I am trying to calculate the average distance of electron above the surface. However when I did the Integral, for the first couple of state(n from 1 to around 15) the results are pretty good. However, for higher value of n, it starts giving the very weird value. Some people told me that it is because of the method of integration and suggested that I should use other numerical method other than just use the default Integral of Mathematica. I would really appreciate it you you guys can help me with this problem.
$$\text{$\chi $n}(\text{n$\_$},\text{z$\_$})\text{:=}-\frac{(2 z) e^{-\frac{z}{a_0 n}} L_{n-1}^1\left(\frac{2 z}{a_0 n}\right)}{\sqrt{a_0 n^3} \left(a_0 n\right)}$$