Finding Bohr Orbit's Quantum # for 0.01mm Hydrogen Atom

[asdf1]

hydrogen atoms in states of high quantum number have been created in the labortatory and observed in space. Find the quantum number of the Bohr orbit in a hydrogen atom whose radius is 0.01mm.

my problem:
n=(0.00001/(5.29*10^-11))^(1/2)=434.7
i think that n should be 434, because the electron doesn't have enough energy to move up to 435
but the correct answer is 435...

 

[alfredblase]

I'm not sure but I think this may explain it. Orbits in the Bohr model are quantized. If they were not then the answer could be 434.7. Which means that the orbit was measured (inevitably) with some uncertainty as if the Bohr model is correct then it couldn't possibly be of 0.01mm radius. Now if we know that our value of 434.7 must be either 434 or 435, we look to see which "true" value our answer is closest to. And we find the value of n = 435. The point is we are not sure of the exact value of the atoms energy, but we know it is much more likely that our atom is in the 435 orbit than the 434 orbit.

 

[asdf1]

that's logical~ thank you very much! :)