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

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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.

 

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I guess modern physics can't describe the characteristic size of an atom. Thanks for absolutely no responses.