How can radial probability densities be huge when they should be less than 1?

[jaejoon89]

I have ~5.24a_o where a_o is the Bohr radius given by 5.291772E-11 m. This is my r value. But I am getting HUGE radial probability densities ~10^8! How is this possible? I thought they have to be less than 1 since it's a probability!

P(r) = |rR(r)|^2 = [r^2 / (8a_o^3)] [(2-r/a_o)^2] exp(-r/a_o)

 

[lanedance]

i think you're confusing probability denisty with probabilty

the probability of finding the electron in between r and r = dr is P(r).dr

So the integral of P(r).dr must be 1.

Although the limit of the integral goes from 0 to infinity, P(r) is only really non-zero for a few a_0. Thinking of the intergal in terms of area, as the span of r is so small, P(r) must be large for the integral to add up to one