Amount of Energy to Fuse Two Atoms

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Discussion Overview

The discussion revolves around the energy required to fuse two atoms, specifically exploring the fusion of a sodium atom with a hydrogen atom to form a magnesium atom. Participants examine various aspects of fusion energy, including theoretical equations, concepts of mass-energy equivalence, and the forces involved in nuclear interactions.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants propose using the mass-energy equivalence formula E=mc² to calculate the energy released during fusion, based on the difference in mass between reactants and products.
  • Others argue that the energy required to hold the atoms together, influenced by the strong nuclear force, is a critical factor in fusion processes.
  • A participant questions whether energy is required to hold nucleons together, suggesting that no work is done in maintaining their position within the nucleus.
  • Another participant highlights the necessity of overcoming Coulomb repulsion between nuclei to initiate fusion, indicating that kinetic energy is required for this process.
  • One participant requests a worked example of the energy required to fuse hydrogen and sodium into magnesium, expressing curiosity about the calculations involved.
  • Another participant provides an equation for calculating the Coulomb barrier, noting that the energy required for fusion in a collection of particles is more complex due to quantum mechanical effects.

Areas of Agreement / Disagreement

Participants express differing views on the factors influencing fusion energy, particularly regarding the roles of mass-energy equivalence and the forces at play. The discussion remains unresolved, with multiple competing perspectives on the topic.

Contextual Notes

Some assumptions about the conditions for fusion, such as the lack of isotopes and the specific atomic interactions, are not fully explored. The discussion also touches on the complexity of calculating fusion energy in practical scenarios.

Who May Find This Useful

This discussion may be of interest to students and professionals in physics, particularly those focusing on nuclear physics, energy calculations, and atomic interactions.

JordanGo
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I was wondering if there was a simplified equation to determine the amount of energy required to fuse two atoms together (for example a sodium atom with a hydrogen atom to form a magnesium atom).
 
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JordanGo said:
I was wondering if there was a simplified equation to determine the amount of energy required to fuse two atoms together (for example a sodium atom with a hydrogen atom to form a magnesium atom).

Yes. You simply find the difference in mass * c2 between the starting products and ending products.

MNa-23*c2 + MH-1*c2 - MMg-24*c2 = Energy released

There is a simple calculator located at this link which does it for you: http://www.nndc.bnl.gov/qcalc/
 
Thank you, I wasn't sure if it was as simply as E=mc2 or there was something else more to it. But I guess not! Thanks again, highly appreciate you time!

Actually, I thought of something...

Does it not depend on the energy required to hold the atoms together instead of the energy of rest mass?
 
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JordanGo said:
Thank you, I wasn't sure if it was as simply as E=mc2 or there was something else more to it. But I guess not! Thanks again, highly appreciate you time!

Actually, I thought of something...

Does it not depend on the energy required to hold the atoms together instead of the energy of rest mass?

It does not require energy to hold the nucleus together, that is done by the strong nuclear force. When you fuse two nuclei together, if the end product of the reaction is less massive than the combined mass of the nuclei prior to fusion, the reaction is exothermic and will release energy. If it is more massive then it is endothermic and will require energy to react. Do you know what energy is?
 
Not sure... Can you describe this energy? Don't hold back on description, I'm in my third year university physics, so the more complex the better!
 
JordanGo said:
Not sure... Can you describe this energy? Don't hold back on description, I'm in my third year university physics, so the more complex the better!

To my knowledge energy is the ability of one system to perform work on another. If a proton and a neutron are being held together inside the nucleus, is work being done? No. This is similar to a book being left on a table. Is work being performed to keep the book on the table? No, there is no change in the system so no work is being done. Since no work is being done then energy isn't a useful way of describing anything in the system. AKA it takes zero energy to keep a book on a table or to keep two nucleons bound together.
 
@JordanGo - are you, perhaps, referring to the kinetic energy required to overcome the Coulomb repulsion between the two nuclei in order to get them close enough together for fusion to be able to happen?

For nuclei whose combinations are below Iron, fusion is either exothermic or just doesn't occur (an example of the latter would be 4He + 4He → 8Be). But before the reaction can happen you do need to provide enough energy to allow the nuclei to overcome the electromagnetic force and get to within the (fm-scale) range of one another where the nuclear force kicks in. Once the latter happens, though, it releases further energy, while the original KE remains.
 
Yes, that is what I was wondering about. Thank you Drakkith, that was also a very good answer, its interesting!

Now, I've never taking a particle class yet, I'm just being curious! So can someone do a worked example for me: let's say you want to fuse a hydrogen atom to a sodium atom to make magnesium (there's no isotopes). How much energy is required to do this?
 
JordanGo said:
Yes, that is what I was wondering about. Thank you Drakkith, that was also a very good answer, its interesting!

Now, I've never taking a particle class yet, I'm just being curious! So can someone do a worked example for me: let's say you want to fuse a hydrogen atom to a sodium atom to make magnesium (there's no isotopes). How much energy is required to do this?

Use the link I provided in my first post.
 
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Oh, were you asking how to calculate the coulomb barrier? In that case the equation for a single particle pair is [itex]E = \frac{k Z_1 Z_2 e^2}{r}[/itex] where k is the coulomb constant, the Z's are the atomic numbers, and r is the interaction radius.

Calculating the temperature for fusion for a collection of particles is a bit more complicated as there are quantum mechanical and statistical effects to consider. It is lower than the required energy for a single particle.
 

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