Amount of Energy to Fuse Two Atoms

In summary: For a collection of two particles, the temperature required is: T = \frac{2}{3} \log \frac{(2M_1+M_2)}{(M_1+M_2)^3} where M_1 and M_2 are the masses of the two particles, and \log is the natural logarithm.As you can see, it is considerably more complicated than just calculating the energy required to fuse two atoms together!First off, thank you so much for doing this! 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!In summary
  • #1
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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  • #2
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/
 
  • #3
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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  • #4
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?
 
  • #5
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!
 
  • #6
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.
 
  • #7
@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.
 
  • #8
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?
 
  • #9
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.
 
  • #10
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.
 

1. How much energy is required to fuse two atoms?

The amount of energy required to fuse two atoms depends on the specific atoms being fused. Generally, the larger the atoms, the more energy is required to overcome the repulsive forces between their nuclei. The energy required can range from several million to billions of electron volts (eV).

2. What factors influence the amount of energy needed for fusion?

The amount of energy needed for fusion is influenced by the type and size of the atoms, as well as the temperature and density of the environment in which the fusion is taking place. Additionally, the stability and arrangement of the atoms' nuclei also play a role in the required energy.

3. Is it possible to fuse atoms without using a lot of energy?

No, the process of fusion requires a significant amount of energy. In order to overcome the repulsive forces between the nuclei of two atoms, a high amount of energy is needed to bring them close enough together for fusion to occur. However, scientists are constantly researching and developing more efficient ways to achieve fusion with less energy.

4. How does the amount of energy needed for fusion compare to that of fission?

The amount of energy required for fusion is much higher than that of fission. Fission is the process of splitting a large atom into smaller ones, whereas fusion is the process of combining two smaller atoms into a larger one. In fission, the energy released is typically in the range of millions of electron volts, while in fusion, it can be billions of electron volts.

5. Can the amount of energy needed for fusion be reduced?

Yes, scientists are constantly working on ways to reduce the amount of energy needed for fusion. One approach is to use powerful lasers to heat and compress the atoms, reducing the amount of energy needed to overcome the repulsive forces. Another approach is to use magnetic fields to contain and heat the atoms, reducing the energy needed for fusion. However, achieving net energy gain from fusion is still a major challenge that requires further research and development.

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