Potential Energy: Why Electron in Hydrogen -Negative?

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SUMMARY

The potential energy of an electron in a hydrogen atom is negative due to the nature of the attractive force between the electron and the proton, described by the formula U = -GMm/r. This contrasts with gravitational potential energy, which is typically considered positive for objects in Earth's gravitational field. The negative value indicates a bound state, where energy must be supplied to remove the electron from the atom, whereas gravitational potential energy can be adjusted by setting an arbitrary constant. Understanding these distinctions is crucial for grasping atomic and gravitational interactions.

PREREQUISITES
  • Understanding of classical mechanics and gravitational forces
  • Familiarity with atomic structure and quantum mechanics
  • Knowledge of potential energy concepts in physics
  • Basic mathematical skills for manipulating equations
NEXT STEPS
  • Research the concept of bound states in quantum mechanics
  • Explore the implications of potential energy in atomic physics
  • Learn about gravitational potential energy and its applications
  • Investigate the role of arbitrary constants in potential energy equations
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Physics students, educators, and anyone interested in the fundamental principles of atomic interactions and gravitational forces.

MHD93
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Why is the potential energy of an electron in hydrogen atom negative, where that of an object around the Earth is positive, although both systems have attractive forces, that have the same proportionality with distance 1/(distance)^2
 
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Mohammad_93 said:
where that of an object around the Earth is positive

It's not?

U=-\frac{GMm}{r}

Of course, there is an arbitrary constant hiding here which I tacitly set to zero. I suppose you could set it to be large enough that a given object has positive potential energy.
 

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