Quantum tunneling as a means for perpetual energy generation?

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Offline Supercryptid

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The name of this topic should obviously set an alarm off in your head thanks to the first law of thermodynamics. According to what I know, either:

A. Quantum tunneling can, in principle, produce energy from "nothing".


B. Something about my understanding is flawed.

Either way, I hope to learn something today (or this week). So here is my illustration:

Let's say that you have a single hydrogen atom in its ground state inside of a tiny, closed universe (or an impenetrable box, whichever you prefer). The electron is bound via electromagnetism to the proton that makes up the nucleus. The electron does not have sufficient energy to escape from the proton's pull, and thus is stuck in its 1s orbital. Until we consider quantum tunneling, that is. After some period of time, perhaps some very long period of time, it becomes statistically likely that the electron will simply tunnel out of its orbital without the needed energy input of 13.6 electronvolts. This tiny universe now contains a free proton and a free electron.

Since this is in a closed universe, the electron and proton float around aimlessly and are likely to come close to one another again at some time in the future. When this happens, the two particles feel one-another's charges and come together to reform the original hydrogen atom. However, since a hydrogen atom is 13.6 electronvolts more stable than a lone proton and electron, the atom must emit a photon with 13.6 electronvolts of energy. This is a photon that did not exist before. Where did this energy come from? After some period of time, quantum tunneling may allow the electron to escape a second time, which might form a second photon, and so on and so forth.

So what am I misunderstanding?
« Last Edit: 26/04/2008 12:18:32 by Supercryptid »
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Offline graham.d

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Quantum tunneling as a means for perpetual energy generation?
« Reply #1 on: 26/04/2008 14:28:47 »
My understanding of quantum tunnelling is not that a particle has a finite chance to move into a much higher energy state, as in your example, but that it can overcome a potential barrier to get to the same state on the other side. This is used in semiconductor storage devices and occurs (to detrimental efects) in other semiconductor devices. Both these cases involve charge carriers (usually electrons) being able to pass through a Silicon Dioxide insulating barrier without (classically) having the energy to do so.

In your example the electron moves to a much higher energy state. I don't think this can happen in the idealised circumstances you envisgage. It would require interaction with something (like another atom or the walls of the container) to acquire the extra energy.