How Do You Determine the Characteristic Size of an Atom in a Given State?

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SUMMARY

The characteristic size of an atom in a given state, such as the hydrogen atom in its ground state, can be determined using quantum mechanics rather than classical methods. The approach involves equating the energy of the state to the potential energy, represented by the equation -Ke^2/r, and solving for the radius (r). This method is essential for accurately calculating atomic sizes, as classical physics fails to provide a complete description of atomic behavior. Understanding these principles is crucial for tackling problems related to atomic structure.

PREREQUISITES
  • Quantum mechanics fundamentals
  • Understanding of atomic structure
  • Familiarity with potential energy equations
  • Basic knowledge of the hydrogen atom model
NEXT STEPS
  • Study the Schrödinger equation for hydrogen atoms
  • Learn about quantum numbers and their significance in atomic states
  • Explore the concept of atomic orbitals and their shapes
  • Investigate the Bohr model of the hydrogen atom for initial insights
USEFUL FOR

Students of physics, particularly those studying quantum mechanics and atomic theory, as well as educators seeking to clarify concepts related to atomic sizes and states.

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Homework Statement


There are a few problems I have with my HW that involve the characteristic size of an atom in a certain state. For example, the hydrogen atom in the ground state.

Homework Equations


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The Attempt at a Solution


I don't know where to begin to find the characteristic size of an atom in a given state. My first thought would be to take the energy of the state and set it equal to the potential energy -Ke^2/r and then solve for r. However, alarms and bells are going off in my head doing this because this seems more like a classical method to find this so called characteristic size. Can someone push me into the right direction to find the characteristic size of an atom?
 
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Is my question too vague for any type of response? I can explain the problems more deeply if required. I don't need or want a direct answer to my problem. All I want is a little guidance.
 
I guess modern physics can't describe the characteristic size of an atom. Thanks for absolutely no responses.
 

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