Binding energy/position of maximum energy value

In summary, the conversation discussed the binding energy of the ion H2+ at equilibrium separation, and the application of the Hellman-Feynman theorem in calculating the force between nuclei in a molecule. The theorem also indicates that the squared modulus of the electron wave function in H2+ must have its maximum value in a specific location. The equations used to solve for the repulsion and attraction energies were also mentioned.
  • #1
lcr2139
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Homework Statement


The binding energy of the ion H2+ is -16.3 eV at the equilibrium separation 0.106 nm. The Hellman-Feynman theorem states taht the force between the nuclei in a molecule can be calculated from the electrostatic repulsion between the nuclei and the electrostatic attraction of the nuclei to the electron distribution. According to this theorem, where must the squared modulus of the electron wave function in H2+ have its maximum value?

Homework Equations


P(x) = abs(psi(x))^2=1

The Attempt at a Solution


Urepulsion = 1/(4*pi*epsilonnaught)*q^2/r= 13 eV
Uattraction = Ebinding + Urepulsion = -2.7 eV
 
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  • #2
The sum of attraction plus repulsion is the binding energy. -2.7 eV + 13 eV is positive, so the whole system would be unbound.

How do you find the attraction as function of the electron position?
 

1. What is binding energy?

Binding energy is the amount of energy required to separate an atom's nucleus into its individual protons and neutrons. It is also known as the energy of nuclear binding.

2. How is binding energy related to mass defect?

Binding energy and mass defect are closely related. Mass defect is the difference between the mass of an atom's nucleus and the sum of the masses of its individual protons and neutrons. This mass difference is converted into binding energy, which holds the nucleus together.

3. What is the significance of the position of maximum energy value in the binding energy curve?

The position of maximum energy value on the binding energy curve corresponds to the most stable nucleus. Nuclei with lower or higher numbers of protons and neutrons have less binding energy and are less stable.

4. How does binding energy affect the stability of an atom?

The higher the binding energy, the more stable the nucleus is. This is because the strong nuclear force, which is responsible for binding the nucleus together, is at its strongest when the binding energy is at its maximum value.

5. What is the role of binding energy in nuclear reactions?

Binding energy plays a crucial role in nuclear reactions. In nuclear fusion, where two lighter nuclei combine to form a heavier one, binding energy is released, resulting in a net decrease in mass and a release of energy. In nuclear fission, where a heavy nucleus splits into smaller ones, binding energy is also released, leading to a chain reaction and the release of large amounts of energy.

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