Nuclear and elctronic binding energy

In summary: This is not the case, as the binding energy per nucleon is roughly the same for all nuclei, indicating a short range of nuclear force. This is supported by the fact that the binding energy per nucleon increases only as ~A^2 and not as ~A (where A is the number of constituents), as it would if the range were longer. Therefore, the nuclear force can be considered to have a short range of the order of inter-nucleon separation. In summary, the binding energy per nucleon in a nucleus is roughly the same, indicating a short range of nuclear force, unlike electrons in atoms where the mean binding energy is higher for higher Z atoms due to stronger Coloumb interaction and reduced orbital size.
  • #1
spaghetti3451
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"For almost all nuclei, the binding energy/nucleon is roughly the same. Hence the total binding energy of a nucleus is roughly proportional to the number A of the constituents. Every constituent of the nucleus is more or less equally strongly bound unlike electrons in atoms where the mean binding energy is higher for higher Z atoms.

This implies that the nuclear force has a short range of the order of inter-nucleon separation. If the force had a much longer range then the binding energy/nucleon would not be constant but would increase as ~A2."

I don't get the part in italics:

1. I understand that every constituent of the nucleus is more or less equally strongly bound because the binding per nucleon is roughly the same. But how is the mean binding energy of electrons in atoms higher for higher Z atoms? Is it because the Coloumb interaction (at the same radial separation) is stronger for bigger Z and so more energy is needed to free the electron from the evil grasp of the nucleus?

2. I have no idea how the implication in the second paragraph comes about! I'd appreciate any comments!
 
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  • #2
Is it because the Coloumb interaction (at the same radial separation) is stronger for bigger Z and so more energy is needed to free the electron from the evil grasp of the nucleus?
Correct. In addition, the higher charge of the nucleus reduces the size of the orbitals, which is an additional increase in binding energy.If the range of the interaction is very short, the binding energy for a nucleon just depends on its neighborhood (a very classical view, but fine here) - which is similar in all large nuclei: Nucleons are surrounded by other nucleons.
If the range would be large compared to the size of a nucleus, the binding energy for a nucleon would depend on the total amount of nucleons in it.
 

Related to Nuclear and elctronic binding energy

1. What is nuclear binding energy?

Nuclear binding energy is the amount of energy required to hold the nucleus of an atom together. It is the result of the strong nuclear force that overcomes the repulsive forces between protons in the nucleus.

2. How is nuclear binding energy calculated?

Nuclear binding energy is calculated using the famous equation E=mc^2, where E is energy, m is mass, and c is the speed of light. The difference in mass between the individual nucleons (protons and neutrons) and the combined mass of the nucleus is the amount of binding energy.

3. What is electronic binding energy?

Electronic binding energy is the amount of energy required to hold the electrons in an atom together. It is the result of the electrostatic force between the positively charged nucleus and the negatively charged electrons.

4. How is electronic binding energy different from nuclear binding energy?

While both nuclear and electronic binding energy refer to the energy required to hold particles together, they differ in terms of the particles involved and the forces at play. Nuclear binding energy involves the strong nuclear force, while electronic binding energy involves the electrostatic force.

5. Can nuclear and electronic binding energy be harnessed for practical use?

Yes, both types of binding energy can be harnessed for practical use. Nuclear binding energy is used in nuclear power plants to generate electricity, while electronic binding energy is used in various electronic devices such as batteries and solar cells.

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