# Kinetic energy of a nucleus

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Yes.

Anything in nature that has a motion is translated into, say linear or rotational kinetic energies.

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What confuses me though, is when we speak of hyperfine structure, I tend to think of the Zeeman effect and in terms of angular motion, it translates into a spin orbit coupling equation and tends to split the hyperfine energy levels. The spin orbit coupling equations are actually quite beautiful.

Still, anything that rotates, actually has a correction term

$E_{kin} = E+ E_{rot}$

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13 hours ago, Giorgio T. said:

Does the kinetic energy of the nucleus then affect the hyperfine frequency and is it a component in the rate stability of atomic clocks ?

The hyperfine splitting is based on the electron spin and magnetic field it experiences. The magnetic field arises from the presence of nuclear spin.

18 hours ago, Dubbelosix said:

Yes.

What's the relationship? i.e. what is the rotational KE for a proton?

18 hours ago, Dubbelosix said:

Anything in nature that has a motion is translated into, say linear or rotational kinetic energies.

Spin does not indicate motion. It's intrinsic angular momentum.

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It is a rotational motion. And will be translated into a kinetic rotational part.

Read for yourself on the rotational kinetic energy. It contributes to the entire kinetic energy of the system https://en.wikipedia.org/wiki/Rotational_energy

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38 minutes ago, Dubbelosix said:

It is a rotational motion. And will be translated into a kinetic rotational part.

How fast is an electron spinning? What is its rotational KE?

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Just now, swansont said:

How fast is an electron spinning? What is its rotational KE?

So we have went from the proton to an electron in your question?

Is this intended or designed to try and trip me up somewhere? The electron is normally classified as a point like particle so probably best to stick with protons. Since protons do have spin, and since quantum mechanical spin is the same as classical spin, you will expect there to be corrections to the total kinetic energy of the system.

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38 minutes ago, Dubbelosix said:

Read for yourself on the rotational kinetic energy. It contributes to the entire kinetic energy of the system https://en.wikipedia.org/wiki/Rotational_energy

Nothing about the proton in there. The spin of a proton is the sum of the spin of the quarks.

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Oh but you did, you asked first of all, ''What's the relationship? i.e. what is the rotational KE for a proton?''

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Just now, Dubbelosix said:

So we have went from the proton to an electron in your question?

If it holds for a proton, it should hold for an electron.

Just now, Dubbelosix said:

Is this intended or designed to try and trip me up somewhere? The electron is normally classified as a point like particle so probably best to stick with protons. Since protons do have spin, and since quantum mechanical spin is the same as classical spin, you will expect there to be corrections to the total kinetic energy of the system.

The electron is evidence that QM spin is NOT the same as classical spin, which is why I brought it up.

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Just now, swansont said:

If it holds for a proton, it should hold for an electron.

If the electron is truly a pointlike system, then it is not classically-rotating, and so no, would not hold.

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Just now, Dubbelosix said:

Oh but you did, you asked first of all, ''What's the relationship? i.e. what is the rotational KE for a proton?''

I did what? You claimed the proton spin means it has rotational KE. How does one calculate it?

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3 minutes ago, swansont said:

If it holds for a proton, it should hold for an electron.

The electron is evidence that QM spin is NOT the same as classical spin, which is why I brought it up.

Pointless, I know the differences thank you.

2 minutes ago, swansont said:

I did what? You claimed the proton spin means it has rotational KE. How does one calculate it?

The proton has a spin. It is not a point system. Take a guess how it's done.

Edited by Dubbelosix
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5 minutes ago, Dubbelosix said:

Pointless, I know the differences thank you.

The proton has a spin. It is not a point system. Take a guess how it's done.

I don't want to guess. It's your claim. Back it up. (And in terms of the quarks having spin, which accounts for all of the spin of the proton.)

How much rotational KE is in a proton? A link should suffice. If this is standard physics, surely it's been measured or at least calculated.

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11 minutes ago, swansont said:

I did what? You claimed the proton spin means it has rotational KE.

Where did I initially say this anyway? It was you who started talking about the proton, then you stepped it up a gear and started talking about an electron. The question to me is simple, does it cost energy to rotate a thing, the answer is yes. In physics, the rotational energy is a correction to the total kinetic energy.

When you get to subjects like protons and electrons, it just complicates the issue. The poster was asking about the spin of a nucleus. Which is of course, related to the dynamics of the spin of its constituents. Just as a proton is the sum of quarks.

It still has rotational energy - the electron is the only particle in the standard model with exception since it has no classical rotation in our current model.

3 minutes ago, swansont said:

I don't want to guess. It's your claim. Back it up. (And in terms of the quarks having spin, which accounts for all of the spin of the proton.)

How much rotational KE is in a proton? A link should suffice. If this is standard physics, surely it's been measured or at least calculated.

Yeah, again, when was this actually my claim? You were the one who brought up the discussion of protons and electrons.

Edited by Dubbelosix
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10 minutes ago, Dubbelosix said:

Where did I initially say this anyway? It was you who started talking about the proton, then you stepped it up a gear and started talking about an electron. The question to me is simple, does it cost energy to rotate a thing, the answer is yes. In physics, the rotational energy is a correction to the total kinetic energy.

When you get to subjects like protons and electrons, it just complicates the issue. The poster was asking about the spin of a nucleus. Which is of course, related to the dynamics of the spin of its constituents. Just as a proton is the sum of quarks.

It still has rotational energy - the electron is the only particle in the standard model with exception since it has no classical rotation in our current model.

Yeah, again, when was this actually my claim? You were the one who brought up the discussion of protons and electrons.

The specific question that was asked was if the spin of a nucleus means it has KE.

You said yes. I disagree, and want you to justify your response.

I didn't start talking about the proton, it was inherent in the OP. If you missed that, then say so. No harm, no foul.

But if you deny this, then we can use Hydrogen as a system. Spin-1/2 nucleus, which is a single proton. What is its rotational KE?

If you choose another nucleus, then we must wonder how it can have rotational KE, which requires it have angular momentum, but the angular momentum is the sum of its spins. There is no angular momentum left over to account for any physical rotation of the nucleus.

So...do you want to change your answer, or do you want to answer my objections to it?

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3 minutes ago, swansont said:

The specific question that was asked was if the spin of a nucleus means it has KE.

You said yes. I disagree, and want you to justify your response.

I didn't start talking about the proton, it was inherent in the OP. If you missed that, then say so. No harm, no foul.

But if you deny this, then we can use Hydrogen as a system. Spin-1/2 nucleus, which is a single proton. What is its rotational KE?

If you choose another nucleus, then we must wonder how it can have rotational KE, which requires it have angular momentum, but the angular momentum is the sum of its spins. There is no angular momentum left over to account for any physical rotation of the nucleus.

So...do you want to change your answer, or do you want to answer my objections to it?

Let's do one better and change the format of the question. If my assumptions hold for protons, they should hold for molecules as well. You will actually find much more literature on that subject

Here, the first poster seems to agree with me, compound particles do actually have rotational kinetic energy

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2 hours ago, Dubbelosix said:

Let's do one better and change the format of the question. If my assumptions hold for protons, they should hold for molecules as well. You will actually find much more literature on that subject

No, that does not follow. You are citing a classical system, not a quantum one. The inference that classical systems behave the same as quantum ones is laughable, and you know this.

2 hours ago, Dubbelosix said:

Here, the first poster seems to agree with me, compound particles do actually have rotational kinetic energy

Because you've changed the scope of the question.

2 hours ago, Dubbelosix said:

And the first two responses here agree with my assessment.

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We've had this problem about your interpretation of things, including the interpretation of the work of accelerations on different superpositioned energy states. I will come back to this later, as I will chase what this poster said and explain it how I understand it, then we can compare differences afterwards.

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2 hours ago, Dubbelosix said:

We?

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21 hours ago, swansont said:

We?

Yes, the royal ''we'' have you never seen someone use it in such a context?

Let me get one thing clear before we continue, I want to hear it again from you. You do not believe rotational kinetic energy exists? You question that a classical rotating object has any rotational kinetic energy?

I just want to get this clear. And you also think the links I provided shows you are right? Is also what you claim?

See, you said the ''first poster agreed with you.'' And actually he didn't if you read him carefully. The only thing he agrees in is that a pointlike particle does not rotate. To do so, it has to rotate something like 720 degrees just to return to its original orientation. He clearly said:

If you're talking about a single particle, the rest mass is defined to be the total energy when the particle is at rest - there is no way to separately discuss contributions to this energy. Furthermore, "spin" does not represent a degree of freedom - there is no motion associated with it, and hence no kinetic energy.

This only applies to systems that have no internal degree's of freedom, ie. electrons as we model them

Some compound particles on the other hand have genuine rotational degrees of freedom. A deformed (non-spherical) nucleus can rotate, and may therefore possess rotational bands: excited states with increasing angular momentum, and associated rotational kinetic energy.

Now I said the nucleus has rotational energy, you came in here, tried to start an argument because you didn't agree with something. Let's just reflect on the evidence.

Edited by Dubbelosix
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14 minutes ago, Dubbelosix said:

Yes, the royal ''we'' have you never seen someone use it in such a context?

Let me get one thing clear before we continue, I want to hear it again from you. You do not believe rotational kinetic energy exists? You question that a classical rotating object has any rotational kinetic energy?

How can you hear it again, when I never said any such thing? I have not questioned anything classical. Don't be obtuse.

14 minutes ago, Dubbelosix said:

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I don't think I am the one being obtuse here.

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55 minutes ago, swansont said:

How can you hear it again, when I never said any such thing? I have not questioned anything classical. Don't be obtuse.

You never said such a thing, so you are saying you did not disagree with me?

Let's try again, did you not say

''The specific question that was asked was if the spin of a nucleus means it has KE. You said yes. I disagree.''

Since this is a direct quote, this is a no brainer. You disagree with something, so would be nice if you were not obtuse and get to the point.

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43 minutes ago, Dubbelosix said:

I don't think I am the one being obtuse here.

He refers to quantum spin as not having kinetic energy because it is not the same as classical spin...and you get from that he thinks classical spin has no kinetic energy...that's not obtuse?

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I know fine well what it means, it was me who explained it was not a classical property of the electron in our current models. Maybe you should read the conversation properly. He was the one who mentioned the electron and then claimed the links I provided suggested he was correct and I was somehow wrong.

Point is, and what is frustrating about this, is even when you [provide] the material, certain posters are still incapable of understanding its content and in what context.

14 minutes ago, J.C.MacSwell said:

...and you get from that he thinks classical spin has no kinetic energy...that's not obtuse?

That's just wrong - the electron is the only system subject to these ''non-internal degree's of freedom'' it is the only pointlike particle in existence since we cannot measure the radius (yet). We have attempted to measure the shape of electrons which suggests they are in fact spherical.

Classically rotating systems always possess a kinetic energy associated to the rotation. This even applies to a nucleus.

Edited by Dubbelosix

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