit more waves in any given space, this gives the light a higher frequency which effectively shifts the spectra produced towards the blue end of the electromagnetic spectrum, hence the blue light. This phenomenon is usually only observed in nuclear reactor cores, as this image on the previous page shows, and in certain particle physics experiments. Seeing as electrons in a carbon nanotube travel much faster than light in water, an open-ended nanotube cable in even a small amount of water could produce enormous quantities of photons which would become visible as blue light. Seeing as a very little amount of electricity is needed (this is only the case with carbon nanotubes, usually lots of energy is needed), this could act as a reliable and cheap light source.

That's all :)
 
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  • #2
I have looked at Cerenkov light in Lucite from pulsed electron beams through a 4-foot water window, and Cerenkov light in a pool-type reactor through about 25 feet of water. It's not very bright. If you want enough light to read by, you will get a lethal radiation dose in a few seconds. A single relativistic particle in water will create ~ 400 visible photons per cm, so the light is very dim. See Eq (11) in
http://ab-div-bdi-bl-blm.web.cern.c...ectors/Literature/schaefer_biw02_tutorial.pdf

or for derivation see Schiff Quantum Mechanics (second edition) 267-271.

Bob S
 

Related to Cherenkov Radiation for lighting

1. What is Cherenkov radiation?

Cherenkov radiation is a type of electromagnetic radiation that is produced when a charged particle, such as an electron, travels through a medium at a speed faster than the speed of light in that medium.

2. How is Cherenkov radiation used for lighting?

Cherenkov radiation can be used for lighting by directing a beam of high-energy charged particles, such as electrons, into a transparent medium, such as water or glass. As the particles travel through the medium, they emit Cherenkov radiation, which can be visible as a blue light.

3. What are the benefits of using Cherenkov radiation for lighting?

Using Cherenkov radiation for lighting can be more energy-efficient and cost-effective compared to traditional lighting sources. It also produces a bright, uniform light that can be easily controlled and directed.

4. What are some applications of Cherenkov radiation for lighting?

Cherenkov radiation has been used in various applications, such as in nuclear power plants for monitoring and detecting radioactive materials, in medical imaging for producing images of internal organs, and in particle accelerators for studying the properties of particles.

5. Are there any safety concerns with using Cherenkov radiation for lighting?

Cherenkov radiation is generally considered safe for use in lighting applications, as the levels of radiation emitted are very low. However, precautions should still be taken to ensure that the source of the radiation is properly shielded and that exposure to the radiation is limited.

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