Principal Quantum number by size?

[physics(L)10]

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.

 

[Redbelly98]

Just use the nearest integer value.

 

[physics(L)10]

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.

 

[Redbelly98]

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.

 

[physics(L)10]

Alrighty, thank you very much :)