Solving potential of electron inside the nucleus

In summary, the conversation discusses the derivation of an equation for the potential energy of an electron inside a uniformly charged sphere. The equation being derived is V'(r) = (-Ze2/4πε0R)(3/2 - (1/2)(r/R)^2), with the attempt at a solution yielding E = Ze2r/(4πε0R^3). The conversation also mentions checking the electric field at the boundary of the nucleus to see if it agrees with the electric field of a point charge, and suggests using the shell theorem to derive the equation mathematically.
  • #1
haseeb
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Homework Statement


I want to derive the following equation. It is the potential energy of an electron inside a nucleus assumed to be a uniformly charged sphere of R.

Homework Equations



V'(r) =( -Ze2/4∏ε0R)(3/2 - (1/2)(r/R)^2)

The Attempt at a Solution


I get E = Ze2r/(4∏ε0R3)

But I am having problem in integration limits and hence going towards final required result!
 
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  • #2
Something went wrong with the formatting.

The electric field should be linear with the distance - right. You can check if the electric field at the border of the nucleus agrees with the electric field of a point-charge. If yes, your result is right.
 
  • #3
mfb said:
Something went wrong with the formatting.

The electric field should be linear with the distance - right. You can check if the electric field at the border of the nucleus agrees with the electric field of a point-charge. If yes, your result is right.
First, Electrical field is not linearly dependent on distance! And I am not trying to find the field at the nucleus border but inside it. Can you help please to reach the desired formula?
 
  • #4
haseeb said:
Electrical field is not linearly dependent on distance!
Inside a homogeneously charged sphere, it is proportional to the radius, its magnitude is proportional to the distance to the center.

If your formula reproduces this relationship and agrees at the boundary, then it is right. Hence the suggestion to check if it fits at the boundary.
 
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  • #5
mfb said:
Inside a homogeneously charged sphere, it is proportional to the radius, its magnitude is proportional to the distance to the center.

If your formula reproduces this relationship and agrees at the boundary, then it is right. Hence the suggestion to check if it fits at the boundary.
Yup! You are right... But How to drive it mathematically?
 
  • #6
The shell theorem should help.
 

Related to Solving potential of electron inside the nucleus

What is the potential of an electron inside the nucleus?

The potential of an electron inside the nucleus is the amount of energy required to remove the electron from its position within the nucleus. This is also known as the binding energy or ionization energy.

How is the potential of an electron inside the nucleus calculated?

The potential of an electron inside the nucleus is calculated using the Coulomb's Law, which states that the force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

Why is it important to understand the potential of an electron inside the nucleus?

Understanding the potential of an electron inside the nucleus is important in understanding the stability and behavior of atoms and elements. It also plays a crucial role in nuclear reactions and the study of subatomic particles.

Can the potential of an electron inside the nucleus be changed?

Yes, the potential of an electron inside the nucleus can be changed by altering the number of protons and neutrons in the nucleus. This can be done through nuclear reactions or radioactive decay.

What is the relationship between the potential of an electron inside the nucleus and the size of an atom?

The potential of an electron inside the nucleus is directly related to the size of an atom. As the potential increases, the size of the atom decreases, and vice versa. This is because the stronger the force of attraction between the nucleus and the electrons, the more tightly the electrons are held and the smaller the size of the atom.

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