Understanding Bohr Theory (Wavelengths for Electron States)

[Xcellerator]

Ok, I am having some trouble with the maths regarding Bohr Theory. I understand that the orbit radius is
r=n^2xa₀
where a₀=0.0529

and that the wavelength for an electron with l=0 (circular orbit), is
λ=2∏r

so for n=1, λ=6.28a₀.

So, following the same maths, for n=2, I get λ=2x∏x2^2=8∏a₀.

However, according to http://hyperphysics.phy-astr.gsu.edu/hbase/bohr.html#c5, The answer is 4∏a₀, which means that n is not squared.

Can anyone please explain whether or not n is squared to work out the orbital radius?

 

[DrClaude]

On that Hyperphysics page, it is clearly shown that $r \propto n$, not $n^2$.

http://hyperphysics.phy-astr.gsu.edu/hbase/Bohr.html#c2