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TechmoUnity
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- TL;DR Summary
- I need to know how to calculate the difference in energy during nuclear fusion so I can figure out the energy release from it. However, there is no-where that seems to explain where the formulas for that get their numbers from
Hello!
I have finished high school quite a few years ago. I did a physics course that went over nuclear fusion and fission, and I quite enjoyed it. However, I unfortunately no longer have those textbooks (I sold them on as many people do). Now I am doing a bit of programming in the field of nuclear physics for a bit of fun at home, and I've realized that I've forgotten how to calculate the energy release of a fusion reaction.
Upon looking into it on google, a lot of people point out that:
- 1U = 1.661 * 10^(-27)
- Alpha particle mass (Helium) = 4.0026U
- Proton mass = 1.0072U
- Neutron mass = 1.0084U
I understand that to get the energy of, for example, helium would be calculated by doing:
2 * 1.0072 + 2 * 1.0084 = 4.0312U
Now just take the difference between the calculated energy (4.0312U) and the given energy (4.0026U) and you get out 0.0286U, which turns out to be 26.641MeV energy difference. From here, I can do the same for hydrogen fusing into helium to calculate the difference in energy to figure out the net release of energy.
Now that's all fine. The question however, is this number: "4.0026U" for the alpha particle. How is this found? Is it something I can calculate with the number of protons and neutrons in a nucleus alone? I'm presuming something about the distances between the protons and neutrons involving the strong nuclear force would be involved, but is there actually a way to calculate that given only information like the number of proton/neutrons in an atomic nucleus, the mass/energy of a proton, and the mass/energy of a neutron?
I'm trying to create a coding library that handles all this, but I don't want to have a massive index of every single possible variation of an atom with varying numbers of neutrons. I want to be able to throw it in a function and have it spit out that original "4.0026U" or even "6.64832 * 10^(-27) Kg". I don't mind if the equation ends up being very large and complicated (With nuclear physics like this, I kinda expect it to be). I just want to know if this is something that can be calculated on the fly. For example, if I throw in uranium 214, I want to know what the expected energy of that would be so that I can calculate the energy loss when it splits WITHOUT the need for searching through a multi-hundred megabyte list of information to find uranium 214.
The trouble is that I keep running in circles. Everything that shows me how to calculate an atoms nucleus binding energy result in the formula:
B = (Mn + Mp - Mo)*c
Where Mn is the mass of neutrons, Mp is the mass of protons, Mo is the observed mass, and c is obviously the speed of light. The issue is the Mo. How do we get that? Is there a way to calculate it without needing to experimentally measure it and put it in a massive array of data?
Any help would be greatly appreciated, as I am completely stumped by this point. All my research in this matter just runs me in circles, and google really isn't helping, as any attempts to look it up either produce that formula for binding energy, or it gives me back calculating atomic mass, which really isn't what I'm after.
Kind regards,
Andrey
I have finished high school quite a few years ago. I did a physics course that went over nuclear fusion and fission, and I quite enjoyed it. However, I unfortunately no longer have those textbooks (I sold them on as many people do). Now I am doing a bit of programming in the field of nuclear physics for a bit of fun at home, and I've realized that I've forgotten how to calculate the energy release of a fusion reaction.
Upon looking into it on google, a lot of people point out that:
- 1U = 1.661 * 10^(-27)
- Alpha particle mass (Helium) = 4.0026U
- Proton mass = 1.0072U
- Neutron mass = 1.0084U
I understand that to get the energy of, for example, helium would be calculated by doing:
2 * 1.0072 + 2 * 1.0084 = 4.0312U
Now just take the difference between the calculated energy (4.0312U) and the given energy (4.0026U) and you get out 0.0286U, which turns out to be 26.641MeV energy difference. From here, I can do the same for hydrogen fusing into helium to calculate the difference in energy to figure out the net release of energy.
Now that's all fine. The question however, is this number: "4.0026U" for the alpha particle. How is this found? Is it something I can calculate with the number of protons and neutrons in a nucleus alone? I'm presuming something about the distances between the protons and neutrons involving the strong nuclear force would be involved, but is there actually a way to calculate that given only information like the number of proton/neutrons in an atomic nucleus, the mass/energy of a proton, and the mass/energy of a neutron?
I'm trying to create a coding library that handles all this, but I don't want to have a massive index of every single possible variation of an atom with varying numbers of neutrons. I want to be able to throw it in a function and have it spit out that original "4.0026U" or even "6.64832 * 10^(-27) Kg". I don't mind if the equation ends up being very large and complicated (With nuclear physics like this, I kinda expect it to be). I just want to know if this is something that can be calculated on the fly. For example, if I throw in uranium 214, I want to know what the expected energy of that would be so that I can calculate the energy loss when it splits WITHOUT the need for searching through a multi-hundred megabyte list of information to find uranium 214.
The trouble is that I keep running in circles. Everything that shows me how to calculate an atoms nucleus binding energy result in the formula:
B = (Mn + Mp - Mo)*c
Where Mn is the mass of neutrons, Mp is the mass of protons, Mo is the observed mass, and c is obviously the speed of light. The issue is the Mo. How do we get that? Is there a way to calculate it without needing to experimentally measure it and put it in a massive array of data?
Any help would be greatly appreciated, as I am completely stumped by this point. All my research in this matter just runs me in circles, and google really isn't helping, as any attempts to look it up either produce that formula for binding energy, or it gives me back calculating atomic mass, which really isn't what I'm after.
Kind regards,
Andrey
