Equation for the energy of an electron

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As an electron moves away from the nucleus, its energy increases, which aligns with the work equation indicating more work is needed to separate them. The confusion arises from the Coulomb equation, where the force decreases with increased distance, suggesting energy should also decrease. However, integrating the force reveals that work done is actually inversely related to distance, leading to an increase in potential energy as the electron moves away. The key point is that the work done is the negative of the change in potential energy. Clarifying this integral will resolve the misunderstanding about energy changes with distance.
compuser123
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Hello,

I would like to thank all of the contributors on this site. You have helped me in more ways than I can count. I am struggling with the following concept and was wondering if anyone could clarify this.

As the electron gets further away from the nucleus, its energy increases. This makes sense when we look at the work equation, we do more work to pull it further away from where it wants to be.

What I am struggling with is the coulomb equation, where the the force is inversely proportional to distance squared. As the distance increases the force should decrease. Then, if we were to integrate that force to get work, the work would be inversely proportional to the distance, which tells us that work or energy should decrease as you get further away. I am not sure where my mistake is. Any help is much appreciated
 
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Just write down the actual integral, perform the integration from an initial distance to a final distance from the nucleus, and you will see why. Remember that the work done is the negative of the change in potential energy
 
Chandra Prayaga said:
Just write down the actual integral, perform the integration from an initial distance to a final distance from the nucleus, and you will see why. Remember that the work done is the negative of the change in potential energy

Thank you very much, will do it right away.
 
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