Principal Quantum number by size?

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SUMMARY

The principal quantum number (n) for a hydrogen atom to achieve a size of one micron is calculated to be approximately 97. This is derived from the equation r = (5.3 x 10-11)(n2), where r represents the radius. While the theoretical limit for n is infinite, practical constraints such as electron collision with other atoms or container walls limit the feasibility of such high quantum numbers. Thus, while n can reach 97, it is not practically achievable.

PREREQUISITES
  • Understanding of quantum mechanics principles
  • Familiarity with the hydrogen atom model
  • Knowledge of the principal quantum number concept
  • Basic algebra for solving equations
NEXT STEPS
  • Research the implications of high principal quantum numbers in atomic physics
  • Explore the limitations of quantum states in real-world applications
  • Study the behavior of electrons in high-energy states
  • Learn about quantum mechanics and atomic structure in greater detail
USEFUL FOR

Students of physics, particularly those studying quantum mechanics, educators teaching atomic theory, and researchers interested in atomic behavior at high energy levels.

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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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