I thought binding energy was calculated as:
“(mass of a neutron) x (number of neutrons in the nucleus) + (mass of a proton) x (number of protons in the nucleus)” to compare with the mass of the nucleus that was measured (experimentally). The mass difference is then converted into energy according to E = mc².
Take e.g. U235, Kr92 and Ba142 and the reaction
U + 1n –> 2n + Kr + Ba + E
U, Kr and Ba each have their own (nuclear) mass and their own binding energy in the nucleus. The binding energy for these 3 “particles” is determined for each by comparing the theoretical (neutron + proton) mass to the measured mass.
I agree that the binding energy of U is greater than the sum of the binding energies of Kr and Ba. But I would think that difference is just a mass difference of neutrons and protons in the nucleus. Precisely because the separate reasoning must also be valid: for each atom I can determine the binding energy separately by comparing the theoretical mass with what I measure. The difference is binding energy.
If I then make 2 atoms of an arbitrary atom, then the sum of “mass and binding energy_mass” must be preserved for neutrons and protons, I would think.
I don’t understand that some of the binding energy can be released.
The only thing I can think of is that it must have to do with the released neutrons:
U + 1n –> 2n + Kr + Ba + E
That 1n and that 2n, what mass do they have? I would think you have to calculate with the theoretical mass for that?
mass(U) + mass(U binding energy) + mass_n = 2.mass_n + mass(Kr) + mass(Kr binding energy) + mass(Ba) + mass(Ba binding energy) + E
In my reasoning you then arrive at:
E = mass_n
+ mass_n – 2.mass_n
this mass_n is a remnant of the calculation of the binding energy of U.
I also use: number of neutrons of U = number of neutrons of Kr + number of neutrons Ba + 1
number of protons of U = number of protons of Kr + number of protons of Ba
Thank you so much for reading this far!
Andy, 26 years old
Answer
Quite a story indeed!
I’m trying to use a very classic image to explain nuclear energy. Its advantage is that it is ‘simple’ and explains the essence, the disadvantage is that the model is too simple to obtain quantitative results, but that is not the intention here. Besides, I don’t need any formula 😉
Suppose you want to make your own ‘atomic nucleus’ with feathers and billiard balls. The red billiard balls are the protons. They are interconnected with strong springs that try to push them apart. This is a picture for the electrostatic repulsive force between the positively charged protons. It is clear that you can never make a stable construction with red, repelling billiard balls alone. That’s where your white billiard balls or the neutrons come into play. The neutrons have no electrostatic charge and repel each other and the protons. But they do have attractive forces (nuclear forces) that you can use to hold the entire structure together. You can now connect the white billiard balls with each other and with the protons via tightening springs.
You can imagine that this way you can (with difficulty) make a stable construction of a number of red and white billiard balls, where the springs between the red balls try to push the matter apart and the springs between the white and between the white and the rode trying to keep things together. If you get 235 balls together like this, you have what looks like a uranium nucleus.
The ‘binding energy’ you speak of is the total potential energy that is in your construction as a result of the compressed and tensioned springs: after all, you had to supply energy to deform those springs during your construction of your core, that energy is still in the springs and can be released when the springs relax. Your built-up ‘atomic core’ contains more energy than the sum of its parts (all billiard balls and all unstretched feathers separately). According to the theory of relativity, that core also weighs more than the parts separately, but I cannot explain this aspect with my simple model.
Now suppose that someone throws a white billiard ball at your construction from a distance at high speed (a red one will not work, because they repel each other). That ball will break through springs and disrupt the entire fragile balance between attractive and repulsive forces. It is now conceivable that your construction will fall apart into fragments that are pushed apart by the tensioned springs: these fragments acquire kinetic energy and this is heat. Ultimately, potential energy that was in the springs (in the binding forces) (and that the person who made the core once had to provide) has been converted into kinetic energy of the debris.
Answered by
Physics Acoustics
Catholic University of Leuven
Old Market 13 3000 Leuven