# Radial expectation value for particle in a cubic box [closed]

A hydrogen atom is in a cubic box with side lengths equal to $\require{mediawiki-texvc}\pu{100 \AA{}}$. For what value of $n$ (principal quantum number) will the expectation value of the radius be equal to one-half the box size?

$\left< r_{nl} \right> = n^2\cdot a_0\ \left\{ 1+ \frac{1}{2} \left[1-\frac{l(l+1)}{n^2}\right] \right\}$