Principal Quantum number by size?

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Homework Help Overview

The discussion revolves around determining the principal quantum number for a hydrogen atom to achieve a size of one micron. The context involves quantum mechanics and atomic structure.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to calculate the principal quantum number using a formula related to atomic radius. Some participants question the validity of the resulting high quantum number and its implications.

Discussion Status

Participants are exploring the implications of a high principal quantum number, with some suggesting that while the calculation yields a large value, practical limitations exist for such states. There is an acknowledgment of theoretical versus practical constraints in atomic behavior.

Contextual Notes

There is a discussion about the typical range of principal quantum numbers and the implications of reaching very high values, including potential interactions with other atoms or boundaries.

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Homework Statement


What is the value of the principal quantum number for a hydrogen atom to have a size of one micron?

Homework Equations


r=(5.3x10-11)(n2)
r=1x10-6/2=5x10-7

The Attempt at a Solution



5x10-7=(5.3x10-11)(n2)

97.1 = n

How is this possible? lol Maybe it's more complicated then I'm thinking.
 
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Just use the nearest integer value.
 
So I'm right? The answer is just 97? I thought the principal quantum numbers (n) only go up to like 5 or 6 or something like that though.
 
Yes, you're right. n can go up to infinity in theory. In practice, an atom with such a high n would eventually collide with another atom or perhaps a container wall, and completely lose the electron.
 
Alrighty, thank you very much :)
 

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