Formula of potential energy of a nucleus

Thread starter Bestfrog
Start date Aug 27, 2017
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Energy Formula Nucleus Potential Potential energy

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The term 3/5 in the electrostatic potential energy formula for a nucleus, U_e = (3/5) * (Ze)^2 / (4πε_0 R), arises from integrating the potential energy of a uniformly charged sphere. This factor reflects the distribution of charge within the sphere, influencing the overall potential energy calculation. A similar derivation exists for gravitational binding energy, as noted on Wikipedia. Understanding this term is crucial for accurately calculating nuclear interactions. The discussion emphasizes the mathematical foundations underlying nuclear electrostatics.

Aug 27, 2017

Bestfrog

Why there is the term ##\frac{3}{5}## in the formula of the electrostatic potential of a nucleus $$U_e = \frac{3}{5} \cdot \frac{(Ze)^2}{4 \pi \epsilon_0 R}$$

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Aug 27, 2017

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It is a result of the integration for a sphere of uniform charge. For the analog system of gravitational binding energy, Wikipedia has a derivation.

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