I read an interesting criticism of the Bohr model of he hydrogen atom. The criticism was that if we considered the 137th electron state the atom would be one micrometer large, which is ridiculous, obviously.

Then I went back to look at Schrodinger's solution. substituting in n=137 you'll notice the probability density of finding the electron to exp(-1) is r=137a0 or 137 times the Bohr radius. that is very large. and when you compare that with the solution Bohr gives you find Schrodinger has the same problem Bohr did. At higher quantum numbers the atoms become unreasonably large.

is there an explanation for this?