# How does conservation of energy apply at the nuclear level?

• B
• Vandenburg
In summary, subatomic particles such as electrons do not actually rotate or vibrate around the nucleus, but their behavior can be described by the mathematics of waves. The wave function gives the probability of finding a particle in a certain location or with a certain property, and this can change as measurements are taken. The concept of temperature also plays a role in the energy of subatomic particles. Ultimately, energy is conserved and the wave function is not something that can be physically seen.
Vandenburg
TL;DR Summary
At the atomic level, there appears to be "perpetual motion". How does that work?
Electrons rotate around a nucleus for long periods of time. Where does the energy for this motion come from?
Ok, I realize that electrons don't actually rotate around the nucleus, like a tiny solar system. But if the electron is wave function, it's still constantly vibrating, constant oscillating. That seems like perpetual motion.

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Vandenburg said:
Ok, I realize that electrons don't actually rotate around the nucleus, like a tiny solar system. But if the electron is wave function, it's still constantly vibrating, constant oscillating. That seems like perpetual motion.
Not quite. In fact, nothing is waving or oscillating at all. It turns out that at the very small scale of atoms and subatomic particles, the math that best describes their behavior is a more complicated version of that which describes normal waves even though nothing is oscillating. It might be better to think of the wave function as something that describes the change in probability density with either a change in space or time. That is, the wave function gives us the probability of finding a particle in a certain location or finding one of its properties at a certain value, and this probability can change as you measure at a different point in space or if you measure again after some time interval.

Note that finding an electron on one side of an atom, and then measuring again and finding it on the other side, doesn't mean that the electron needed to be given some energy to move from the first to the second measuring points. It's simply due to the uncertainty associated with the electrons position.

So my next question would have been, well why do I hear of subatomic particles "vibrating" or having a certain "frequency", but I've just been off looking that up, and what I seem to see is, no, there is no actual motion, there is a static state which happens to be best described by the mathematics of waves.

Vandenburg said:
So my next question would have been, well why do I hear of subatomic particles "vibrating" or having a certain "frequency", but I've just been off looking that up, and what I seem to see is, no, there is no actual motion, there is a static state which happens to be best described by the mathematics of waves.
That's a question I'll have to let someone else answer, as I don't know enough about the subject to explain it with any real confidence.

Vandenburg said:
why do I hear of subatomic particles "vibrating" or having a certain "frequency"
Because popular science loves descriptions that sound cool, independent of their accuracy.

But aside from that: You don't need energy to keep orbiting something. In Newtonian mechanics two things could orbit each other based on gravitational attraction forever. General relativity tells us they cannot because they emit gravitational waves, but even there you could make e.g. a disk that rotates forever. You just need a completely lossless system, and you cannot extract any energy from it.

There is also temperature to consider. Matter at a temperature higher than absolute zero has motions that might be described as vibrations. It depends partly on whether the object is solid, liquid, or gas. The temperature is directly proportional to the average kinetic energy of particles in motion.

If the matter was perfectly isolated, it would not need any additional energy to maintain the same temperature. But perfect isolation is not really possible. Therefore an object can gain or lose heat energy to other objects or via radiation. When it does gain or lose, its temperature changes.

So fear not. Energy is conserved.

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Vandenburg said:
So my next question would have been, well why do I hear of subatomic particles "vibrating" or having a certain "frequency", but I've just been off looking that up, and what I seem to see is, no, there is no actual motion, there is a static state which happens to be best described by the mathematics of waves.
That's right.
The wave function vs the probability amplitude of the function is what has to be distinguished and some writings do not do that very well. Electron in a box and all that stuff.

Just an addendum to post of @Drakkith as another way of looking at it.- One can also consider the wave function, and the associated orbital of the electron, not as being used to describe points where the electron is to be found, but rather the orbital is the electron itself. No electron - no orbital. Yes an electron - an orbital.

By the way, no one has seen the actual wave function that the math describes.

Thank you all for your various answers. I'm trying to gain some intuitive understanding of quantum behaviour, despite having been told that this is a perfectly useless endeavor.

Delta2 and PeroK
Vandenburg said:
Thank you all for your various answers. I'm trying to gain some intuitive understanding of quantum behaviour, despite having been told that this is a perfectly useless endeavor.
Many things are counter intuitive in the quantum world, or even worst they don't make a lot of sense if you think about them with common logic or the usual common scientific logic.

bob012345
Vandenburg said:
Thank you all for your various answers. I'm trying to gain some intuitive understanding of quantum behaviour, despite having been told that this is a perfectly useless endeavor.
I was told by my quantum professor not to ask such questions regarding what is really happening. That's when I adopted the "shut up and calculate" attitude.

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Delta2

## 1. How is energy conserved in nuclear reactions?

Energy is conserved in nuclear reactions through the principle of mass-energy equivalence, as described by Einstein's famous equation E=mc^2. This means that the total energy before and after a nuclear reaction remains constant, with any changes in mass resulting in an equivalent change in energy.

## 2. Can nuclear energy be created or destroyed?

No, nuclear energy cannot be created or destroyed. It can only be converted from one form to another, such as from potential energy in the nucleus to kinetic energy in the form of radiation or heat.

## 3. How does the conservation of energy apply to nuclear power plants?

In nuclear power plants, the energy released from splitting atoms in a nuclear reaction is used to heat water, producing steam that turns turbines to generate electricity. This process follows the principle of energy conservation, as the energy released is converted into a different form for practical use.

## 4. Does the conservation of energy apply to both fission and fusion reactions?

Yes, the conservation of energy applies to both fission and fusion reactions. In fission reactions, energy is released when a heavy atom splits into smaller fragments, while in fusion reactions, energy is released when two small atoms combine to form a larger one. In both cases, the total energy before and after the reaction remains constant.

## 5. How does the law of conservation of energy relate to nuclear weapons?

The law of conservation of energy applies to nuclear weapons in the same way as it does to any other nuclear reaction. The energy released from the splitting of atoms in a nuclear explosion is a result of the conversion of mass into energy, following the principle of mass-energy equivalence. This energy release is what makes nuclear weapons so destructive.

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